ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 The rate of induced scattering is known to depend on the particle recoil. i.e. on the difference of the initial and final directions of the photons. and therefore the scattering within the beam is of no interest here.," The rate of induced scattering is known to depend on the particle recoil, i.e. on the difference of the initial and final directions of the photons, and therefore the scattering within the beam is of no interest here."3 On the other hand. by definition the induced scattering cannot transfer the beam photons into the states where the photon occupation numbers are initially zero.," On the other hand, by definition the induced scattering cannot transfer the beam photons into the states where the photon occupation numbers are initially zero."4 However. the photons can still be subject to induced scattering out of the beam. since some background photons are expected to be always present in space.," However, the photons can still be subject to induced scattering out of the beam, since some background photons are expected to be always present in space."5 la particular. (hev may result [rom the spontaneous scattering of the beam. which. in contrast to the induced one. provides the photons of any orientation.," In particular, they may result from the spontaneous scattering of the beam, which, in contrast to the induced one, provides the photons of any orientation."6 Although in pulsar case the spontaneous scattering is very inefficient and the scattered photons are too scanty to be detectable (see. e.g.. eq.[13] below). thev can still stimulate a substantial induced scattering [rom the radio beam.," Although in pulsar case the spontaneous scattering is very inefficient and the scattered photons are too scanty to be detectable (see, e.g., eq.[13] below), they can still stimulate a substantial induced scattering from the radio beam."7 The beam photons should predominantly. undergo induced scattering into the background state ky. which corresponds to the maximum scattering probability.," The beam photons should predominantly undergo induced scattering into the background state ${\bf k_1}$, which corresponds to the maximum scattering probability."8 If (he induced scattering is ellicient enough. the background radiation in this state may grow significantlv aud become almost as strong as the initial radio beam.," If the induced scattering is efficient enough, the background radiation in this state may grow significantly and become almost as strong as the initial radio beam."9 It should be noted (hat in the particle rest Iraane the photon lrequencey is approximately unchanged in the scattering act., It should be noted that in the particle rest frame the photon frequency is approximately unchanged in the scattering act.10 Therefore in the laboratory [rame d=wy., Therefore in the laboratory frame $\omega\eta=\omega_1\eta_1$.11 Thus. we examine (he problem on induced scattering between the (wo photon states. k=(2xv/c.0.0) and ky=(2z154/6.04.04). one of which corresponds (ο the beam and another one to the backeround state characterized by (he maximum scattering probability: the frequencies are related as 7)=ry. and the occupation number of the background photons is initiallymuch less (han Chat of the beam photons. ny«& n.," Thus, we examine the problem on induced scattering between the two photon states, ${\bf k}=(2\pi\nu /c,\theta,\phi)$ and ${\bf12k_1}=(2\pi\nu_1/c,\theta_1,\phi_1)$, one of which corresponds to the beam and another one to the background state characterized by the maximum scattering probability; the frequencies are related as $\nu\eta=\nu_1\eta_1$, and the occupation number of the background photons is initiallymuch less than that of the beam photons, $n_1\lll n$ ."13"where ps is the eas pressure. pry, the magnetic pressure. D - the maguetic field. aud ./ is a coustaut paramcter.","where $p_\mathrm{g}$ is the gas pressure, $p_\mathrm{m}$ - the magnetic pressure, $B$ - the magnetic field, and $\beta$ is a constant parameter."14 The pressure. the rest mass density py and the sound velocity eg are related: Iu our calculations we use a two temperature plasma with a small amount of magnetic field to represent the matter properties.," The pressure, the rest mass density $\rho_0$ and the sound velocity $c_\mathrm{S}$ are related: In our calculations we use a two temperature plasma with a small amount of magnetic field to represent the matter properties."15 Thus the ion pressure dominates. the eas is nou-relativistic aud the specific cuthalpy pi is given an: where e is the total (vest mass plus thermal) energy clensity.," Thus the ion pressure dominates, the gas is non-relativistic and the specific enthalpy $\mu$ is given as: where $\epsilon$ is the total (rest mass plus thermal) energy density."16 Iu the ADAF set of equations only the vertically averaged sound speed is used., In the ADAF set of equations only the vertically averaged sound speed is used.17 It is im spirit of our approxinatious to postulate: which means that the gas is isothermal ou spheres., It is in spirit of our approximations to postulate: which means that the gas is isothermal on spheres.18 The clectrou temperature Tis much lower than the ion temperature. so its influence on the equation of state aud the structure of the flow can be ucelected.," The electron temperature $T_\mathrm{e}$ is much lower than the ion temperature, so its influence on the equation of state and the structure of the flow can be neglected."19 Om detailed (but approximate) description of the fiud kinematics makes it possible to fud the density dependence on the augular coordinate 0., Our detailed (but approximate) description of the fluid kinematics makes it possible to find the density dependence on the angular coordinate $\theta$.20 The set of Qquatious describing ADAF contains viscosity terms. which are inclided in the euergy equation. but ucelected oe1 the mechanical equilibrium equatious (ACGL. Peitz Appl 1997.. Paper I).," The set of equations describing ADAF contains viscosity terms, which are included in the energy equation, but neglected in the mechanical equilibrium equations (ACGL, Peitz Appl \cite{peitz}, Paper I)."21" Thus it is sufficicut to use the ideal fiuid energy momentum tensor: The @ conservation equation. Z5,=0 reads: After some algebra we obtain: Since V does not depend on 0. the LIS of the equation is a full eradieut of a quantity which can be called a potential c."," Thus it is sufficient to use the ideal fluid energy momentum tensor: The $\theta$ conservation equation, $T^a_{\theta;a}=0$ reads: After some algebra we obtain: Since $V$ does not depend on $\theta$, the LHS of the equation is a full gradient of a quantity which can be called a potential $\psi$."22 This tuplies the solution for the censity: where the poa4. Cog denote the values measured at the equatorial plane.," This implies the solution for the density: where the $\rho_{0,\mathrm{eq}}$, $\psi_\mathrm{eq}$ denote the values measured at the equatorial plane."23 The constant sound speed on the spheres may suggest that the exponential atmosphere never euds., The constant sound speed on the spheres may suggest that the exponential atmosphere never ends.24 For the rotating coufiguration there is. however. an infinite poteutia barrier close to the rotation axis. where d;>xX and py20.," For the rotating configuration there is, however, an infinite potential barrier close to the rotation axis, where $u_t 25\rightarrow \infty$ and $\rho_0 \rightarrow 0$."26 Thus the vicinity of the rotation axis is cuipty and the deusitv falls steeply down near this region., Thus the vicinity of the rotation axis is empty and the density falls steeply down near this region.27 In this respect he ADAF solutions arc similar to he so called thick accretion disks (Abramowicz. Javoszvisski. Sikora 19758).," In this respect the ADAF solutions are similar to the so called thick accretion disks (Abramowicz, Jaroszyńsski, Sikora \cite{AJS78}) )."28" Both have curpty funnels around their rotation ANCR,", Both have empty funnels around their rotation axes.29 The uass flow through the 7=const surface cau be calculated as: Combining the last equation aud the foriuula for tle 0 dependence of the density we obtain the equatorial valuc of the deusity., The mass flow through the $r=const$ surface can be calculated as: Combining the last equation and the formula for the $\theta$ dependence of the density we obtain the equatorial value of the density.30 While modeling the dvuamics of ADAF we neglect the heat transfer and all the radiation processes. assmuine that only a small part of the total energv. generated by viscous processes can be affected by them.," While modeling the dynamics of ADAF we neglect the heat transfer and all the radiation processes, assuming that only a small part of the total energy generated by viscous processes can be affected by them."31 Now we are eoing to model the radiation processes., Now we are going to model the radiation processes.32 We asse that the whole energy dissipated is transferred to the ions., We assume that the whole energy dissipated is transferred to the ions.33 The ious heat the electrous via Coulomb collisious and the electrons lose their energv by the svuchrotrou. brenisstralluus aud inverse Compton cooling processes.," The ions heat the electrons via Coulomb collisions and the electrons lose their energy by the synchrotron, bremsstrahlung and inverse Compton cooling processes."34 In the ADAFs thermalization time-scale ercatly exceeds the dynamical time-scale aud the plasma roiuaius two temperature., In the ADAFs thermalization time-scale greatly exceeds the dynamical time-scale and the plasma remains two temperature.35" We find the electron aud ion temperatures. Tif(0) aud Ti(r.0). sclt-cousisteutlv using the equation of state where p;=1.29 aud 44.=1.18 are effective molecular weights of the ious aud electrous. aud the condition of thermal equilibriuni applied locally where 4! is the rate of Coulomb heatiug of electrous bv djous (eee. Mahadevan 1997)). (a ald (qu are the syuchrotron and breinissstraliluug cooling rates and qq and qi,¢ are the Comptou cooling rate of synchrotron aud byenissstralilluug photons. respectively."," We find the electron and ion temperatures, $T_\mathrm{e}(r,\theta)$ and $T_\mathrm{i}(r,\theta)$, self-consistently using the equation of state where $\mu_\mathrm{i}=1.29$ and $\mu_\mathrm{e}=1.18$ are effective molecular weights of the ions and electrons, and the condition of thermal equilibrium applied locally where $q^\mathrm{+}$ is the rate of Coulomb heating of electrons by ions (e.g. Mahadevan \cite{mahadevan}) ), $q^\mathrm{-}_\mathrm{S}$ and $q^\mathrm{-}_\mathrm{br}$ are the synchrotron and strahlung cooling rates, and $q^\mathrm{-}_\mathrm{S,C}$ and $q^\mathrm{-}_\mathrm{br,C}$ are the Compton cooling rate of synchrotron and lung photons, respectively."36 The caleulatiou of the svuchrotron cooling rate is solmewhat complicated because the optical depth to absorption (Self Svuchrotron Absorption) for majority of the svuchrotron photons is high., The calculation of the synchrotron cooling rate is somewhat complicated because the optical depth to absorption (Self Synchrotron Absorption) for majority of the synchrotron photons is high.37 Iu our approach we, In our approach we38Tf the mass of the stars changes. then both the period and separation ought to readjust.,"If the mass of the stars changes, then both the period and separation ought to readjust."39 This behaviour can be shown by taking the time derivative of the total angular momentum of a system of two point mass orbiting cach other with an eccentricity e: Equation 1. shows that as the masses of the stars change aud as inass and angular momentum are bee lost from) the svstem. both the orbital separation and the eccentricity change.," This behaviour can be shown by taking the time derivative of the total angular momentum of a system of two point mass orbiting each other with an eccentricity $e$: Equation \ref{eq:jdot3} shows that as the masses of the stars change and as mass and angular momentum are being lost from the system, both the orbital separation and the eccentricity change."40 The exact behaviour of these quantities depends of course on the degree of conservation of both total mass and augular momenta., The exact behaviour of these quantities depends of course on the degree of conservation of both total mass and angular momentum.41" For the usual assumptions of circulu orbits and conservative nass transfer. we can further impose that e—0. M;=My, and Ay=0, therefore reducing Equation | to Assuniug A, to be the donor aud more massive AA<0 and AL,> Af) we find that the separation « decreases uutil the mass ratio is reversed. at which point the separation starts increasing again."," For the usual assumptions of circular orbits and conservative mass transfer, we can further impose that $e=0$, $\dot{M_2}=-\dot{M_1}$ and $\dot{J}_{tot}=0$, therefore reducing Equation \ref{eq:jdot3} to Assuming $M_1$ to be the donor and more massive $\dot{M}_1<0$ and $M_1>M_2$ ) we find that the separation $a$ decreases until the mass ratio is reversed, at which point the separation starts increasing again."42 For mai-sequence binaries. where the most massive star is expected to overfill its Roche lobe first. the separation is therefore expected to decrease upon lass transfer.," For main-sequence binaries, where the most massive star is expected to overfill its Roche lobe first, the separation is therefore expected to decrease upon mass transfer."43 The theoretical framework derived iu this section has ecnerally been applied to the study of close binaries., The theoretical framework derived in this section has generally been applied to the study of close binaries.44 Towever. strictly speaking. it is not valid in most instances.," However, strictly speaking, it is not valid in most instances."45 Close binaries are uot all circular aud svuchrouized. and the Roche lobe formalisur therefore does not apply.," Close binaries are not all circular and synchronized, and the Roche lobe formalism therefore does not apply."46 This. iu turi. males estimates of mass transfer rates rather uucertain.," This, in turn, makes estimates of mass transfer rates rather uncertain."47 Moreover. conservative luass trauster is more an ideal study case than a realistic oue aud the secular evolution of binary svsteu becomes a coniplex problem.," Moreover, conservative mass transfer is more an ideal study case than a realistic one and the secular evolution of binary system becomes a complex problem."48 To cicunveut these difficulties. approxinatious to the mass transfer aud accretion rates as well as to the degree of mass loss have to be mace.," To circumvent these difficulties, approximations to the mass transfer and accretion rates as well as to the degree of mass loss have to be made."49 However. to better constrain these approximation or avoid over-simplificatious. oue cau use hvdrodyuauies. which is well suited for modeling aud characterizing episodes of mass fransfer.," However, to better constrain these approximation or avoid over-simplifications, one can use hydrodynamics, which is well suited for modeling and characterizing episodes of mass transfer."50 We therefore discuss our lydrodvuamiics technique aud show how it can be used to better constrain niass transfer rates m binary svstenis., We therefore discuss our hydrodynamics technique and show how it can be used to better constrain mass transfer rates in binary systems.51 Sunoothed Particle Uvdvodvuamics (SPIT) was introduced by Lucy(1977) and Gingold& Mon-agehan(1977) in the context of stellar astroplysics.," Smoothed Particle Hydrodynamics (SPH) was introduced by \citet{lucy}52 and \citet{gingold} in the context of stellar astrophysics."53 Its relatively suuple coustruction and versatility lave allowed for the modeling of many different plysical problems such as star formation (PriceBateetal. 1995)). accretion disks citealtiiwer2007)). stellar collisions (Lombardietal.1995:Sillsetal.1997. 2001)). galaxw formation aud cosmolocical simulations citealtinasliclienko2006.stinson2009.e60veruato2009)].," Its relatively simple construction and versatility have allowed for the modeling of many different physical problems such as star formation \citealt{price2009,bate1995a}) ), accretion disks \\citealt{mayer2007}) ), stellar collisions \citealt{lombardi1995,sillsetal1997,sills2001}) ), galaxy formation and cosmological simulations )."54 Our code derives from that of Date(1995).. which is based onu the earlier version of Benz(1990) and Deuzetal.(1990).," Our code derives from that of \citet{bate1995b}, which is based on the earlier version of \citet{benz1990} and \citet{benzetal1990}."55.. Tere. we only enmiphasize ou the main constitucuts of our code.," Here, we only emphasize on the main constituents of our code."56 The reader is referred to these carly works for complementary details., The reader is referred to these early works for complementary details.57 SPI relies on the basic assumption that the value of any smooth fiction at any point iu space can be obtained bv averaging over the kuown- values of the function around this point., SPH relies on the basic assumption that the value of any smooth function at any point in space can be obtained by averaging over the known values of the function around this point.58 This averaging is done using a so-called ‘smoothing kernel to determine the contribution from ucielibouriug particles., This averaging is done using a so-called `smoothing kernel' to determine the contribution from neighbouring particles.59 The zioothiug kernel can take many forms (sec citealtprice2005)): here wei use the compact aud spherically svinmetric Καπα first sugeested bv Monaghan&Lattanzio(1985)., The smoothing kernel can take many forms (see \\citealt{price2005}) ); here we use the compact and spherically symmetric kernel first suggested by \citet{monaghan1985}.60 To prevent —the interpenetration of particles iu shocks aud allow for the dissipation of kinetic energy into heat. we iuclude an artificial viscosity fermi in the momentum and energv equations.," To prevent the interpenetration of particles in shocks and allow for the dissipation of kinetic energy into heat, we include an artificial viscosity term in the momentum and energy equations."61 The artificial viscosity cau also take various forms citealtlonibardil999)): wei use the form given by Monaghan(1989) with a=land ο)=2., The artificial viscosity can also take various forms \\citealt{lombardi1999}) ); we use the form given by \citet{monaghan1989} with $\alpha=1$ and $\beta=2$.62 We allow for the smoothing Ἰοπο to change both in time and space. aud we use individual timesteps for the evolution of all the required quantities.," We allow for the smoothing length to change both in time and space, and we use individual timesteps for the evolution of all the required quantities."63 In this work. we asstume an equation of state for ideal gases of the form P=(> l)pu. where 5—5/3 is the ratio of the heat capacities.," In this work, we assume an equation of state for ideal gases of the form $P=(\gamma-1)\rho u$ , where $\gamma=5/3$ is the ratio of the heat capacities."64 Finally. we use the parallelized version of our code (OpenAIP). which scales lineulyv up to ~21 CPUs for simmlatious of 109 particles.," Finally, we use the parallelized version of our code (OpenMP), which scales linearly up to $\sim 24$ CPUs for simulations of $\sim 10^6$ particles."65 As discussed by Dewpree&Warakas(2005)... the Inner parts of stars in close binaries generally remain unaffected by the presence of a companion. aud only the structure of the outermost lavers is modified by close idal interactions.," As discussed by \citet{deupree2005}, the inner parts of stars in close binaries generally remain unaffected by the presence of a companion, and only the structure of the outermost layers is modified by close tidal interactions."66 This result prompted us to model ouly he outer parts of the stars with appropriate boundary conditions., This result prompted us to model only the outer parts of the stars with appropriate boundary conditions.67 Such au approach effectively reduces the total ΠΙΟ of SPILT particles iu our simulations without decreasing the spatial resolution., Such an approach effectively reduces the total number of SPH particles in our simulations without decreasing the spatial resolution.68 C'onverselv. for the sale amount of CPU time. modeling only the outermost avers of stars allows for the use of more particles. herefore enhauciug the spatial and mass resolutions.," Conversely, for the same amount of CPU time, modeling only the outermost layers of stars allows for the use of more particles, therefore enhancing the spatial and mass resolutions."69 Moreover. CPU time is spent solely on particles actually aking part iu the mass transter or being affected by the companions tidal field.," Moreover, CPU time is spent solely on particles actually taking part in the mass transfer or being affected by the companion's tidal field."70 SPIT codes calculate livcdvodvuamical quantitics bv averaging over a sufficiently large ummber of ucighbours., SPH codes calculate hydrodynamical quantities by averaging over a sufficiently large number of neighbours.71 For particles located close to an edge or a boundary. two thines happen.," For particles located close to an edge or a boundary, two things happen."72 First. since there are no particles ou one side of the boundary. a pressure gradient exists and the particles tend. to be pushed further out of the domain of interest.," First, since there are no particles on one side of the boundary, a pressure gradient exists and the particles tend to be pushed further out of the domain of interest."73 Second. if the muuber of ucielibours for cach particle is kept fixed by requirements. as if is in our code. then the smoothing leugth is changed until enough neighbours are euclosed by the particle’s smoothed volume.," Second, if the number of neighbours for each particle is kept fixed by requirements, as it is in our code, then the smoothing length is changed until enough neighbours are enclosed by the particle's smoothed volume."74 This lack of neighbours therefore effectively decreases the spatial resolution at the boundary auduuderestimutes the particles deusity., This lack of neighbours therefore effectively decreases the spatial resolution at the boundary andunderestimates the particle's density.75 Iu such circunmistauces. the inpleimieutation of boundary conditions is required.," In such circumstances, the implementation of boundary conditions is required."76voung radio sources stay in equipartition while evolving in a self-similar wav.,young radio sources stay in equipartition while evolving in a self-similar way.77 ‘Vhis would require that the magnetic fields in CSS sources are tvpically a factor 20 lower than in GPS sources., This would require that the magnetic fields in CSS sources are typically a factor $\sim20$ lower than in GPS sources.78 The linear correlation itself only indicates a constant ratio between the magnetic field. ancl particle energies., The linear correlation itself only indicates a constant ratio between the magnetic field and particle energies.79 This constant does not have to be equal to unity. as required. for equipartition.," This constant does not have to be equal to unity, as required for equipartition."80 However. for a ratio of unity in energies. the bottom right panel of Figure 1. requires a ratio of overall to component size of typically ο6. which is close to the result seen in VLBI observations.," However, for a ratio of unity in energies, the bottom right panel of Figure \ref{morph} requires a ratio of overall to component size of typically $5-6$, which is close to the result seen in VLBI observations."81 This means that the energy ratio is not only constant. but also close to unity. which indicates that equipartition probably holds.," This means that the energy ratio is not only constant, but also close to unity, which indicates that equipartition probably holds."82 Figure 1 demonstrates that the data is consistent with a combination of SSA. equipartition. and self-similar growth.," Figure \ref{morph} demonstrates that the data is consistent with a combination of SSA, equipartition, and self-similar growth."83 ]!t is not obvious that the same correlation should. apply or [ree-free. absorption., It is not obvious that the same correlation should apply for free-free absorption.84 Although other more complicated combinations of mechanisms such as free-free. absorption with induced Compton scattering. (Ixuncic.. Bieknell Dopita. 1998) may also fit the data. the simplest explanation v far ds to assume that SSA. equipartition and self-similar source growth all individually hold.," Although other more complicated combinations of mechanisms such as free-free absorption with induced Compton scattering (Kuncic, Bicknell Dopita, 1998) may also fit the data, the simplest explanation by far is to assume that SSA, equipartition and self-similar source growth all individually hold."85 We therefore. believe hat SSA is indeed the cause of the spectral turnovers in GPS and CSS sources., We therefore believe that SSA is indeed the cause of the spectral turnovers in GPS and CSS sources.86 Lt may not be surprising that voung radio sources evolve in a self-imilar wav., It may not be surprising that young radio sources evolve in a self-similar way.87 Leahy and Williams (1984). shower that the cocoons of ΙΙΙ sources of very dilferent. physica size Πας similar axial ratios., Leahy and Williams (1984) showed that the cocoons of FRII sources of very different physical size had similar axial ratios.88 More recently. Subrahmanvan. Savipalli Llunsteacd (1996) found very. similar ratios for sources of linear sizes above 900 Ixpc. also suggesting tha radio sources evolve in a self-similar wav.," More recently, Subrahmanyan, Saripalli Hunstead (1996) found very similar ratios for sources of linear sizes above 900 Kpc, also suggesting that radio sources evolve in a self-similar way."89 An analvtica nmiocel for radio sources with pressure confinedjets developec by Waiser Alexander (1997) shows that the properties of the bow shock and of the surrounding gas the sources to grow in a self-similar wav. provided that the density of the surrounding gas falls off less steeply than 17/07," An analytical model for radio sources with pressure confined jets developed by Kaiser Alexander (1997) shows that the properties of the bow shock and of the surrounding gas the sources to grow in a self-similar way, provided that the density of the surrounding gas falls off less steeply than $1/r^2$."90 The number count statistics and. linear size. clistributions used in studies to constrain the luminosity evolution of radio sources. have all been averaged over a wide redshil range and only include the brightest. objects in the sky (Fanti et al.," The number count statistics and linear size distributions used in studies to constrain the luminosity evolution of radio sources, have all been averaged over a wide redshift range and only include the brightest objects in the sky (Fanti et al."91 1995. Reacheacd et al.," 1995, Readhead et al."92 1996. οDea Daum 1997).," 1996, O'Dea Baum 1997)."93 Llowever. in Dux density limited samples. the redshif distribution of GPS galaxies is significantly dillerent. fron that of large size radio galaxies (see figure 2)).," However, in flux density limited samples, the redshift distribution of GPS galaxies is significantly different from that of large size radio galaxies (see figure \ref{reddis}) )."94 This suggests that the interpretation of the number count statistics is no straightforward., This suggests that the interpretation of the number count statistics is not straightforward.95 Note that given the expected: luminosity evolution as sources evolve in size. many of the presen day GPS sources will have FRI luminosities.," Note that given the expected luminosity evolution as sources evolve in size, many of the present day GPS sources will have FRI luminosities."96 It is therefore assumed that GPS galaxies evolve into both FRI and FRI SOULCES., It is therefore assumed that GPS galaxies evolve into both FRI and FRII sources.97 The bias of GPS galaxies towards higher redshifts than large size radio galaxies itself. provides an important clue. about the luminosity evolution of radio sources., The bias of GPS galaxies towards higher redshifts than large size radio galaxies itself provides an important clue about the luminosity evolution of radio sources.98 [t implies that GPS galaxies are more likely to have higher radio power than extended objects in Lux density [limitec samples., It implies that GPS galaxies are more likely to have higher radio power than extended objects in flux density limited samples.99 LE CPS and large size radio sources are identica objects. observed at dillerent ages. their cosmologica density evolution. for example their birth rate as function of recishift. should be the same.," If GPS and large size radio sources are identical objects, observed at different ages, their cosmological density evolution, for example their birth rate as function of redshift, should be the same."100 Since their lifetimes are shor compared to the Hubble time. the redshift distributions of he GPS galaxies. and the objects they evolve to. shoulk also be the same.," Since their lifetimes are short compared to the Hubble time, the redshift distributions of the GPS galaxies, and the objects they evolve to, should also be the same."101 The bias of GPS sources towards higher redshifts and. radio powers therefore. implies that. their uminosity function must be fHlatter than that of large size radio sources., The bias of GPS sources towards higher redshifts and radio powers therefore implies that their luminosity function must be flatter than that of large size radio sources.102 We argue that the luminosity evolution of he individual objects stronely inlluences their collective uminosity function. and. propose an evolution scenario in which GPS sources increase in luminosity and [large size sources decrease in Luminosity with time (see section 4.1).," We argue that the luminosity evolution of the individual objects strongly influences their collective luminosity function, and propose an evolution scenario in which GPS sources increase in luminosity and large size sources decrease in luminosity with time (see section 4.1)."103 In he simplified case. in which source to source variations in he surrounding medium can be ignored. the luminosity of a radio source depends only on its age and jet power.," In the simplified case, in which source to source variations in the surrounding medium can be ignored, the luminosity of a radio source depends only on its age and jet power."104 Consider irst the luminosity. function. of large size sources., Consider first the luminosity function of large size sources.105 [t is expected that large size sources decrease in Luminosity with age (see section 4.1)., It is expected that large size sources decrease in luminosity with age (see section 4.1).106 Therefore high Iuminosity sources will end to be biased towards objects with both small ages and ugh jet powers., Therefore high luminosity sources will tend to be biased towards objects with both small ages and high jet powers.107 The intrinsic space density for high power jet sources will of course tend to be small., The intrinsic space density for high power jet sources will of course tend to be small.108 Furthermore. for a given jet. power there are fewer voung sources than old sources. simply. because sources spend only a small fraction of their time being voung.," Furthermore, for a given jet power there are fewer young sources than old sources, simply because sources spend only a small fraction of their time being young."109 The result is a very. low space density of large size sources of high power., The result is a very low space density of large size sources of high power.110 In contrast. large size sources of low power are biased to be both old and with ow jet power. both common conditions. hence the space density of large size sources with low power is much higher han that for those with high power. and the luminosity unction for large size sources is steep.," In contrast, large size sources of low power are biased to be both old and with low jet power, both common conditions, hence the space density of large size sources with low power is much higher than that for those with high power, and the luminosity function for large size sources is steep."111 In contrast. the uminositv of GPS sources is expected. to. increase with sources age (see section 4.1).," In contrast, the luminosity of GPS sources is expected to increase with sources age (see section 4.1)."112 Llieh luminosity GPS sources are therefore biased to be old and of high jet. power. while ow luminosity objects are biased to be voung and of low jet," High luminosity GPS sources are therefore biased to be old and of high jet power, while low luminosity objects are biased to be young and of low jet"113four well-studied systems.,four well-studied systems.114 In very brief summary. although we recommend the interested reader to read FBGOA. the models major components are: Empirical aspects of this model were contirmed for a different system in Corbel et al. (," In very brief summary, although we recommend the interested reader to read FBG04, the model's major components are: Empirical aspects of this model were confirmed for a different system in Corbel et al. ("1152004).,2004).116 In this paper we take a far larger sample of black hole X-ray binary outbursts and use them to test and retine the model of FBGOA in the context of X-ray spectral states., In this paper we take a far larger sample of black hole X-ray binary outbursts and use them to test and refine the model of FBG04 in the context of X-ray spectral states.117 In addition we extend the model by making for the first time a comprehensive attempt to include the X-ray short-timescale variability properties of the systems., In addition we extend the model by making for the first time a comprehensive attempt to include the X-ray short-timescale variability properties of the systems.118 The X-ray data presented in this paper were obtained with the Proportional Counter Array (PCA) onboard theExplorer (RXTE)., The X-ray data presented in this paper were obtained with the Proportional Counter Array (PCA) onboard the (RXTE).119 In our analysis we make extensive use of the hardness-intensity diagram (ΠΙΟ) as an indicator of the ray spectral state of a black hole binary in outburst., In our analysis we make extensive use of the hardness-intensity diagram (HID) as an indicator of the X-ray spectral state of a black hole binary in outburst.120 The HIDs presented here were taken from Homan et (in prep.), The HIDs presented here were taken from Homan et (in prep.).121" They were constructed from mode data from the PCA,", They were constructed from mode data from the PCA.122 These data were corrected for background. but not for dead time (typically a few percent).," These data were corrected for background, but not for dead time (typically a few percent)."123 Averaged count rates were extracted for each observation in three bands: channel 20-40. 3-10. and. 1-129. roughly corresponding to 9.5—17.0 keV. 2.8—5.5 keV and 2-60 KeV. respectively.," Averaged count rates were extracted for each observation in three bands: channel 20-40, 3-10, and 1-129, roughly corresponding to 9.5–17.0 keV, 2.8–5.5 keV and 2–60 keV, respectively."124 The ratio of the count rates in first two bands was used as an indicator of the spectral hardness and the third band as the broadband intensity., The ratio of the count rates in first two bands was used as an indicator of the spectral hardness and the third band as the broadband intensity.125 In case fast intensity or hardness variations were observed within an observation. the observation was split into two or more parts and hardness and intensity were calculated for each individual part.," In case fast intensity or hardness variations were observed within an observation, the observation was split into two or more parts and hardness and intensity were calculated for each individual part."126 In addition to HIDs we also studied the X-ray variability properties of all sources., In addition to HIDs we also studied the X-ray variability properties of all sources.127 Again. these data were taken from Homan et (Cin prep.).," Again, these data were taken from Homan et (in prep.)."128 Power spectra were constructed from high-time-reolution data from the Proportional Counter Array (PCA). using most of the PCA energy range and following standard fast-fourier techniques (see HHoman et al.," Power spectra were constructed from high-time-reolution data from the Proportional Counter Array (PCA), using most of the PCA energy range and following standard fast-fourier techniques (see Homan et al."129 2005 for a detailed description)., 2005 for a detailed description).130 As a measure of the strength of the X-ray variability we extracted the rms-normalized power from the 0.01—64 Hz frequency range. for each observation (or observation segment).," As a measure of the strength of the X-ray variability we extracted the rms-normalized power from the 0.01–64 Hz frequency range, for each observation (or observation segment)."131 Radio data presented in this paper were gathered exclusively from the literature. and references are provided in the brief descriptions for each outburst in section 2.," Radio data presented in this paper were gathered exclusively from the literature, and references are provided in the brief descriptions for each outburst in section 2."132 As noted above. in the following analysis we use Hardness-Intensity Diagram (HID) as an indicator of the X-ray spectral state of a black hole binary in outburst.," As noted above, in the following analysis we use Hardness-Intensity Diagram (HID) as an indicator of the X-ray spectral state of a black hole binary in outburst."133 This is the framework within which the analyses of FBGO4. HBOS and others were also set.," This is the framework within which the analyses of FBG04, HB05 and others were also set."134" In the HID the vertical axis simply corresponds to X-ray count rate within some band. and the horizontal axis to the ""hardness. or ratio of counts measured in two narrower sub-bands. such that ""harder. spectra (those with a relatively higher proportion of energy to low-energy X-rays within the band) are on the right hand side. and ‘softer’ spectra are on the left hand side."," In the HID the vertical axis simply corresponds to X-ray count rate within some band, and the horizontal axis to the `hardness', or ratio of counts measured in two narrower sub-bands, such that `harder' spectra (those with a relatively higher proportion of high-energy to low-energy X-rays within the band) are on the right hand side, and `softer' spectra are on the left hand side."135 Black hole and neutron star binaries (and maybe also white dwarfs) are known to demonstrate hysteresis in the tracks they trace in such diagrams during outburst. typically making hard = soft transitions at higher luminosities than the return soft > hard transition (FBGO4: HBOS: Koerding et al.," Black hole and neutron star binaries (and maybe also white dwarfs) are known to demonstrate hysteresis in the tracks they trace in such diagrams during outburst, typically making hard $\rightarrow$ soft transitions at higher luminosities than the return soft $\rightarrow$ hard transition (FBG04; HB05; Koerding et al."136 2006)., 2006).137 Section 2.1 (above) gives the X-ray bands used for the hardness ratios in this paper., Section 2.1 (above) gives the X-ray bands used for the hardness ratios in this paper.138 In Fig | we present HIDs for 14 outbursts from 11 different black hole X-ray binaries. annotated with symbols indicating imes of radio detections. radio flares. and times when the radio counterpart was undetectable.," In Fig 1 we present HIDs for 14 outbursts from 11 different black hole X-ray binaries, annotated with symbols indicating times of radio detections, radio flares, and times when the radio counterpart was undetectable."139 Note that we do not discriminate between levels of radio emission in these figures: it is either detected. a special case of which is the peak flux. or it is not.," Note that we do not discriminate between levels of radio emission in these figures: it is either detected, a special case of which is the peak flux, or it is not."140 evertheless this is enough to give us a good test of the scenario resented in FBGOJ., Nevertheless this is enough to give us a good test of the scenario presented in FBG04.141 In the following we describe the systems and heir outbursts individually. in the order in which they are presented in Fig |.," In the following we describe the systems and their outbursts individually, in the order in which they are presented in Fig 1."142 Note that while there are more RXTE data on black hole outbursts than those which are presented here. (1) these were all the outbursts for which we had useful X-ray and/or radio coverage. (ii) we are not aware of any other data set of results which contradict the empirical conclusions drawn here.," Note that while there are more RXTE data on black hole outbursts than those which are presented here, (i) these were all the outbursts for which we had useful X-ray and/or radio coverage, (ii) we are not aware of any other data set of results which contradict the empirical conclusions drawn here."143 This black hole binary is famous as the second known superluminal source in the galaxy (Tingay et al., This black hole binary is famous as the second known superluminal source in the galaxy (Tingay et al.144 1995: Hjellming Rupen 1995)., 1995; Hjellming Rupen 1995).145 The 1994 outburst with which these superluminal ejections were associated was not covered by RXTE (which was launched in December 19953). but two subsequent outbursts. in 1996 and 2005. have been well covered in X-rays.," The 1994 outburst with which these superluminal ejections were associated was not covered by RXTE (which was launched in December 1995), but two subsequent outbursts, in 1996 and 2005, have been well covered in X-rays."146 Radio coverage of this outburst was poor. but comparing a VLA non-detection (κ 3mJy) and a subsequent MOST detection at level of 55+5 mJy (843 MHz) indicates that a radio flare (i.e. probable ejection event) occurred somewhere between 1996 May 20-28 (MID 50223-50231).," Radio coverage of this outburst was poor, but comparing a VLA non-detection $<3$ mJy) and a subsequent MOST detection at level of $55 \pm 5$ mJy (843 MHz) indicates that a radio flare (i.e. probable ejection event) occurred somewhere between 1996 May 20-28 (MJD 50223-50231)."147 This radio flare occurred about half way in the transition between hard and soft X-ray states., This radio flare occurred about half way in the transition between hard and soft X-ray states.148 The radio and RXTE coverage of this outburst was much better, The radio and RXTE coverage of this outburst was much better149exchanges.,exchanges.150" In the “pure ice” case, the atmospheric mixing ratios are in simple proportion of the pure vapor pressures at the relevant ice temperatures (which may be different for different species) and, except for the main species which controls the pressure, of the fractional area covered by each ice."," In the “pure ice"" case, the atmospheric mixing ratios are in simple proportion of the pure vapor pressures at the relevant ice temperatures (which may be different for different species) and, except for the main species which controls the pressure, of the fractional area covered by each ice."151" Focussing on the case of CH4 on Pluto, Stansberry et al. ("," Focussing on the case of $_4$ on Pluto, Stansberry et al. ("152"1996) demonstrated that pure CH, lag deposits (whose existence is proved by observations, see Douté et al.","1996) demonstrated that pure $_4$ lag deposits (whose existence is proved by observations, see Douté et al."153 1999) assume higher temperatures than N> due to their reduced sublimation cooling and preferential formation in regions of high insolation., 1999) assume higher temperatures than $_2$ due to their reduced sublimation cooling and preferential formation in regions of high insolation.154" Even if covering only a few percent of Pluto’s surface, such patches can explain the observed atmospheric abundance of methane."," Even if covering only a few percent of Pluto's surface, such patches can explain the observed atmospheric abundance of methane."155" Alternatively, the “detailed balanced” model (Trafton, 1990; Trafton et al."," Alternatively, the “detailed balanced"" model (Trafton, 1990; Trafton et al."156 1998) predicts that surface-atmosphere exchanges in presence of atmospheric escape and seasonal transport lead to an atmospheric composition reflecting that of the accessible ice reservoir from which it is replenished., 1998) predicts that surface-atmosphere exchanges in presence of atmospheric escape and seasonal transport lead to an atmospheric composition reflecting that of the accessible ice reservoir from which it is replenished.157" When no fractionation (e.g. diffusive) occurs during escape or transport, the atmospheric mixing ratios are identical to those in the volatile reservoir."," When no fractionation (e.g. diffusive) occurs during escape or transport, the atmospheric mixing ratios are identical to those in the volatile reservoir."158" This is accomplished by the thin surface veneer enriched in the less volatile species, throttling off the Nz sublimation, and in permanent equilibrium with the atmosphere according to Raoult’s law."," This is accomplished by the thin surface veneer enriched in the less volatile species, throttling off the $_2$ sublimation, and in permanent equilibrium with the atmosphere according to Raoult's law."159The right haud axes of Figure 1 translate a to f using (he relationship given in equation (3) and. a lifetime for [O III|-bright PNs of 500 vr.,The right hand axes of Figure \ref{fig1} translate $\alpha$ to $f$ using the relationship given in equation (3) and a lifetime for [O III]-bright PNs of 500 yr.160 The absolute numbers are intriguing: despite the scatter. ancl (he uncertainties inherent in our estimation of /. i( is clear (hat in early-type systems. only a small fraction of the stars ever reach the tip of the |O III] A5007 luminosity function.," The absolute numbers are intriguing: despite the scatter, and the uncertainties inherent in our estimation of $t$, it is clear that in early-type systems, only a small fraction of the stars ever reach the tip of the [O III] $\lambda 5007$ luminosity function."161 In small galaxies. and galaxies with recent star formation. e25% of the stars which turn off (he main sequence eventually evolve into planetaries which populate the bright end of thePNLF.," In small galaxies, and galaxies with recent star formation, $\sim 25\%$ of the stars which turn off the main sequence eventually evolve into planetaries which populate the bright end of the."162 In redder svstems. this fraction drops to only ~55.," In redder systems, this fraction drops to only $\sim 5\%$."163 These small values provide an important clue for understanding the planetary nebula Iuminosity [unction., These small values provide an important clue for understanding the planetary nebula luminosity function.164 To sunnuarize the above section: (he progenitors of the PNs which populate the top 0.5 mag of the PNLF a) have core masses of ZO.GAL.. b) are present in all galaxies. and ϱ) are raver in redder populations than in svstems which mav have undergone recent star formation.," To summarize the above section: the progenitors of the PNs which populate the top 0.5 mag of the PNLF a) have core masses of $\gtrsim 0.6 M_{\odot}$, b) are present in all galaxies, and c) are rarer in redder populations than in systems which may have undergone recent star formation."165 Obviously. the greatest challenge to satisfving these conditions lies in reconciling the need for high mass central stars with the observed. colors and spectral line indices of elliptical ancl lenticular galaxies.," Obviously, the greatest challenge to satisfying these conditions lies in reconciling the need for high mass central stars with the observed colors and spectral line indices of elliptical and lenticular galaxies."166 In principle. there are two wavs to generate high-core mass planetaries in early-lvpe svslems.," In principle, there are two ways to generate high-core mass planetaries in early-type systems."167 The first is through the normal evolution of a trace population of stars with LurnolÉ masses greater than e2M..., The first is through the normal evolution of a trace population of stars with turnoff masses greater than $\sim 2 M_{\odot}$.168 If as Figure 1. demonstrates. intermediate mass objects contribute between ~5% and ~25% of an elliptical galaxv's total luminosity. then all the constraints provided by the PN observations are satisfied.," If, as Figure \ref{fig1} demonstrates, intermediate mass objects contribute between $\sim 5\%$ and $\sim 25\%$ of an elliptical galaxy's total luminosity, then all the constraints provided by the PN observations are satisfied."169 Unfortunately. there is good reason to believe that Chis is not the case.," Unfortunately, there is good reason to believe that this is not the case."170 Turnoll masses of ~2M. belong to populations with ages of ~1 Gvr (hen&Laughlin1939)., Turnoff masses of $\sim 2 M_{\odot}$ belong to populations with ages of $\sim 1$ Gyr \citep{ibenlaughlin}.171. Components this voung should be detectable via their effect on a galaxv's colors and spectral line indices. even if they comprise only ~5% of the svstems total light (Worthey1994;Tantalo&Chiosi2004).," Components this young should be detectable via their effect on a galaxy's colors and spectral line indices, even if they comprise only $\sim 5\%$ of the system's total light \citep{worthey, tantalo}."172. More importantly. as Figure 1 indicates. every earlv-tvpe galaxy. would have to have such a component.," More importantly, as Figure \ref{fig1} indicates, every early-type galaxy would have to have such a component."173 While il is possible that some objects (such as NGC 1316 and. 4382) have acquired. an intermediate age population via a recent accretion or merger (Goudlrooijetal. 2002).. this explanation cannot work for all objects.," While it is possible that some objects (such as NGC 1316 and 4382) have acquired an intermediate age population via a recent accretion or merger \citep{goudfrooij, terlevich}, this explanation cannot work for all objects."174" Galaxies. such as the ""standard elliptical NGC 3379 (deVaucouleurs&Capaccioli1979). and the bulge of M31. clisplay no evidence of interaction or star formation in the recent past (Tragerοἱal.2000)."," Galaxies, such as the “standard” elliptical NGC 3379 \citep{devauc} and the bulge of M31 display no evidence of interaction or star formation in the recent past \citep{trager}."175. A second. more plausible. explanation for the PNLF cutoff invokes an alternative form of stellar evolution.," A second, more plausible, explanation for the PNLF cutoff invokes an alternative form of stellar evolution."176 In the solar neighborhood. roughly two-thirds of the stars are binaries. ancl a large fraction of these svstems interact at some time during their evolution," In the solar neighborhood, roughly two-thirds of the stars are binaries, and a large fraction of these systems interact at some time during their evolution"177spc) than the compact (E10 kpc) radio galaxies in the Morganti et al. (,kpc) than the compact $\le$ 10 kpc) radio galaxies in the Morganti et al. (1781992) sample.,1992) sample.179 The far infrared properties of NGC 1110 are consistent with those of a radio galaxy with dust reatecl by star formation., The far infrared properties of NGC 4410 are consistent with those of a radio galaxy with dust heated by star formation.180 From he low ratio of far-infrared to radio luminosity 'effutro)). the radio emission Is €early coimiuated by au active nucleus.," From the low ratio of far-infrared to radio luminosity \\ref{Intro}) ), the radio emission is clearly dominated by an active nucleus."181 However. stroug far-infrared enilssion Is not unust aliuradio οalaxies.," However, strong far-infrared emission is not unusual in radio galaxies."182 In the Colombek. Miley. Neugebauer (1055) study of 131 adio galaxies. E156 were cletectec- half with [ar-1ufrarec luminosities greater than that of NGC E110.," In the Golombek, Miley, Neugebauer (1988) study of 131 radio galaxies, $\%$ were detected, half with far-infrared luminosities greater than that of NGC 4410."183 Siuilar 'esults were ound by huyey. Wyun-Williams. Becklin (1990) for a racdio-selececd saiple.," Similar results were found by Impey, Wynn-Williams, Becklin (1990) for a radio-selected sample."184 In NGC 1110. as well as in maly of the other radio galaxies detected by URAS. this ar-infrared CLUISSIOL is due to iterstellar [1st. uot direct syuchrotron radiation from the active itcleus.," In NGC 4410, as well as in many of the other radio galaxies detected by IRAS, this far-infrared emission is due to interstellar dust, not direct synchrotron radiation from the active nucleus."185 This is demonstrated for NGC LL10i i Figure L. where we plot the global spectral enerey dis‘bution of NGC III0A4B. A clear far-iπι excess Is seen above the power-law radio continuu1.," This is demonstrated for NGC 4410 in Figure \ref{fig9}, where we plot the global spectral energy distribution of NGC 4410A+B. A clear far-infrared excess is seen above the power-law radio continuum."186 Such an excess is also found iu most oftie racio galaxies surveyed Nw hnpey et al. (, Such an excess is also found in most of the radio galaxies surveyed by Impey et al. (1871990).,1990).188 In NGCΕΠ. the 60 gan/LOO jun flux deusity ratic pis ~0.5 (Mazzarella et al.," In NGC 4410, the 60 $\mu$ m/100 $\mu$ m flux density ratio is $\sim$ 0.5 (Mazzarella et al."189 1991). within the range [ος for star forming galaxies (Helou 1986). sipporting the idea the [a: infrared emission could be produced by dust heated by star formation.," 1991), within the range found for star forming galaxies (Helou 1986), supporting the idea the far infrared emission could be produced by dust heated by star formation."190 To distinguish between dist heated by au active nucles aud star formation. the 25 san/G0 fan raio is often used (e.e..oe) cle Cuijp et al.," To distinguish between dust heated by an active nucleus and star formation, the 25 $\mu$ m/60 $\mu$ m ratio is often used (e.g., de Grijp et al."191 1985: Miley. Neugebauer. Soifer 1985): au enhanced Fasjun/ Feojus ratio signals warner cust than expect from star formation alone.," 1985; Miley, Neugebauer, Soifer 1985); an enhanced $_{25~{\mu}m}$ $_{{60~\mu}m}$ ratio signals warmer dust than expect from star formation alone."192 Based on the IAS data or NGC 1110. which provides only a 36 upper limit at 25 4/nn/60 jan of 0.59. we cannot rule out ie possibility that emission from hot dust near the active uucleus may contribute to some the [ar jufrared einisslon.," Based on the IRAS data for NGC 4410, which provides only a $3\sigma$ upper limit at 25 $\mu$ m/60 $\mu$ m of 0.59, we cannot rule out the possibility that emission from hot dust near the active nucleus may contribute to some the far infrared emission."193 Whereas the detectiou of song far-iurared emission [rom nunerous radio galaxies indicates that παν have reasouablv hig[n]i star [ornation rates. the «irect observations of luminous H II regious in radio galaxies vla nar'owband optical imagine Insill uncomme1.," Whereas the detection of strong far-infrared emission from numerous radio galaxies indicates that many have reasonably high star formation rates, the direct observations of luminous H II regions in radio galaxies via narrowband optical imaging is still uncommon."194 One of the lew other radio gaaxies with H II regions Clearly clistinguishable in Ha+[N II] map sis the peculiar galaxy Centaurus A. whic1 bas an incined dusty disk with numerois H IL regiois (Hodge Ixenuicutt 1983: Blaucl. TayloMV Atlerto 1987).," One of the few other radio galaxies with H II regions clearly distinguishable in $\alpha$ +[N II] maps is the peculiar galaxy Centaurus A, which has an inclined dusty disk with numerous H II regions (Hodge Kennicutt 1983; Bland, Taylor, Atherton 1987)."195 The far-infrared |unmiuosivy of Cei Ais ο x 10° L (Rice et al., The far-infrared luminosity of Cen A is 5 $\times$ $^9$ $\sun$ (Rice et al.196 LOSS. usiug a distance of 3.5 Mpe from Hui et al. (," 1988, using a distance of 3.5 Mpc from Hui et al. ("1971993)). sinilar to hat of NGC [110A4B. Most of this far-inrare elnission arises [rom the Cen A cis& Ταher thai its nucleus (Joy et al.,"1993)), similar to that of NGC 4410A+B. Most of this far-infrared emission arises from the Cen A disk rather than its nucleus (Joy et al."198 1055)., 1988).199 Cyenus A (Stockton. Ridgeway. Lilly 1991: Jackson. Tacbuner. Sparks 1998) aud Hydra A (Melnick. Copal-Ixrislina. Terlevich 1997) also appear to have sone circumuuclear star formation. however. the star formaion in these systems is much less prominent than that in Cen A or NGC L110.," Cygnus A (Stockton, Ridgway, Lilly 1994; Jackson, Tadhunter, Sparks 1998) and Hydra A (Melnick, Gopal-Krishna, Terlevich 1997) also appear to have some circumnuclear star formation, however, the star formation in these systems is much less prominent than that in Cen A or NGC 4410."200 Fornas A (Mackie Fabbiano 1998) aud PISS 0319-27 (Cimiberg. Sadler. Simkin 1999) show little evidence for he presence of OB stars.," Fornax A (Mackie Fabbiano 1998) and PKS 0349-27 (Grimberg, Sadler, Simkin 1999) show little evidence for the presence of OB stars."201 Star formation in a radio galaxy may be triggered by density waves ina disk. as is presumably occurring in the Cen A disk.," Star formation in a radio galaxy may be triggered by density waves in a disk, as is presumably occurring in the Cen A disk."202 Alternatively. star formation may be induced by the radio lobe lunpacting the inerstellar medium. which may be the case for Miukowskis object. a star formation region near the radio galaxy NGC 511 (vau Breugel et al.," Alternatively, star formation may be induced by the radio lobe impacting the interstellar medium, which may be the case for Minkowski's object, a star formation region near the radio galaxy NGC 541 (van Breugel et al."203 1985)., 1985).204 This object has au Ha luminosity, This object has an $\alpha$ luminosity205using the definition given above (Section 2.3). and the low occupation are the bottom 5mt%.,"using the definition given above (Section 2.3), and the low occupation are the bottom 5."206. For reference. the mean number of subhalos in the high occupation sample is 17.6 and the mean mass per halo is 3.80107.ΤΑ.," For reference, the mean number of subhalos in the high occupation sample is 17.6 and the mean mass per halo is $3.8 \times 10^{12} \msun$."207 Lhe mean number of subhalos for the bottom sample is 4.1 and the mican mass per halo is 3.9101ΑΙ.," The mean number of subhalos for the bottom sample is 4.1 and the mean mass per halo is $3.9 \times20810^{12} \msun$."209 Looking at Figure 1 we can immediately see that there is a dillerence in the way the two subsamples are tracing out structures., Looking at Figure \ref{slice} we can immediately see that there is a difference in the way the two subsamples are tracing out structures.210 Lower occupation halos appear to outnumber the high occupation halos in the low density regions that fill most of space., Lower occupation halos appear to outnumber the high occupation halos in the low density regions that fill most of space.211 In the censest areas. there are many more high occupation halos.," In the densest areas, there are many more high occupation halos."212 We will see in the following Sections 3.1 and 3.3 that this is borne out quantitatively by considering the halo occupation distribution in clilferent density environments ancl also measuring the correlation function for the two samples we are plotting here., We will see in the following Sections 3.1 and 3.3 that this is borne out quantitatively by considering the halo occupation distribution in different density environments and also measuring the correlation function for the two samples we are plotting here.213 Alany observational measurements of galaxy clustering can be reproduced by theories that include two main ingredients. the clustering of dark. matter halos. and a model for the number of galaxies in a halo.," Many observational measurements of galaxy clustering can be reproduced by theories that include two main ingredients, the clustering of dark matter halos, and a model for the number of galaxies in a halo."214" The Lalo Occupation Distribution (LIOD. see e.g. Berlind Weinberg 2002. Zheng 2002. WKravtsov 2004) is à way of formulating the latter,"," The Halo Occupation Distribution (HOD, see e.g. Berlind Weinberg 2002, Zheng 2002, Kravtsov 2004) is a way of formulating the latter."215 In the case were galaxies are identified. with dark matter subhalos. the LOD can be measured. from a simulation by simply counting the number of subhalos as a [function of halo mass.," In the case were galaxies are identified with dark matter subhalos, the HOD can be measured from a simulation by simply counting the number of subhalos as a function of halo mass."216 In the present paper we will only concern ourselves with the mean number of galaxies in a halo. leaving the form of the probability. distribution for further work.," In the present paper we will only concern ourselves with the mean number of galaxies in a halo, leaving the form of the probability distribution for further work."217 We note that Bovlan-Ixolchin (2010) have found that subhalo abuncances are not well described bv Poisson statistics at low mass. but rather are dominated bv intrinsic scatter.," We note that Boylan-Kolchin (2010) have found that subhalo abundances are not well described by Poisson statistics at low mass, but rather are dominated by intrinsic scatter."218" The simplest assumption that can be mace about the HOD is that the mean number of subhalos. Nou, depends only on halo mass."," The simplest assumption that can be made about the HOD is that the mean number of subhalos, $N_{\rm sub}$ depends only on halo mass."219 This assumption has been shown to hold relatively well by Derlind (2003) in. (ανάνοςνnamic) simulations and is consistent with the e.g.. Yang (2005) observational measurements of galaxy groups.," This assumption has been shown to hold relatively well by Berlind (2003) in (hydrodynamic) simulations and is consistent with the e.g., Yang (2005) observational measurements of galaxy groups."220 Lt is known however that substructure fraction does depend on environments in simulations (c.g. Wang 2011).," It is known however that substructure fraction does depend on environments in simulations (e.g., Wang 2011)."221 We will sce how this translates into changes in the HOD. first bv looking at the local overdensity around halos and then some other measures of the environment.," We will see how this translates into changes in the HOD, first by looking at the local overdensity around halos and then some other measures of the environment."222 We measure the density within a radius of cach halo center of mass., We measure the density within a radius of each halo center of mass.223 We then rank the halos by density. and. plot the HOD for the halos as a function of halo mass for cillerent density subsamples., We then rank the halos by density and plot the HOD for the halos as a function of halo mass for different density subsamples.224 Results are shown in panels (a) and (b) of Figure 2.. where we show the HOD for the top by density. bottom by density and for the whole sample.," Results are shown in panels (a) and (b) of Figure \ref{hod}, where we show the HOD for the top by density, bottom by density and for the whole sample."225 In the top panels of that figure we show the fractional dillerence from the LOD for the whole sample for the two extreme density bins., In the top panels of that figure we show the fractional difference from the HOD for the whole sample for the two extreme density bins.226 To compute the error bars on the fractional dillerence. the volume was split into octants. and a jacknife estimator (Bradley 1982) was used to compute the error on the mean from the standard. deviation of the jacknife subsamples.," To compute the error bars on the fractional difference, the volume was split into octants, and a jacknife estimator (Bradley 1982) was used to compute the error on the mean from the standard deviation of the jacknife subsamples."227 We can see from Figure 2((a) that the number of subhalos in a halo does depend on the local density. with the halos located in the densest (5tA) of environments having a peak dilerence in halo occupation of LO% more subhalos than the set of all halos.," We can see from Figure \ref{hod}( (a) that the number of subhalos in a halo does depend on the local density, with the halos located in the densest $5\%$ ) of environments having a peak difference in halo occupation of $\sim10 \%$ more subhalos than the set of all halos."228 This dilference is most. prominent for halos of masses 10277.10775.TAL. and becomes zero at lower and higher halo mass., This difference is most prominent for halos of masses $10^{12} -10^{13} \msun$ and becomes zero at lower and higher halo mass.229 The dillerence is even larger for halos in underdense regions. which have less subhalos than the set of all halos by up to ~40%. a result. which again depends on halo mass.," The difference is even larger for halos in underdense regions, which have less subhalos than the set of all halos by up to $\sim 40\%$, a result which again depends on halo mass."230 Looking at more extreme ends of the Nou. distribution. the peak shifts to the right (e.g.. ~101TAL. for the top 1% by occupation.," Looking at more extreme ends of the $N_{\rm sub}$ distribution, the peak shifts to the right (e.g., $\sim10^{13.5}\msun$ for the top $1\%$ by occupation."231 The environmental dependence continues out to larger radius. as can be see in Figure 2((b) where we use density measured with 105.Mpe to rank halos.," The environmental dependence continues out to larger radius, as can be see in Figure \ref{hod}( (b) where we use density measured with $10 \hmpc$ to rank halos."232 A third method to measure the density is that within a Lagrangian volume with mass 10775.TAZ..., A third method to measure the density is that within a Lagrangian volume with mass $10^{15} \msun$.233 This is shown in panel (c). where the sign of the clleet is the same. although the amplitude for the low density environments is very cülferent (and therefore the ellect is detected. at a. lower level of. significance).," This is shown in panel (c), where the sign of the effect is the same, although the amplitude for the low density environments is very different (and therefore the effect is detected at a lower level of significance)."234 This is likely to do with the fact that the lowest density environments in this Lagrangian picture are being measured out to very large radii and therefore diluting the effect., This is likely to do with the fact that the lowest density environments in this Lagrangian picture are being measured out to very large radii and therefore diluting the effect.235" For example. the mean radius that encloses 1075.ΑΙ. for the ""bottom line is 235.1Mpce."," For example, the mean radius that encloses $10^{15} \msun$ for the “bottom ” line is $23 \hmpc$."236 The dependence of halo properties on environment has en investigated by many. authors (e.g... Ishivama 2008. Wane 2011).," The dependence of halo properties on environment has been investigated by many authors (e.g., Ishiyama 2008, Wang 2011)."237 Recently Jeeson-Daniel (2011) have shown that environment does not correlate with substructure mass [fraction on a halo by halo basis., Recently Jeeson-Daniel (2011) have shown that environment does not correlate with substructure mass fraction on a halo by halo basis.238 This appears to be at odds with what we find here. but he definition of environment used by Jeeson-Daniel (2011) is clifferent to ours. being chosen so that it is not dependent on halo mass.," This appears to be at odds with what we find here, but the definition of environment used by Jeeson-Daniel (2011) is different to ours, being chosen so that it is not dependent on halo mass."239 Also we count subhalos by number and not by mass fraction., Also we count subhalos by number and not by mass fraction.240 Wang (2011) on the other iud have found a relationship between local tidal field of a halo ancl substructure., Wang (2011) on the other hand have found a relationship between local tidal field of a halo and substructure.241 Jecson-Danicl and. Skibba (2011) find that concentration (closely related to age) is more fundamental in setting a range of halo properties than mass., Jeeson-Daniel and Skibba (2011) find that concentration (closely related to age) is more fundamental in setting a range of halo properties than mass.242 The destruction of substructure over time in halos can explain the anticorrelation between age or concentration and substructure (Gao 2004)., The destruction of substructure over time in halos can explain the anticorrelation between age or concentration and substructure (Gao 2004).243 One might therefore expect there to be less substructure in halos which formed earlier. and have a higher concentration.," One might therefore expect there to be less substructure in halos which formed earlier, and have a higher concentration."244 Our results could be explained therefore. if. halos in higher density regions had. later formation times and lower concentrations. but this is not the case in general (as pointed out by WO06 and CGWOT). so that the situation is more complex.," Our results could be explained therefore if halos in higher density regions had later formation times and lower concentrations, but this is not the case in general (as pointed out by W06 and GW07), so that the situation is more complex."245" In WO6 and Wetzel (2007) it was shown that low concentration halos and late forming halos do preferentially reside in high density environments. but only provided. the halo masses are AMcAl,."," In W06 and Wetzel (2007) it was shown that low concentration halos and late forming halos do preferentially reside in high density environments, but only provided the halo masses are $M>M_{*}$."246 Zentner (2007) pointed out that is the general dependence that would be expected from an excursion set theory analysis (see also further work by Dalal 2008)., Zentner (2007) pointed out that is the general dependence that would be expected from an excursion set theory analysis (see also further work by Dalal 2008).247" These papers argued that high-concentration and carly-forming halos are found in high density environments when Al<Al, because these halos have their growth quenched bv the tidal fields of nearby large halos.", These papers argued that high-concentration and early-forming halos are found in high density environments when $M < M_{*}$ because these halos have their growth quenched by the tidal fields of nearby large halos.248 At z= 1," At $z=1$ ,"249 At z= 1.," At $z=1$ ,"250SII73 Catalogue by Clement (1996).,SH73 Catalogue by Clement (1996).251 The most recent CCD observations of RAR Lyraes in MS ave from WOT and from M. Corwin (private communication), The most recent CCD observations of RR Lyraes in M3 are from K97 and from M. Corwin (private communication).252 In this paper we present a new photometric study of 60 RRO Lwrae variable stars in M3. based on BYL CCD observations taken over à period of 5 vears and a new independent absolute photometric calibration (described in detail by Ferraro et al.," In this paper we present a new photometric study of 60 RR Lyrae variable stars in M3, based on BVI CCD observations taken over a period of 5 years and a new independent absolute photometric calibration (described in detail by Ferraro et al."253 1997. hereafter E97).," 1997, hereafter F97)."254 Here we will present the observations and an initial analysis of the data., Here we will present the observations and an initial analysis of the data.255 A more detailed analysis of the RR Lvrae. properties. is deferred to a separate paper (Cacciari et al., A more detailed analysis of the RR Lyrae properties is deferred to a separate paper (Cacciari et al.256 1998). whereas the new photometry of the extended sample of non-variable stars ( 19.000 stars) and related CMD have been presented and discussed by Buonanno et al. (," 1998), whereas the new photometry of the extended sample of non-variable stars $\sim$ 19,000 stars) and related CMD have been presented and discussed by Buonanno et al. ("2571994: hereinafter. D94) and E97.,1994: hereinafter B94) and F97.258 The observations were obtained αἲ (wo sites. Loiano (Bologna Observatory. Haly). and. the Cierman-Spanish Astronomical Center in Calar Alto (Spain).," The observations were obtained at two sites, Loiano (Bologna Observatory, Italy) and the German-Spanish Astronomical Center in Calar Alto (Spain)."259 The Loiano observations were taken in: March. 3-5. 7- and 11 1990: February. 7 1992: April. 10-11. 1992: ane Alay. 3. 7-9. and Ll 1992 with the 152em FE/S LHitchev-Chretien telescope and an ROA CCD 320x512 pixels. scale —ü.5arcsec/pixel. FOV2407x416.," The Loiano observations were taken in: March, 3-5, 7-9, and 11 1990; February, 7 1992; April, 10-11 1992; and May, 3, 7-9, and 11 1992 with the 152cm F/8 Ritchey-Chretien telescope and an RCA CCD 320x512 pixels, scale =0.5arcsec/pixel, FOV=2'40""x4'16""."260 Because of the limitec size of the field of view. two contiguous fields were observec (sce Figure 1. and Figure 2)) to cover the SE and NW halves of the cluster.," Because of the limited size of the field of view, two contiguous fields were observed (see Figure \ref{fig-f1} and Figure \ref{fig-f2}) ) to cover the SE and NW halves of the cluster."261 Even so. the most external variables could no be observed.," Even so, the most external variables could not be observed."262 The standard Johnson ΝΕ filters were used. and 65 ai 69 [rames in each colour were taken on the NW and SE Lick respectively.," The standard Johnson BVI filters were used, and 65 and 69 frames in each colour were taken on the NW and SE field respectively."263 The exposure times depended on conditions. and were typically ~ 5 min (V). 10-15 min (B) and 4 min (1) for an average seeing of about. 1.5-2 arcsec.," The exposure times depended on conditions, and were typically $\sim$ 5 min (V), 10-15 min (B) and 4 min (I) for an average seeing of about 1.5-2 arcsec."264 In a [few cases. however. the seeing was significantly worse ancl the data have been discarded from the subsequent. analysis.," In a few cases, however, the seeing was significantly worse and the data have been discarded from the subsequent analysis."265 A total of 38 variables in the NW field and 22 variables in the SE field have been measured. based: on previously identified positions (81173). and for several ofthem improved or new periods have been determined. (see Sect.," A total of 38 variables in the NW field and 22 variables in the SE field have been measured based on previously identified positions (SH73), and for several of them improved or new periods have been determined (see Sect."266 3.)., 3.).267 No independent search for variability has been performed., No independent search for variability has been performed.268 The Calar Alto observations are only 5 data. points spread over three almost contiguous nights (March. 26 1995 and April. 1.2 1995). and were taken mainly for calibration purposes.," The Calar Alto observations are only 5 data points spread over three almost contiguous nights (March, 26 1995 and April, 1,2 1995), and were taken mainly for calibration purposes."269 However they provide a good extension of the time baseline and have proven quite helpful in the period analysis., However they provide a good extension of the time baseline and have proven quite helpful in the period analysis.270 The observations were taken with the 1.23 m telescope. using a thinned 1024x1024 ‘Tektronix chip (24 ji pixel. 0.50 aresce/pixel). with Ar-coatines.," The observations were taken with the 1.23 m telescope, using a thinned 1024x1024 Tektronix chip (24 $\mu$ pixel, 0.50 arcsec/pixel), with Ar-coatings."271 The LE filter is in the Ixron-Cousins system. centered at S020A.," The I filter is in the Kron-Cousins system, centered at 8020."272.. For an average seeing of 1.6 aresec the typical exposure times were  6-7 min (V). 20 min (D) and 5-6 min (1).," For an average seeing of 1.6 arcsec the typical exposure times were $\sim$ 6-7 min (V), 20 min (B) and 5-6 min (I)."273 The data reduction and absolute photometric calibration of the RRO Lyrac cata is the same that was obtained anc used. for the construction of the new Colour-Alagnituce diagram of M3. (E97)., The data reduction and absolute photometric calibration of the RR Lyrae data is the same that was obtained and used for the construction of the new Colour-Magnitude diagram of M3 (F97).274 The absolute calibration in particular. which was the basic item for a new and independent. analysis of the M3 characteristics. turnec out to be à rather complicated. and. dillicult. problem to solve with the desired accuracy.," The absolute calibration in particular, which was the basic item for a new and independent analysis of the M3 characteristics, turned out to be a rather complicated and difficult problem to solve with the desired accuracy."275 Since it has been ciscussec in great detail by E97. along with the comparison with all previous relevant photometries. we refer the interestec reader to this paper: we shall quote and use their results when relevant.," Since it has been discussed in great detail by F97, along with the comparison with all previous relevant photometries, we refer the interested reader to this paper; we shall quote and use their results when relevant."276 The photometry of the RR Lyrae variables was carrie out. relatively to the local standard sequence that hac been defined in each field. so as to cover the colour am magnitude range relevant for LIB stars.," The photometry of the RR Lyrae variables was carried out relatively to the local standard sequence that had been defined in each field, so as to cover the colour and magnitude range relevant for HB stars."277 The Ri Lyraes we have measured are identified in Figure 1., The RR Lyraes we have measured are identified in Figure 1.278 Phe local stanclare stars are listed in Table 1.. where we give the photometric values with the new calibration of E97.," The local standard stars are listed in Table \ref{tab-locstan}, where we give the photometric values with the new calibration of F97."279 Star identifications are [rom D94., Star identifications are from B94.280 Theος error. of cach measurement for the lid Lyrae stars depends on the seeing and crowding concitions. and is on average about 0.02-0.03 mag.," The error of each measurement for the RR Lyrae stars depends on the seeing and crowding conditions, and is on average about 0.02-0.03 mag."281 As lar assysfemalic errors are concerned. we recall the conclusion by E97 (see their Sect.," As far as errors are concerned, we recall the conclusion by F97 (see their Sect."282" 2.5) that ""we still cannot exclude errors as high as 0.05 mag in the absolute values. both in magnitude anc in colour (particularly at the blue and red extremes)”."," 2.5) that “ we still cannot exclude errors as high as 0.05 mag in the absolute values, both in magnitude and in colour (particularly at the blue and red extremes)”."283 A comparison with the photometry of WOT for the, A comparison with the photometry of K97 for the284Of the 9 ILAC AGNs with zx0.043 in the PAO field of view. the 7 objects that correlate with energetic PAO cosmic ravs within ον=16.9? are located at an average distance to the SGP of (0225)agp=16.8.,"Of the 9 1LAC AGNs with $z \leq 0.048$ in the PAO field of view, the 7 objects that correlate with energetic PAO cosmic rays within $\psi_3=16.9^\circ$ are located at an average distance to the SGP of $\langle \psi_{\rm sgp}^{\rm agn} \rangle = 16.8^\circ$."285 For comparison. PAO events associated with the ILAC GZIx. AGNs are located at the average distance (iPM)=19.17.," For comparison, PAO events associated with the 1LAC GZK AGNs are located at the average distance $\langle \psi_{\rm sgp}^{\rm PAO} \rangle = 19.7^\circ$."286 This suggests that the nearby 5-rav. bright AGINs associated. with UIIECRs on average fall very close to the nearby local overdensitv of matter in the universe. even though the general distribution of LILAC AGNs does not follow noticeablv the SGP.," This suggests that the nearby $\gamma$ -ray bright AGNs associated with UHECRs on average fall very close to the nearby local overdensity of matter in the universe, even though the general distribution of 1LAC AGNs does not follow noticeably the SGP."287 We analvsed the correlation between the positions of the 5-rav sources in the LAT First Source Catalog (LFGL) and the First LAT AGN Catalog (LLAC) produced during the first eleven months of operation of theTelescope.. and the arrival directions of the hiehest energv cosmic rays measured during 1.2 vears of operation of theObsereatory.," We analysed the correlation between the positions of the $\gamma$ -ray sources in the LAT First Source Catalog (1FGL) and the First LAT AGN Catalog (1LAC) produced during the first eleven months of operation of the, and the arrival directions of the highest energy cosmic rays measured during 1.2 years of operation of the."288. Using our cross-correlation test. we are particularly interested in the value of separation angle & between the positions of PAO events and reference sources (hat maximizes the significance level 5 of rejecting the null hypothesis (that the observed configuration is due to chance assuming an isotropic flux of UIIECRs).," Using our cross-correlation test, we are particularly interested in the value of separation angle $\psi$ between the positions of PAO events and reference sources that maximizes the significance level $S$ of rejecting the null hypothesis (that the observed configuration is due to chance assuming an isotropic flux of UHECRs)."289 Our main results [rom the cross-correlation analvsis of each LFCL subset (in the PAO field of view) with the PAO events are summarized below: For the subset of nine LLAC AGNs eloser than 200 Alpe (2<0.043. roughly the distance to the GZIx horizon). we reject with the highest significance the null hypothesis compared to," Our main results from the cross-correlation analysis of each 1FGL subset (in the PAO field of view) with the PAO events are summarized below: For the subset of nine 1LAC AGNs closer than 200 Mpc $z \leq 0.048$, roughly the distance to the GZK horizon), we reject with the highest significance the null hypothesis compared to"290converting the raw spectroscopic data tables into. the corrected. anc combined: measurements to be usec in the peculiar velocity analyses.,converting the raw spectroscopic data tables into the corrected and combined measurements to be used in the peculiar velocity analyses.291 In order to combine multiple e ancl oobservations for a galaxy. it is first necessary {ο ensure that all the sources of data are on a consistent svstem.," In order to combine multiple $\sigma$ and observations for a galaxy, it is first necessary to ensure that all the sources of data are on a consistent system."292" To this end we correct the EEV93. EEV94 and TEIS94 systems for aperture effects. and scale them onto our new ""standard svstenr using the olfsets listed. in Tables ο and. 7.."," To this end we correct the EEV93, EEV94 and TEK94 systems for aperture effects, and scale them onto our new `standard system' using the offsets listed in Tables \ref{sigcorrs} and \ref{mgcorrs}."293 The distance used in calculating the aperture correction is the median redshift of the relevant cluster. or (if not part of the cluster sample) the individual galaxy recdshift.," The distance used in calculating the aperture correction is the median redshift of the relevant cluster, or (if not part of the cluster sample) the individual galaxy redshift."294 The data for multipls-observed. galaxies are. then combined to give a weighted mean loge. and weighted meanMg».," The data for multiply-observed galaxies are then combined to give a weighted mean $\log\sigma$, and weighted mean."295 Phe weight of each measurement is assigned according to the external error on the dataset [rom which it derives., The weight of each measurement is assigned according to the external error on the dataset from which it derives.296 1n constructing the means. we exclude the (2 3.57) deviant measurcments as [ageed above.," In constructing the means, we exclude the $>3.5\sigma$ ) deviant measurements as flagged above."297 1t should be stressed that the external datasets (LICI. FOCP2. etc.)," It should be stressed that the external datasets (LICK, FOCP2, etc.)"298 are used. only to. derive. the necessary corrections. and to identifv outlving measurements.," are used only to derive the necessary corrections, and to identify outlying measurements."299 The mean parameters are caleulated using data drawn only from EEV93. EEV94 and TEIN94.," The mean parameters are calculated using data drawn only from EEV93, EEV94 and TEK94."300 Reeession velocities are combined. by correcting. the, Recession velocities are combined by correcting the301Numerical simulations of star formation— even the highly idealized simulations to which contemporary astrophysics is limited.— require. very. large computational resources.,Numerical simulations of star formation even the highly idealized simulations to which contemporary astrophysics is limited require very large computational resources.302 The dynamics is scll-eravitating. so the gravitational field. has to be recaleulated at cach time-step.," The dynamics is self-gravitating, so the gravitational field has to be recalculated at each time-step."303" Phe ranges of density (~107 gem to —10 g em. 7) and linear scale (~107"" cmto 107oü em) are very Large. so high. resolution MNis needed."," The ranges of density $\sim 30410^{-22}$ g $^{-3}$ to $\sim 10^1$ g $^{-3}$ ) and linear scale $\sim 10^{20}$ cm to $\sim 10^{10}$ cm) are very large, so high resolution is needed."305 The geometry is complex. so three-dimensional simulations are essential.," The geometry is complex, so three-dimensional simulations are essential."306 The cdvnamies is alfected by a varicty of radiative. thermal. chemical and. magnetic ellects. with the result that the energy. equation is not a local function of state.," The dynamics is affected by a variety of radiative, thermal, chemical and magnetic effects, with the result that the energy equation is not a local function of state."307 The initial ancl boundary conditions are chaotic and xoorlv. constrained by observation., The initial and boundary conditions are chaotic and poorly constrained by observation.308 Smoothec Particle LEvdrodynamies (SPILL) is a particle-wed hyvelrodvnamic seheme which accommodates some of these requirements. automatically. by virtue of being Lagrangian. having no imposed geometrical constraints. and ing readily combined with particle-based. gravity solvers. or example Tree Code Gravity (PCC: Barnes Llut 1986: Lernquist 1987: Llernquist Ixatz 1989).," Smoothed Particle Hydrodynamics (SPH) is a particle-based hydrodynamic scheme which accommodates some of these requirements automatically, by virtue of being Lagrangian, having no imposed geometrical constraints, and being readily combined with particle-based gravity solvers, for example Tree Code Gravity (TCG; Barnes Hut 1986; Hernquist 1987; Hernquist Katz 1989)."309 SPILL is. also relatively straightforward to implement. at least in its most xwic formulation.," SPH is also relatively straightforward to implement, at least in its most basic formulation."310 More. refined. versions have to be used to obtain realistic results when there are large eradients of density (c.g. shocks and ionization fronts) and/or velocity (e.g. shocks and rapidly shearing disces), More refined versions have to be used to obtain realistic results when there are large gradients of density (e.g. shocks and ionization fronts) and/or velocity (e.g. shocks and rapidly shearing discs).311 Since its initial realization. (Lucy LOTT: Cingold. Monaghan. 1977). SPIEL has been developed. and. refined. by several workers. for example Lattanzio et al. (," Since its initial realization (Lucy 1977; Gingold Monaghan 1977), SPH has been developed and refined by several workers, for example Lattanzio et al. ("3121985: artificial viscosity). Nelson Papaloizou (1993. 1994: variable Ah). Date. Bonnell Price (1995: sink particles). Watkins et al. (,"1985; artificial viscosity), Nelson Papaloizou (1993, 1994; variable $h$ ), Bate, Bonnell Price (1995; sink particles), Watkins et al. ("3131995: Navier-Stokes viscosity). Morris Monaghan (1997: ime-varving artificial viscositv). Nelson Langer (1997: scheme for treating the thermal physics). Owen et al. (,"1995; Navier-Stokes viscosity), Morris Monaghan (1997; time-varying artificial viscosity), Nelson Langer (1997; scheme for treating the thermal physics), Owen et al. ("3141998: ensorial smoothing kernels). Inutsuka lmaecca (2001: Godunov scheme for interparticle hydro. forces). Ixessel-Devnet Burkert (2000: scheme for following ionization routs),"1998; tensorial smoothing kernels), Inutsuka Imaeda (2001; Godunov scheme for interparticle hydro forces), Kessel-Deynet Burkert (2000; scheme for following ionization fronts)."315 The principle alternatives to SPL are finite dilference (I'D) codes. or hybrids which combine particles ancl cells.," The principle alternatives to SPH are finite difference (FD) codes, or hybrids which combine particles and cells."316 FD codes are much better at resolving large density and/or velocity. gradients., FD codes are much better at resolving large density and/or velocity gradients.317 They should. probably be the method of choice for simulating Hows with high. Mach. Number., They should probably be the method of choice for simulating flows with high Mach Number.318 llowever. in three dimensions they are not as easy to implement as SPILL. and they are not Lagrangian.," However, in three dimensions they are not as easy to implement as SPH, and they are not Lagrangian."319 Moreover. it should be born in mind that FD codes benefit from having had very many more person-vears of development than SPL.," Moreover, it should be born in mind that FD codes benefit from having had very many more person-years of development than SPH."320 In FD codes. the high local resolution required. for calculations of protostellar collapse can be obtained. by means of nested grids.," In FD codes, the high local resolution required for calculations of protostellar collapse can be obtained by means of nested grids."321 These nested. grids can either, These nested grids can either322all our models are consistent with measurements of the Thomson scattering optical depth. and the metagalactic hvdrogen. photo-ionisation rate at 6.,all our models are consistent with measurements of the Thomson scattering optical depth and the metagalactic hydrogen photo-ionisation rate at $z \sim 6$.323 This empirical approach enables us to explore the consequences of satisfving these observational constraints for reionisation., This empirical approach enables us to explore the consequences of satisfying these observational constraints for reionisation.324 The main outcomes of this study may be summarised as follows., The main outcomes of this study may be summarised as follows.325 Our results highlight the importance of reproducing post-reionisation constraints such as the LGAL temperature ancl background: photo-ionisation rate. for. constraining reionisation miocels., Our results highlight the importance of reproducing post-reionisation constraints such as the IGM temperature and background photo-ionisation rate for constraining reionisation models.326 While these simulations were designed nmeinlv to investigate the impact of helium on hydrogen reionisation and the sources of ionising photons at high redshift. the volume used. is too small to allow a more detailed discussion on helium reionisation (which is thought to be driven. by. quasars and. to be. complete ato. ~2.5. 3) and a more accurate comparison with observational constraints ato.<6.," While these simulations were designed mainly to investigate the impact of helium on hydrogen reionisation and the sources of ionising photons at high redshift, the volume used is too small to allow a more detailed discussion on helium reionisation (which is thought to be driven by quasars and to be complete at $z \sim 2.5-3$ ) and a more accurate comparison with observational constraints at $z<6$."327 We will postpone this further analysis to a future work. together with a more thorough investigation of the impact of unresolved. small scale high density peaks.," We will postpone this further analysis to a future work, together with a more thorough investigation of the impact of unresolved small scale high density peaks."328 The latter will be particularly important for regulating the tail-end. of the reionisation process and for setting the thermal state of the LGAL by absorbing photons close to the and ionisation edges., The latter will be particularly important for regulating the tail-end of the reionisation process and for setting the thermal state of the IGM by absorbing photons close to the and ionisation edges.329 Including these ellects in numerical mocels is therefore necessary for refining the comparison of simulations with observations at 2«6., Including these effects in numerical models is therefore necessary for refining the comparison of simulations with observations at $z<6$.330 The authors would. like to. thank an anonvmous referee. for his/her very constructive comments. and Ix. Finlator and A. Meiksin for useful suggestions.," The authors would like to thank an anonymous referee for his/her very constructive comments, and K. Finlator and A. Meiksin for useful suggestions."331 Vhe hydrodynamical simulation used in this work was performed. using the Darwin Supercomputer of the University of Cambridge High. Performance Computing Service (http://www.hpe.cam.ac.uk/). provided. by Dell Ine. using Strategic Research Infrastructure. Funding from the Higher Education Funding Council for England.," The hydrodynamical simulation used in this work was performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/), provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England."332 BC, BC333When compared with the scalar technique. matrix template matching quadruples the muuber of observational constraints while introducing oulv six degrees of freedom.,"When compared with the scalar technique, matrix template matching quadruples the number of observational constraints while introducing only six degrees of freedom."334 Therefore. arvival time estimates derived from the polarization profile wieght be expected to lave ereater precision than those ¢erived from the total intensity profile alone.," Therefore, arrival time estimates derived from the polarization profile might be expected to have greater precision than those derived from the total intensity profile alone."335 Towever. the effectiveness of matris cluplate matching depends upon both the degree of volarization aud the variability of t16 polarization vector as a function of pulse phase.," However, the effectiveness of matrix template matching depends upon both the degree of polarization and the variability of the polarization vector as a function of pulse phase."336 These xoperties determine he exteut to which the phase shift. 4. is correlated with he free parameters that determune the Joucs matrix.J.," These properties determine the extent to which the phase shift, $\varphi$, is correlated with the free parameters that determine the Jones matrix,."337 To estimate the timing precision attainable by matrix cluplate matching. consider the solution of iu the special case that is known.," To estimate the timing precision attainable by matrix template matching, consider the solution of in the special case that is known."338" After calibration. the winitnization of by variation of y requires finding the appropriate root of where S$),=Spο is the cross-spectral power of the template and observationΛΣ and ο 1s the aretnent of $,,,."," After calibration, the minimization of by variation of $\varphi$ requires finding the appropriate root of where $S_{k,m}=S_k^{\prime*}(\nu_m)\trace[\pauli{k}\;\mbf{\rho}_0(\nu_m)]$ is the cross-spectral power of the template and observation and $\phi_{k,m}$ is the argument of $S_{k,m}$."339" To first order. which is equivaleut to the solution of a line with slope 25 passing through the origin aud the points. (4.015,5)."," To first order, which is equivalent to the solution of a line with slope $2\pi\varphi$ passing through the origin and the points, $(\nu_m, \phi_{k,m})$."340 This Lucar approximation is readily solved for y aud used to determiue the conditional variance. Equation 13 demonstrates that fluctuation power contributes quadratically9 as a function. of frequency to the reduction of the phase shift variance.," This linear approximation is readily solved for $\varphi$ and used to determine the conditional variance, Equation \ref{eqn:conditional_variance} demonstrates that fluctuation power contributes quadratically as a function of frequency to the reduction of the phase shift variance."341 In other words. sharper features in the pulse profile. which generate more power at ligher harmonics. vield ereater arrival time precision.," In other words, sharper features in the pulse profile, which generate more power at higher harmonics, yield greater arrival time precision."342 This general results holds for both matrix aud scalar template matching (nu the scalar case. the stu over index & stops at 0).," This general results holds for both matrix and scalar template matching (in the scalar case, the sum over index $k$ stops at 0)."343 Equation 13. also provides an upper liit on the arrival time precision that may be obtained in the ideal case of a pertectly calibrated iustrument., Equation \ref{eqn:conditional_variance} also provides an upper limit on the arrival time precision that may be obtained in the ideal case of a perfectly calibrated instrument.344 However. the instrumental response is eeucrally uuknuown. aud the Jones matrix nist also be varied iu order to miuiuize(10).," However, the instrumental response is generally unknown, and the Jones matrix must also be varied in order to minimize."345. The covariances between the phase shift. νο. and the free parameters that describe will increase the uncertainty in y anc therefore decrease arrival time precision.," The covariances between the phase shift, $\varphi$, and the free parameters that describe will increase the uncertainty in $\varphi$ and therefore decrease arrival time precision."346 Formally. the variance of y is determined by the covariance niatrix of the free parameters. C=abt. where α is the curvature matrix.," Formally, the variance of $\varphi$ is determined by the covariance matrix of the free parameters, ${\bf C}={\mbf\alpha}^{-1}$, where $\mbf\alpha$ is the curvature matrix."347 Asstuing that the noise power in the DET of cach Stokes parameter is equal. If the free parameters. 5. are partitioned iuto 5=gg aud the seven Jones matrix pariiueters. gj. then may be conformably partitioned into (Stuart.Ord.&Arnold1999) and vary)=eo.," Assuming that the noise power in the DFT of each Stokes parameter is equal, If the free parameters, $\mbf{\eta}$, are partitioned into $\varphi=\eta_0$ and the seven Jones matrix parameters, $\mbf{\eta}_{\bf J}$, then may be conformably partitioned into \citep{soa99}348 and $\var(\varphi)=c_{\varphi\varphi}$."349 Furthermore. if the free paralcters are nmdtinoriunallv distributed. then the inultiple correlation between y ud 93. describes the relationship between the variance aud conditional variauce of 47. The iultiple correlation coeffiient. 0<Reyx1. xovides a useful iieasure of the decrease in arrival time xecisionu that results from an unknown iustruneutal response.," Furthermore, if the free parameters are multinormally distributed, then the multiple correlation between $\varphi$ and $\mbf{\eta}_{\bf J}$, describes the relationship between the variance and conditional variance of $\varphi$, The multiple correlation coefficient, $0\le\Rmult\le1$, provides a useful measure of the decrease in arrival time precision that results from an unknown instrumental response."350" It is iuportaut to note that οσα be computed using oulv the template polarization xofile: that is. though e depends on e, aud «. all factors of « are canceled in(16)."," It is important to note that can be computed using only the template polarization profile; that is, though $\mbf\alpha$ depends on $\mbf{\rho}^\prime_m$ and $\varsigma$, all factors of $\varsigma$ are canceled in."351.. Therefore. lis unique to cach pulsar aud is iudependent of the S/N of he observations.," Therefore, is unique to each pulsar and is independent of the S/N of the observations."352 Tlowever. the precision aud accuracy with which οσα be estimated docs depend on the S/N of the template.," However, the precision and accuracy with which can be estimated does depend on the S/N of the template."353" Iu fact. nicasureieut noise in the template polarization profile artificially decreases both the multiple correlation and the couditional variance of νο,"," In fact, measurement noise in the template polarization profile artificially decreases both the multiple correlation and the conditional variance of $\varphi$."354 To minimize the impact of noise on the computation ofvar(y|J). aud τος). the stummatious over the iudex a in and (L1)) are performed up to a maxima harmonic. Af. the highest frequency at which the fuctuation power spectra exhibit three consecutive larmouics with power eyxeater than three times the mean noise power.," To minimize the impact of noise on the computation of $\var(\varphi|{\bf J})$, and $\var(\varphi)$, the summations over the index $m$ in and \ref{eqn:curvature}) ) are performed up to a maximum harmonic, $M$, the highest frequency at which the fluctuation power spectra exhibit three consecutive harmonics with power greater than three times the mean noise power."355" To completely clininate the depeudencee on s. να) and var(y) are normalized by the correspouding variance iu the phase shift. νο, vielded by the conventional ucthod of scalar template matching the total intensity profile."," To completely eliminate the dependence on $\varsigma$, $\var(\varphi|{\bf J})$ and $\var(\varphi)$ are normalized by the corresponding variance in the phase shift, $\bar\varphi$, yielded by the conventional method of scalar template matching the total intensity profile."356 That is. is used to predict the relative conditional timing error in the case of a known iustrumental response. where G is the absolute eain. ancl Sinularly. vields the relative timing error in the general case of au πιοναι response.," That is, is used to predict the relative conditional timing error in the case of a known instrumental response, where $G$ is the absolute gain, and Similarly, yields the relative timing error in the general case of an unknown response."357 Caven a template polarization profile. (21)) can be used to predict arrival time uncertzintv in the case of either kuown or unknown poludnetie response.," Given a template polarization profile, – \ref{eqn:relerr}) ) can be used to predict arrival time uncertainty in the case of either known or unknown polarimetric response."358 These equatious provide the basis for comparing the precision of scalar aud matrix template matching methods for cach pulsar iu L., These equations provide the basis for comparing the precision of scalar and matrix template matching methods for each pulsar in \ref{sec:application}. .359ete.,"etc.,"360 this percentage will likely stay constant. requiring a similar number of fibres be allocated. to sky per unit spectrograph rather than per telescope Γἶνο observing strategy is assumed to move one out of the read-noise limit. tthe error budget is dominated by [rom the sky background.," this percentage will likely stay constant, requiring a similar number of fibres be allocated to sky per unit spectrograph rather than per telescope The observing strategy is assumed to move one out of the read-noise limit, the error budget is dominated by from the sky background."361 When limited by the arrival rate of photons from one's target source. one is not likely to require the sky subtraction accuracies provided by nocd-anc-shullle observations in order to remove one's background signal.," When limited by the arrival rate of photons from one's target source, one is not likely to require the sky subtraction accuracies provided by nod-and-shuffle observations in order to remove one's background signal."362 The combined ellect on the signal-to-noise ratio. given the baseline assumptions. of observing with the nod-and-shullle observing mode is a 2/2 reduction in the signal-to-noise ratio achieved for a given integration time.," The combined effect on the signal-to-noise ratio, given the baseline assumptions, of observing with the nod-and-shuffle observing mode is a $\sqrt{2}$ reduction in the signal-to-noise ratio achieved for a given integration time."363 This reduction comes from the following A [actor of 2 is lost in exposure time since half of the time must be spent on sky., This reduction comes from the following A factor of 2 is lost in exposure time since half of the time must be spent on sky.364 This is à V2 loss in A factor of 2 is lost in the number of targets that are observed. since one can only use half the libres as the remaining half must be masked. in. order to provide the storage area into which charge can be shullled., This is a $\sqrt{2}$ loss in A factor of 2 is lost in the number of targets that are observed since one can only use half the fibres as the remaining half must be masked in order to provide the storage area into which charge can be shuffled.365 'Pherefore to recover the same number of targets. one must observe two target sets for half of the exposure tine each. a VO) signal-to-noise There is a factor of two increase in the cllective sky background. with respect to the objects signal. due to the presence of sky emission in both the A ancl B positions.," Therefore to recover the same number of targets, one must observe two target sets for half of the exposure time each, a $\sqrt(2)$ signal-to-noise There is a factor of two increase in the effective sky background, with respect to the object's signal, due to the presence of sky emission in both the A and B positions."366 The noise component from the sky spectrum can not be suppressed as is the case with dedicated sky fibres., The noise component from the sky spectrum can not be suppressed as is the case with dedicated sky fibres.367 Essentially the sky is observed for the full exposure duration while the target is only observed for half of this time., Essentially the sky is observed for the full exposure duration while the target is only observed for half of this time.368 This doubling of the sky signal is a further V2 elfeet in the SN calculation., This doubling of the sky signal is a further $\sqrt{2}$ effect in the SN calculation.369 There are a number of strategies which can be used. to minimise the impact of on the loss. of signal-to-noise ratio., There are a number of strategies which can be used to minimise the impact of on the loss of signal-to-noise ratio.370" When all can be applied. the loss in signal-to-noise can be reduced from 24/2 to v2. In the limit of a reduced. number of valid targets per field. the loss from losing half of the fibres is ""he mintshullling strategv outlined. in section AS’ can be used to allow the full fibre multiplex to be In the limit of a reduced number of valid targets per field. two fibres can be allocated per target to remove the on-source duty evele οσοι."," When all can be applied the loss in signal-to-noise can be reduced from $\sqrt{2}$ to $\sqrt{2}$ In the limit of a reduced number of valid targets per field, the loss from losing half of the fibres is The mini-shuffling strategy outlined in section \ref{mini-shuffle} can be used to allow the full fibre multiplex to be In the limit of a reduced number of valid targets per field, two fibres can be allocated per target to remove the on-source duty cycle effect."371 Again. the mini-shullling strategy allows the maximum ‘The increased sky background cannot be mitigated. and so the V2/5 signal-to-noise reduction per unit time from this component remains.," Again, the mini-shuffling strategy allows the maximum The increased sky background cannot be mitigated, and so the $\sqrt{2}$ signal-to-noise reduction per unit time from this component remains."372 Hlowever. this is a random) error and not à svstematic elfect and so scales with the square root of an increased. exposure time.," However, this is a random error and not a systematic effect and so scales with the square root of an increased exposure time."373 ln circumstances where a gain is found from the N|S technique the observing strategy when emploved with a fibre multi-object spectrograph can deliver sky subtraction at the Poisson limit over a wide field of view and with a high multiplex., In circumstances where a gain is found from the N+S technique the observing strategy when employed with a fibre multi-object spectrograph can deliver sky subtraction at the Poisson limit over a wide field of view and with a high multiplex.374 Our recommended observing strategy. for using N[5 with the AAOmeea facility at the AAT is as the target field using either standard noc-anc-shullle with fibre masking (200 fibres) or using mini-shullling (400 fibres to targets in pairs using cross-beame-switching (CDS) to alleviate the on source duty in blocks of 20 pairs of X/D telescope nods. with GOsseconcds dwell. per position. for. individual exposures of mminutes per three/four such. integrations per 301 fibres configuration. in order to avoid Losses [from atmospheric perturbations on target positions (cue to differential atmospheric refraction across the should. be performed. using aarcsecond. olfsets to minimise telescope slew time while allowing sullicient separation between X. anc D positions on the 241 field plate to allow CBS fibre pairs to be in the pattern of variation in the OLLI sky lines can be mitigated by observing in the classic ABBA pattern.," Our recommended observing strategy for using N+S with the AAOmega facility at the AAT is as the target field using either standard nod-and-shuffle with fibre masking (200 fibres) or using mini-shuffling (400 fibres to targets in pairs using cross-beam-switching (CBS) to alleviate the on source duty in blocks of 20 pairs of A/B telescope nods, with seconds dwell per position, for individual exposures of minutes per three/four such integrations per 2dF fibres configuration in order to avoid losses from atmospheric perturbations on target positions (due to differential atmospheric refraction across the should be performed using arcsecond offsets to minimise telescope slew time while allowing sufficient separation between A and B positions on the 2dF field plate to allow CBS fibre pairs to be in the pattern of variation in the OH sky lines can be mitigated by observing in the classic ABBA pattern."375 This has the added advantage of removing the requirement for a significant number of intermediate telescope should be performed in. the Declination (north-south) axis to minimise telescope settling time for an equatorial telescope such as the AAT., This has the added advantage of removing the requirement for a significant number of intermediate telescope should be performed in the Declination (north-south) axis to minimise telescope settling time for an equatorial telescope such as the AAT.376of galaxies have top-heavy initial mass functions (IMEs:?).. which cuhance the efficiency in clearing lines of sight. due to the larger outflow velocities eonerated by massive stars.,"of galaxies have top-heavy initial mass functions \citep[IMFs;][]{2008ApJ...675.1319H}, which enhance the efficiency in clearing lines of sight, due to the larger outflow velocities generated by massive stars."377 Another property which has been shown to possibly evolve with redshift is the stellar miass-to-dark matter ratio., Another property which has been shown to possibly evolve with redshift is the stellar mass-to-dark matter ratio.378 Receut work by ?.. have reported that local massive ealaxies have iore centrally concentrated dark matter han higher redshift galaxies (270.7) with comparable stellar masses.," Recent work by \citet{2010MNRAS.401.2113E}, have reported that local massive galaxies have more centrally concentrated dark matter than higher redshift galaxies $z\sim0.7$ ) with comparable stellar masses."379 A higher stellar iuass-to-dark imatter nass ratio at lower redshift would result in a larger eravitational potential. aud iu turn the requircient for arecr galactic winds to achieve the same “porosity” of he ISAL (reduciug the probability for iouizing plotous ο escape their host galaxies).," A higher stellar mass-to-dark matter mass ratio at lower redshift would result in a larger gravitational potential, and in turn the requirement for larger galactic winds to achieve the same “porosity” of the ISM (reducing the probability for ionizing photons to escape their host galaxies)."380 Thicker disks due to dense concentrations of eas have also been shown in to impede or slow the development of galactic outflows. duc to a üeher eravitational potential (?)..," Thicker disks due to dense concentrations of gas have also been shown in to impede or slow the development of galactic outflows, due to a higher gravitational potential \citep{2008ApJ...674..157C}."381 Au evolving intrinsic LyC-to-UV flux density ratio could also be respousible for the observed. evolution iu Foeass," An evolving intrinsic LyC-to-UV flux density ratio could also be responsible for the observed evolution in $f_{\mathrm{esc,rel}}$."382 The escape fraction is nieasured by comparing the UV (1500À)) flux of a galaxy to flux below the Lyman limit., The escape fraction is measured by comparing the UV ) flux of a galaxy to flux below the Lyman limit.383 One kev assumption that is made involves the inherent LvC-to-U ratio of starbursts., One key assumption that is made involves the inherent LyC-to-UV ratio of starbursts.384 Typically. this ratio is considered Vconstant with redshift. but if there were an order of magnitude larger production rate of the LwC relative to theL500A.. fux at :>3 than at z« 1. the observed chauge in fosrey would be expected.," Typically, this ratio is considered constant with redshift, but if there were an order of magnitude larger production rate of the LyC relative to the, flux at $z>3$ than at $z<1$ , the observed change in $f_{\mathrm{esc,rel}}$ would be expected."385 7? found that three of the six Εδω» with detected escaping LyC in their sample. had SEDs intrinsically bluer than those expected from population svutlesis models. assuming a standard IME with moderate dust attenuation.," \citet{2009ApJ...692.1287I} found that three of the six LBGs with detected escaping LyC in their sample, had SEDs intrinsically bluer than those expected from population synthesis models, assuming a standard IMF with moderate dust attenuation."386 They show that an intrinsically bluer SED (~0.3 mae bluer in NB359-R than those of Starburst99). in the absence of QSO activity. can be produced with a top-leavy IME.," They show that an intrinsically bluer SED $\sim0.3$ mag bluer in NB359-R than those of Starburst99), in the absence of QSO activity, can be produced with a top-heavy IMF."387 They also sugeest that a deviation from the 7? dust attenuation law. with less dust absorption at900A... compared to that at1500À.. can come close to achieving the observed bluer colors of those LBCs.," They also suggest that a deviation from the \citet{2000ApJ...533..682C} dust attenuation law, with less dust absorption at, compared to that at, can come close to achieving the observed bluer colors of those LBGs."388 It has been shown that the UV. luminosity density at Do6 nav be insufficient to explain the ionized universe at;>7 unless the IME allowed for the production of more massive stars (?).., It has been shown that the UV luminosity density at $z\sim6$ may be insufficient to explain the ionized universe at $z>7$ unless the IMF allowed for the production of more massive stars \citep{2008ApJ...680...32C}.389 A top-heavy IMF at higher redshift could help explain the larger umuber of LyC detections at 2~3 as lassive stars produce more LyC photons. aud stronger supernova driven winds.," A top-heavy IMF at higher redshift could help explain the larger number of LyC detections at $z\sim3$ as massive stars produce more LyC photons, and stronger supernova driven winds."390 A top-heavy IME requires regions of potentially low mctallicity eas which is consistent with the metallicity aud dust evolution seen from 2~3 to 1(?).., A top-heavy IMF requires regions of potentially low metallicity gas which is consistent with the metallicity and dust evolution seen from $z\sim3$ to 1 \citep{2002ApJ...569L..65F}.391 LvC photous produced m massive starbursts likely plaved an müportaut role iu the reionization of the nuiverse., LyC photons produced in massive starbursts likely played an important role in the reionization of the universe.392 However. their contribution depeuds upou the fraction of ionizing radiation that can escape the high cohuun density of IIT eas suvrouudiue these star-forming ealaxies.," However, their contribution depends upon the fraction of ionizing radiation that can escape the high column density of HI gas surrounding these star-forming galaxies."393 We have presceuted irest-frame UV slitless spectroscopy of 32 5; ~0.7 LBC analogs in the COSMOS field to investigate the LyC escape fraction., We have presented rest-frame UV slitless spectroscopy of 32 $z\sim$ 0.7 LBG analogs in the COSMOS field to investigate the LyC escape fraction.394 These UW spectra have achieved the deepest liuits to date on the escape fraction im individual sources at amy redshift., These UV spectra have achieved the deepest limits to date on the escape fraction in individual sources at any redshift.395 A sununuuwv of our results is as follows., A summary of our results is as follows.396 Aside from the detection of leaking Lv€ from an ACNstarburst composite. we fud no detections of LyC in our saluple of 31 star-forming galaxies.," Aside from the detection of leaking LyC from an AGN--starburst composite, we find no detections of LyC in our sample of 31 star-forming galaxies."397" The individual 36 lower limits of f£,(1500A. fp J) ratio range from 20 to 201 μουαι of 73.5) and 378.7 iu the stack of 18 galaxies.", The individual $3\sigma$ lower limits of $f_{\nu}$ $f_{\nu}$ ) ratio range from 20 to 204 (median of 73.5) and 378.7 in the stack of 18 galaxies.398 Assuming an intrinsic Lyman break of 3.1 and an IGAL transmission of SN!55. we report a escape fraction in individual galaxies of 0.02-0.19 and 0.01 in the stack (30 upper huit)," Assuming an intrinsic Lyman break of 3.4 and an IGM transmission of $85\%$, we report a escape fraction in individual galaxies of 0.02-0.19 and 0.01 in the stack $3\sigma$ upper limit)."399 There is uo indication of the near uuitv escape fractious fouud at 2~3., There is no indication of the near unity escape fractions found at $z\sim3$.400 The striking contrast between the nearly zero escape fractious found in the 22 5~0.7 LBC analogs with the near unity escape fractious discovered in of the :~3 LBG population strongly arenes for an evolving escape fraction., The striking contrast between the nearly zero escape fractions found in the 22 $z\sim0.7$ LBG analogs with the near unity escape fractions discovered in of the $z\sim3$ LBG population strongly argues for an evolving escape fraction.401" It is unclear. however. if the lack of near unity escape fraction detections at low redshift is due to an evolution in actual value of the fiiiνα itself or if it is just that the umuber of galaxies that in fact have larec amounts of leaking Τσο, decrease with redshift."," It is unclear, however, if the lack of near unity escape fraction detections at low redshift is due to an evolution in actual value of the $f_{\mathrm{esc,rel}}$ itself, or if it is just that the number of galaxies that in fact have large amounts of leaking LyC, decrease with redshift."402 Both scenarios could explain absence of galaxies with larger amounts of leaking LyC. Possible causes for a change in the perceived escape fraction with redshift involve a top-heavy IME. larecr SFR densities. stellay mnass-to-dark matter ratios. and/or fraction of SSCs at hüehler redshifts.," Both scenarios could explain absence of galaxies with larger amounts of leaking LyC. Possible causes for a change in the perceived escape fraction with redshift involve a top-heavy IMF, larger SFR densities, stellar mass-to-dark matter ratios, and/or fraction of SSCs at higher redshifts."403 All these mmechanisius enhance the efficiency of ealaxy winds. increasing the porosity of the ISAL facilitating LvC escape.," All these mechanisms enhance the efficiency of galaxy winds, increasing the porosity of the ISM, facilitating LyC escape."404 However. if galaxy mergers aid in the escape of LvC radiation then an evolving galaxy merger rate could account for the high number of LyC leaking ealaxies at 2~3.," However, if galaxy mergers aid in the escape of LyC radiation then an evolving galaxy merger rate could account for the high number of LyC leaking galaxies at $z\sim3$."405 The lack of low-redshift salaxies with escaping LyC could then be explained by the simall munber of galaxy mergers that have been observed below the Lyman lait., The lack of low-redshift galaxies with escaping LyC could then be explained by the small number of galaxy mergers that have been observed below the Lyman limit.406 An additional cousideration is that a fraction of the detections of escaping LyC at 2~3 may be a consequence of foreground contamination. which would reduce the streneth of the evolution iu. [ρω ποσα when conrpariug to low-z studies.," An additional consideration is that a fraction of the detections of escaping LyC at $z\sim$ 3 may be a consequence of foreground contamination, which would reduce the strength of the evolution in $f_{esc,rel}$ seen when comparing to $z$ studies."407 The escape fraction of UV radiation iu 21 Iumninous starburst galaxies ix au inportant quantity to uudoerstaud sjuce it provides insight iuto the sources (1uassiwe star formation or QSOs} responsible for reionization., The escape fraction of UV radiation in $z\sim1$ luminous starburst galaxies is an important quantity to understand since it provides insight into the sources (massive star formation or QSOs) responsible for reionization.408 Our study has preseuted a robust measure of the ον n the low-redshift uuiverse and suggests that the escape fraction in objects that are analogous to : ~3 LBC population. evolves with redshift.," Our study has presented a robust measure of the $f_{\mathrm{esc,rel}}$ in the low-redshift universe and suggests that the escape fraction in objects that are analogous to $z\sim$ 3 LBG population, evolves with redshift."409 ITowever. future study is required to isolate the cause of this evolution.," However, future study is required to isolate the cause of this evolution."410 We thank Mark Dickinson aud Colin Borvs for their contributions to this work aud the anouvimous referee for their constructive comüiuenuts which added to the clarity of this paper., We thank Mark Dickinson and Colin Borys for their contributions to this work and the anonymous referee for their constructive comments which added to the clarity of this paper.411 The research described in this paper was carried out. im part. by the Jet Propulsion Laboratory. California Tustitute of Technology. aud obscrvatious obtained at the Hale Telescope. Palomar Observatory as part of a continuug collaboration between the California Tustitute of Technology. NASA /JPL. aud Cornell University.," The research described in this paper was carried out, in part, by the Jet Propulsion Laboratory, California Institute of Technology, and observations obtained at the Hale Telescope, Palomar Observatory as part of a continuing collaboration between the California Institute of Technology, NASA /JPL, and Cornell University."412 Support for programs IIST-CO 11236 was provided by NASA through erauts from the Space Telescope Science.Tustitute. which is operated by the Association of Universities for Researcli in Astrouoniv," Support for programs HST-GO 11236 was provided by NASA through grants from the Space Telescope ScienceInstitute, which is operated by the Association of Universities for Research in Astronomy,"413 Support for programs IIST-CO 11236 was provided by NASA through erauts from the Space Telescope Science.Tustitute. which is operated by the Association of Universities for Researcli in Astrouoniv.," Support for programs HST-GO 11236 was provided by NASA through grants from the Space Telescope ScienceInstitute, which is operated by the Association of Universities for Research in Astronomy,"414emperatures within z3 AU of the stellar core at the launching of he outflows exceed 1500 K. While most of this material is no doubt be accreted by the star. a fraction produces the outflows which reach beyond 50 AU.,"temperatures within $\approx 3$ AU of the stellar core at the launching of the outflows exceed 1500 K. While most of this material is no doubt be accreted by the star, a fraction produces the outflows which reach beyond $50$ AU."415 If chondrules were formed in this outburst event. some might be entrained in the outflow and eventually fall back into he circumstellar dise at large distances from the star.," If chondrules were formed in this outburst event, some might be entrained in the outflow and eventually fall back into the circumstellar disc at large distances from the star."416 Again. if such events were cyclic this would help because chondrule formation is hought to have occurred over several million years (2)..," Again, if such events were cyclic this would help because chondrule formation is thought to have occurred over several million years \citep{Scott2007}."417 We have presented results from the first three-dimensional radiation ivdrodynamical calculations to follow the collapse of a molecular cloud core beyond the formation of the stellar core., We have presented results from the first three-dimensional radiation hydrodynamical calculations to follow the collapse of a molecular cloud core beyond the formation of the stellar core.418 We find the evolution before the formation of the stellar core is very similar o that found in the past using barotropic equations of state., We find the evolution before the formation of the stellar core is very similar to that found in the past using barotropic equations of state.419 In particular. the evolution of the first hydrostatic core which. depending on its rotation rate. may be dynamically unstable to he growth of non-axisymmetrie perturbations and the generation of spiral structure. is very similar to that found in barotropic calculations.," In particular, the evolution of the first hydrostatic core which, depending on its rotation rate, may be dynamically unstable to the growth of non-axisymmetric perturbations and the generation of spiral structure, is very similar to that found in barotropic calculations."420 As found in earlier calculations. a rapidly rotating first core actually evolves into a dise so that the dise actually forms the stellar core.," As found in earlier calculations, a rapidly rotating first core actually evolves into a disc so that the disc actually forms the stellar core."421 However. we find that the evolution following the formation of the stellar core is different in. radiation ivdrodynamical calculations.," However, we find that the evolution following the formation of the stellar core is different in radiation hydrodynamical calculations."422 In. barotropic calculations. the ormation of the stellar core deep inside the first core (or disc) ias no effect on the surrounding dise because the temperature of he gas is simply set by the density of the gas.," In barotropic calculations, the formation of the stellar core deep inside the first core (or disc) has no effect on the surrounding disc because the temperature of the gas is simply set by the density of the gas."423 However. with radiation hydrodynamics. the energy released by the formation of he stellar core within the optically thick dise is similar to the binding energy of the disc.," However, with radiation hydrodynamics, the energy released by the formation of the stellar core within the optically thick disc is similar to the binding energy of the disc."424 This heats the inner regions of the disc. drives a shock wave outwards through the disc. dramatically decreases the accretion rate on to the stellar core. and launches a bipolar outflow perpendicular to the rotation axis that can travel in excess of 50 AU out into the infalling envelope in less than 50 yeurs.," This heats the inner regions of the disc, drives a shock wave outwards through the disc, dramatically decreases the accretion rate on to the stellar core, and launches a bipolar outflow perpendicular to the rotation axis that can travel in excess of 50 AU out into the infalling envelope in less than 50 years."425 We speculate that such outflows may assist the young protostar in launching a conventional magnetic jet by clearing a path perpendicular to the dise and adding substantial thermal pressur[27 to the force provided by the magnetic field., We speculate that such outflows may assist the young protostar in launching a conventional magnetic jet by clearing a path perpendicular to the disc and adding substantial thermal pressure to the force provided by the magnetic field.426 It may also be that such events are cyclic. occurring every time the accretion rate onto the protostar exceeds a certain level rather than simply being a one-off event associated with the formation of the stellar core.," It may also be that such events are cyclic, occurring every time the accretion rate onto the protostar exceeds a certain level rather than simply being a one-off event associated with the formation of the stellar core."427 If so. suc= events may provide the mechanism for intense bursts of accretion separated by long periods of relatively quiescent accretion which may be necessary to solve the protostellar luminosity problem and the apparent age spread of young stars.," If so, such events may provide the mechanism for intense bursts of accretion separated by long periods of relatively quiescent accretion which may be necessary to solve the protostellar luminosity problem and the apparent age spread of young stars."428 Finally. such outbursts may provide another mechanism for the formation of chondrules in meteorites and the associated outflows may be able to transport them to large distances in the circumstellar disc.," Finally, such outbursts may provide another mechanism for the formation of chondrules in meteorites and the associated outflows may be able to transport them to large distances in the circumstellar disc."429 2. ὁ (2).., \ref{images} \ref{vectors} \citep{Price2007}.430The Hyades cluster has a distance of 46 pe and covers z 20° of the sky.,The Hyades cluster has a distance of 46 pc and covers $\approx$ $^{\circ}$ of the sky.431 The Hyades has. until recently. been thought to contain almost no low mass members.," The Hyades has, until recently, been thought to contain almost no low mass members."432 Extensive searches such as those (' Gizis.Reid&Monet(1999). and Dobbieetal.(2002). turned up no brown dwarf members., Extensive searches such as those of \citet{gizis99} and \citet{dobbie02} turned up no brown dwarf members.433 It was hypothesised that being an older open star cluster (625 Myr: Perrymanetal. 1998)) any low mass members would have evaporated from the cluster through dynamical evolutionary processes., It was hypothesised that being an older open star cluster (625 Myr; \citealt{perryman98}) ) any low mass members would have evaporated from the cluster through dynamical evolutionary processes.434 For a cluster of this age ~ of stars and ~ of brown dwarfs are expected to have escaped the cluster (Adamsetal.2002)., For a cluster of this age $\sim$ of stars and $\sim$ of brown dwarfs are expected to have escaped the cluster \citep{adams02}.435. Recently however. studies using deep. wide field surveys such as the UKIRT Deep Infrared Sky Survey (Hoganetal.2008) have unearthed 12 L dwarf candidate members.," Recently however, studies using deep, wide field surveys such as the UKIRT Deep Infrared Sky Survey \citep{hogan08} have unearthed 12 L dwarf candidate members."436 Bouvieretal.(2008) have also claimed two T dwarf members from a 16 square degree survey of the cluster's centre., \citet{bouvier08} have also claimed two T dwarf members from a 16 square degree survey of the cluster's centre.437 Chereul.Creze&Bienayme(1998). first identified escaped Hyads. and more recently Bannister&Jameson(2007) have identified 7 L and T field dwarfs that belong to the Hyades moving group.," \citet{chereul98} first identified escaped Hyads, and more recently \citet{bannister07} have identified 7 L and T field dwarfs that belong to the Hyades moving group."438 ZapateroOsorioetal.(2007) have confirmed that one of these objects (2MASS 71217110-031113) has a radial velocity consistent with being an escaped member of the Hyades cluster. while two (2MASS J0205293-115930 and 2MASS J16241436+40029158) have radial velocities that are only consistent with being moving group members.," \citet{zapatero07} have confirmed that one of these objects (2MASS J1217110-031113) has a radial velocity consistent with being an escaped member of the Hyades cluster, while two (2MASS J0205293-115930 and 2MASS J16241436+0029158) have radial velocities that are only consistent with being moving group members."439 In paper I (Jamesonetal.20082)... we reported the discovery of 15 new moving group candidate members.," In paper I \citep{jameson08}, we reported the discovery of 15 new moving group candidate members."440" The Hyades moving group has its convergent point situated at à—6 29.48"", 8—-67534. and the members have a space velocity of 46 km + (Madsen. Dravins Lindgren. 2002)."," The Hyades moving group has its convergent point situated at $\alpha$ $^{h}$ $^{m}$, $\delta$ $^{\circ}$ 53.4', and the members have a space velocity of 46 km $^{-1}$ (Madsen, Dravins Lindgren, 2002)."441 After using the moving group method. theCruzetal.(2003) distance and the convergent point from Madsenetal.(2002)... we have found 7 new candidate members of the Hyades moving group (Table 62).," After using the moving group method, the\citet{cruz03} distance and the convergent point from \citet{madsen02}, we have found 7 new candidate members of the Hyades moving group (Table \ref{hyadestab}) )."442 These objects are plotted on figure | as well as the Jamesonetal.(20082):Hogan(2008) and Bannisterson(2007) dwarts.," These objects are plotted on figure \ref{mg_hyades} as well as the \citet{jameson08, hogan08} and \citet{bannister07} dwarfs."443 The Ursa Major moving group has been estimated to have an age of between 300 Myr (Soderblom&Mayor1993) and 5003-100 Myr (Kingetal. 2003).., The Ursa Major moving group has been estimated to have an age of between 300 Myr \citep{soderblom93} and $\pm$ 100 Myr \citep{king03}. .444 Castellanietal.(2002). found an age of the group to be 400 Myr., \citet{castellani02} found an age of the group to be 400 Myr.445 The age of 400100 Myr is adopted in, The age of $\pm$ 100 Myr is adopted in446nassive object AIWC 297 preseuted here emphasize the reed for high spatial resolution N-rav aud infrared imagine o verity the origin of X-ray emission attributed to ITerbis Ac/Be stars.,massive object MWC 297 presented here emphasize the need for high spatial resolution X-ray and infrared imaging to verify the origin of X-ray emission attributed to Herbig Ae/Be stars.447 This will assist iu a proper evaluation of he plvsical differences governing low aud higeliauass star onmuation., This will assist in a proper evaluation of the physical differences governing low and high-mass star formation.448PAHs with 30 or less C atoms.,PAHs with 30 or less C atoms.449" There are 255 PAH species available to fit C <30, whereas there are 237 PAH species available to fit C >30, once the other constraints are taken into account."," There are 255 PAH species available to fit C $\le 30$, whereas there are 237 PAH species available to fit C $\ge 30$, once the other constraints are taken into account."450" Even though there are less PAH species included in the fit of large PAHs, it is a superior fit to the small PAHs and has a lower reduced norm value."," Even though there are less PAH species included in the fit of large PAHs, it is a superior fit to the small PAHs and has a lower reduced norm value."451" From this limited wavelength range, we can already deduce that large PAHs are responsible for the main bands, however to have a stronger constraint on size, an analysis using the full 3 - 15 uum range in necessary."," From this limited wavelength range, we can already deduce that large PAHs are responsible for the main bands, however to have a stronger constraint on size, an analysis using the full 3 - 15 $\mu$ m range in necessary."452"The ecolumn clensitv distribution of intergalactic gas clouds. f(Nq;,). is determined. αἱ high redshifts through the analvsis of QSO absorption spectra.","The column density distribution of intergalactic gas clouds, $f(N_{HI})$, is determined at high redshifts through the analysis of QSO absorption spectra."453 The detection of Lyinan continuum absorption and of Lya absorption lines between us ancl (he QSOs has been used (o derive [CNqu) fom Nyyc107 ? (o Nyyc10755 7 (eg.Petitjeanοἱal.1993:Rauch1993:Storrie-Lombardi&Wolle 2000).," The detection of Lyman continuum absorption and of $\alpha$ absorption lines between us and the QSOs has been used to derive $f(N_{HI})$ from $N_{HI}\simeq 10^{12.5}$ $^{-2}$ to $N_{HI}\simeq 10^{21.5}$ $^{-2}$ \citep[e.g.][]{pet93,rau98,sto00}."454". Attempts have been made to fit. /Nj,) over many decades o£N4,; wilh a simple power law.", Attempts have been made to fit $f(N_{HI})$ over many decades of $N_{HI}$ with a simple power law.455 Llowever. it is more physically meaningful to expect a power law behavior for οςΑμ) the total (neutralHionized) column density. distribution.," However, it is more physically meaningful to expect a power law behavior for $g(N_{H})$, the total (neutral+ionized) column density distribution."456" In fact. due to drastic changes in the hvdrogen ionization fraction when the gas becomes optically thin to photons above 13.6 eV. breaks in /(V4) appear for Nyy,~LO 10? em7. where a small decrease of Nyy corresponds to a rapid change in μι."," In fact, due to drastic changes in the hydrogen ionization fraction when the gas becomes optically thin to photons above 13.6 eV, breaks in $f(N_{HI})$ appear for $N_{HI}\sim 10^{18}$ $10^{20}$ $^{-2}$, where a small decrease of $N_{H}$ corresponds to a rapid change in $N_{HI}$ ."457" A more appropriate approach is to compare the observed {CNi.) to the Nyy, distribution function derived from an assumed ος). alter ionization changes corrections have been applied."," A more appropriate approach is to compare the observed $f(N_{HI})$ to the $N_{HI}$ distribution function derived from an assumed $g(N_{H})$, after ionization changes corrections have been applied."458" This method has been used by Corbellietal.(2001) to derive the slope of οη). assumed to be x;N,,"". and (he ionization conditions of the gas at redshifts z2 3."," This method has been used by \citet{cor01} to derive the slope of $g(N_{H})$, assumed to be $\propto N_H^{-\alpha}$, and the ionization conditions of the gas at redshifts $z\sim 2$ $3$."459 Since the frequency of intervening absorption svstemis is high at these redshifts. it has been possible to limit the analysis to hieh column density. absorbers. using data relative to (mostly neutral) Damped Lya absorption svstems. and to (mostlv ionized) Lyman limit svstems.," Since the frequency of intervening absorption systems is high at these redshifts, it has been possible to limit the analysis to high column density absorbers, using data relative to (mostly neutral) Damped $\alpha$ absorption systems, and to (mostly ionized) Lyman limit systems."460" A comparison of models for dark matter confined svstems with the observed. ΓΑμι) led to values of a>2 for 2~ 3: an eX(vapolation of this power law distribution (towards svstems of lower column density. the Ίνα forest. gives reasonable fits for Ny,>LOY 7."," A comparison of models for dark matter confined systems with the observed $f(N_{HI})$ led to values of $\alpha > 2$ for $z\sim 2$ $3$; an extrapolation of this power law distribution towards systems of lower column density, the $\alpha$ forest, gives reasonable fits for $N_{HI}>10^{15}$ $^{-2}$."461 At lower redshilts the number density of absorption svstems is much lower and the poor statistics based on Lyman limit and Damped Lya alone does not allow a determination of the distribution funetion οΑι)., At lower redshifts the number density of absorption systems is much lower and the poor statistics based on Lyman limit and Damped $\alpha$ alone does not allow a determination of the distribution function $g(N_{H})$.462 At zero redshift however these studies can be complemented with detailed observations of 21-cm emission lime radiation [rom nearby galaxies., At zero redshift however these studies can be complemented with detailed observations of 21-cm emission line radiation from nearby galaxies.463 21-11 emission data have the advantage of leaving small uncertainties on μι while saturated Lvman limit breaks in QSOs spectra give only lower limits on (he intervening Vj); (e.g.2001.[oracorrectstatisticaltreatmentofsuch measurements)..," 21-cm emission data have the advantage of leaving small uncertainties on $N_{HI}$, while saturated Lyman limit breaks in QSOs spectra give only lower limits on the intervening $N_{HI}$ \citep[e.g.][for a correct statistical464treatment of such measurements]{ban01}."465 If observations are sensitive enough to column densities where the hydrogen gas is mostly ionized in the presence of a UV radiation ied. (hen we could use these data to infer οςδι) ancl the intensity of the jionizing background radiation in the local Universe. which is not directly observable.," If 21-cm observations are sensitive enough to column densities where the hydrogen gas is mostly ionized in the presence of a UV radiation field, then we could use these data to infer $g(N_{H})$ and the intensity of the ionizing background radiation in the local Universe, which is not directly observable."466 Similarly. (he observed sharp drop of the ecolumu density in (he outerdisk of two nearby spiral galaxies. \133 and NGC3193. interpreted as an (transition zone. made possible an estimate of the UV ionizing Πας al z=0 ," Similarly, the observed sharp drop of the column density in the outerdisk of two nearby spiral galaxies, M33 and NGC3198, interpreted as an transition zone, made possible an estimate of the UV ionizing flux at $z=0$ "467Some of these features have been identified as lines of high ionization species such as OIV-VI and NiIV-VIL but many of them lack proper identification.,"Some of these features have been identified as lines of high ionization species such as OIV-VI and NiIV-VII, but many of them lack proper identification."468 We recall that Peustou et al (1983) listed 20 lines in all in the rauge 3017.3315A. iucludiug five lines of ΟΠ produced in the Bowen mechanisu.," We recall that Penston et al (1983) listed 20 lines in all in the range 3047–3345, including five lines of OIII produced in the Bowen mechanism."469 Iu the UVES spectrum we have detected in the same range about 90 cunission lines inelucing a dozen of ONL Bowen lines., In the UVES spectrum we have detected in the same range about 90 emission lines including a dozen of OIII Bowen lines.470 All lines aud. ideutificatious of Peuston ct al (1983) are confirmed with two exceptions he 3063.30 NIT (2E) feature is missing auc Till 3078.66 ds insteac Fell (181) 3078.69 (κου also Fig., All lines and identifications of Penston et al (1983) are confirmed with two exceptions: the 3063.30 NII (2F) feature is missing and TiII 3078.66 is instead FeII (181) 3078.69 (see also Fig.471 1): no Till line has been positively detected iu our spectra., 1); no TiII line has been positively detected in our spectra.472 Amone other new features in the IUE range we mention also the lines at 3131.21. (€ NiVT 3131.1). 3138.66 Ας NIVII 3138.3). on the wines of the strong OIIICEI2) 3132.86 line. and 3221.12 ( NiVIT 3221.5 ).," Among other new features in the IUE range we mention also the lines at 3131.21 ( NiVI 3131.4), 3138.66 ( NiVII 3138.3), on the wings of the strong OIII(12) 3132.86 line, and 3221.12 ( NiVII 3221.5 )."473 In the coutest of the application of new laboratory analysis of the spectrum of lughly ionized nickel to the ideutification of uuclassiied lines iu the spectra ofj Car aud RR Tel. the NiVII 3221.5 line was mentioned bv Baassen aud Hausen (ApJ 213.217. 1981) as a forbidden line falling in a region difficult to observe.," In the context of the application of new laboratory analysis of the spectrum of highly ionized nickel to the identification of unclassified lines in the spectra of$\eta$ Car and RR Tel, the NiVII 3221.5 line was mentioned by Raassen and Hansen (ApJ 243,217, 1981) as a forbidden line falling in a region difficult to observe."474 An obvious comparison here is with the recent study by Crawford et aL(1999) on AATUCLES data of slightly lower resolution than the VLT-UVES data., An obvious comparison here is with the recent study by Crawford et al.(1999) on AAT–UCLES data of slightly lower resolution than the VLT-UVES data.475 We are aware that the identification of emission lues is a somewhat arbitrary procedure but. on the basis of the FWIIM criterion aud of comuuon astroplivsical scuse. we disagree with Crawford et al.," We are aware that the identification of emission lines is a somewhat arbitrary procedure but, on the basis of the FWHM criterion and of common astrophysical sense, we disagree with Crawford et al."476 on the ideutificatious of low ionization species such as Til. VIL. Mul. Mull ete.," on the identifications of low ionization species such as TiI, VII, MnI, MnII etc."477 We have found alternative identifications generally associated with ligher lonization species., We have found alternative identifications generally associated with higher ionization species.478 We postpone a detailed discussion on lue identifications to the follow-up paper and we just eive rere. in Table 1. a short list of strong lines either uot reported or incorrectly ideuti&ed by Crawford et al.," We postpone a detailed discussion on line identifications to the follow-up paper and we just give here, in Table 1, a short list of strong lines either not reported or incorrectly identified by Crawford et al.,"479 together with our proposed ideutifications., together with our proposed identifications.480 Thanks to the very high spectral resolution of the UVES spectrograph we have been able to detect cussion lines of the Balmer SCLICS down to II38 at 3656.13 (sce Fig 3)., Thanks to the very high spectral resolution of the UVES spectrograph we have been able to detect emission lines of the Balmer series down to H38 at 3656.13 (see Fig 3).481 Also. starting from approximately Is. where the separation between successive lines becomes large enough. it is clearly seen that ALL Balmer enüssious are accompanied by a shortward displaced. uch weaker enuüssiou that we associate with ΠΟΠ lines of the Pickering (lu) series.," Also, starting from approximately H18, where the separation between successive lines becomes large enough, it is clearly seen that ALL Balmer emissions are accompanied by a shortward displaced, much weaker emission that we associate with HeII lines of the Pickering (4-n) series."482 This is confirmed by the presence of the other ΠΟ lines of the same series that fall iu between the Balmer lines., This is confirmed by the presence of the other HeII lines of the same series that fall in between the Balmer lines.483 Crawford ct al discarded a possible contribution of {STI 3721.70 to the WILL Balmer line at 3721.91A.. as in Ac I&euna et al (1997). on the basis ofthe EWIIM of the feature. which agreed well with that of other Π lines.," Crawford et al discarded a possible contribution of [SIII] 3721.70 to the H14 Balmer line at 3721.94, as in Mc Kenna et al (1997), on the basis of the FWHM of the feature, which agreed well with that of other H lines."484 Asy. a matter of fact. the feature we observe at 3721.89 (see also Fig.," As a matter of fact, the feature we observe at 3721.89 (see also Fig."485 3) has the same FWIAL (55 lau 1) as the other II lines. but clearly shows au intensity excess with respect to the adjacent IT lues that requires an additional contribution at a waveleugth uccessarily very close to that of the ITLL liue.," 3) has the same FWHM (55 km $^{-1}$ ) as the other H lines, but clearly shows an intensity excess with respect to the adjacent H lines that requires an additional contribution at a wavelength necessarily very close to that of the H14 line."486 The preseuce of the two ΟΠ LF lines at 3726.03 and 3728.81 is questionable: we recall that Contini aud. Formigeiiao (1999) from the presence of [OII|3727 iuferred an electron density in the οπήτις eas not much hieher than 3«LO%cm a disturbingly," The presence of the two OII 1F lines at 3726.03 and 3728.81 is questionable: we recall that Contini and Formiggini (1999) from the presence of [OII]3727 inferred an electron density in the emitting gas not much higher than $3\times 10^3\rm cm^{-3}$ , a disturbingly"487again show the blue-shifted features aud lower coutinua with increasing metallicity.,again show the blue-shifted features and lower continua with increasing metallicity.488 The optical pseuco-continuuin ellects (Figure 7)) are still present. but smaller.," The optical pseudo-continuum effects (Figure \ref{fig:10zopt}) ) are still present, but smaller."489 We again see lines that deepen with increased metallicity such as 3650 (Ca LL HI). 1250 ((Fe IL Me IL Si HI). and 6100 ((Si II). but these effects are less dramatic than at day 7.," We again see lines that deepen with increased metallicity such as 3650 (Ca II H+K), 4250 (Fe II, Mg II, Si III), and 6100 (Si II), but these effects are less dramatic than at day 7."490 The $1 I feature (Figure Sbb) still shows the changiug depth aud slopes of the line edges with metallicity. but. at day 10 the depth of the Si II feature in the lowest metallicity moclel is larger than iun the same model on day 7. relative to the highest ο) layer metallicity in the respective epoch.," The Si II feature (Figure \ref{fig:sigrid}b b) still shows the changing depth and slopes of the line edges with metallicity, but, at day 10 the depth of the Si II feature in the lowest metallicity model is larger than in the same model on day 7, relative to the highest C+O layer metallicity in the respective epoch."491 These elfects ou the optical lines inclicate that liue formation for certain strong lines is now taking place in layers below the C+O laver., These effects on the optical lines indicate that line formation for certain strong lines is now taking place in layers below the C+O layer.492 The effects of liue formation below the C+O layer becomes more inmportaut as tle supernova atmosphere expaucs aud becomes less opaque., The effects of line formation below the C+O layer becomes more important as the supernova atmosphere expands and becomes less opaque.493 Our grid of synthetic spectra of WT on day 15 with C+O metallicity variations (Figure 8)) are again similar to those in the day 7 and LO spectra (Figures 1 6)).," Our grid of synthetic spectra of W7 on day 15 with C+O metallicity variations (Figure \ref{fig:15zall}) ) are again similar to those in the day 7 and 10 spectra (Figures \ref{fig:07zall}494 \ref{fig:10zall}) )."495 The decreasing ellects of C+O layer metallicity are apparent., The decreasing effects of C+O layer metallicity are apparent.496 The UV pseudo-continuuur variation with metallicity remains strong., The UV pseudo-continuum variation with metallicity remains strong.497 The optical (Figure 9)) and the near infrared (Figure 10)) show the backwarming optical/IR pseuco-continuuin flux effect which occurred iu the optical at day 10. aud extended well iuto the IR at day 7.," The optical (Figure \ref{fig:15zblue}) ) and the near infrared (Figure \ref{fig:15znir}) ) show the backwarming optical/IR pseudo-continuum flux effect which occurred in the optical at day 10, and extended well into the IR at day 7."498 Features which increased in streugth with iucreasiug C+O metallicity are a bleuc of Fe IL. Me IL Si Ul at. 1250A.. the multi-species blend at 3300A.. Mg II at 8850.A. and an wicentiliecl feature at 10100 ((possibly Si D).," Features which increased in strength with increasing C+O metallicity are a blend of Fe II, Mg II, Si III at 4250, the multi-species blend at 3300, Mg II at 8850, and an unidentified feature at 10400 (possibly Si I)."499 The feature at 3300 lis a blencl of weak lines that forms in the C+O layer., The feature at 3300 is a blend of weak lines that forms in the C+O layer.500 Figure 9 illustrates the blue shifting of eatures as chauges in metal content move the depth (aud thus velocity) of line formation., Figure \ref{fig:15zblue} illustrates the blue shifting of features as changes in metal content move the depth (and thus velocity) of line formation.501 The two component feature at 3700-3900 iis usually labeled Ca IE H4. ? have ideutified this ‘Ca split’ as arising from a bleud of Ca II H+Is with $i IL AB858&., The two component feature at 3700–3900 is usually labeled Ca II H+K. \citet{nughydro97} have identified this `Ca split' as arising from a blend of Ca II H+K with Si II $\lambda 3858$.502 We have calculated a series of diagnostic spectra at this epoch using the same eniperature structure. but without backgrouud opacity.," We have calculated a series of diagnostic spectra at this epoch using the same temperature structure, but without background opacity."503 We have coulirmect the ideutilicatiou of the due wing with the Si Ε line., We have confirmed the identification of the blue wing with the Si II line.504 When spectra are caleulated without any other line opacities. Ca II orum a pair of features.," When spectra are calculated without any other line opacities, Ca II forms a pair of features."505 The blue Ca II absorption forms from the A3727 liue. the red absorption rom the H4-Ix lines.," The blue Ca II absorption forms from the $\lambda 3727$ line, the red absorption from the H+K lines."506 The Si II feature falls on the peak between the two Ca IH absorptions., The Si II feature falls on the peak between the two Ca II absorptions.507 As the Si IHE feature strenetheus. the {lux displacecl by its absorption fille-in. the Ca II HI absorption creating a split’.," As the Si II feature strengthens, the flux displaced by its absorption `fills-in' the Ca II H+K absorption creating a `split'."508 With enough Si 11 ouly the blue absorption feature remains. while the red (eature becomes an inflection.," With enough Si II only the blue absorption feature remains, while the red feature becomes an inflection."509 The lack of a split in some ündicates that either the Si IE feature is weaker or the Ca II H+Iy is strouger. preventing the formation of a split.," The lack of a split in some indicates that either the Si II feature is weaker or the Ca II H+K is stronger, preventing the formation of a split."510 This helps to illustrate that in supernovae of all types. features are often the result of more than oue multiplet. or even ionic species.," This helps to illustrate that in supernovae of all types, features are often the result of more than one multiplet, or even ionic species."511demonstrate that the Bayesian method successfully recovers the true optical counterparts as the most probable counterpart of the time (and the first or second most probable of the time).,demonstrate that the Bayesian method successfully recovers the true optical counterparts as the most probable counterpart of the time (and the first or second most probable of the time).512 The main errors occur in assigning the wrong optical counterparts or in assigning optical counterparts to sources with no true optical counterpart and this problem is likely to be generic to all matehing methods., The main errors occur in assigning the wrong optical counterparts or in assigning optical counterparts to sources with no true optical counterpart and this problem is likely to be generic to all matching methods.513 Although the measured completeness is ~98%.. the true completeness is likely to be fz:955c..," Although the measured completeness is $\approx$, the true completeness is likely to be $\approx$."514 In Table 2 we present a sample of the matched optical and X-ray catalog for the ssources in the Boóttes field of the NDWFS., In Table 2 we present a sample of the matched optical and X-ray catalog for the sources in the Boöttes field of the NDWFS.515 The complete version of this table is in the electronic edition of the Journal., The complete version of this table is in the electronic edition of the Journal.516 The X-ray properties of each X-ray source are presented in Kenter et al (2005) (the sources can be cross-matched using their. X-ray names)., The X-ray properties of each X-ray source are presented in Kenter et al (2005) (the sources can be cross-matched using their X-ray names).517" The full catalog containing both the X-ray and optical parameters can be found at: ftp://archive.noao.edu/pub/catalogs/xbootes/xbootes_cat_xray 21jun, v1.0.txt and off the NDWFS homepage (http://www.noao.edu/noao/noaodeep/).", The full catalog containing both the X-ray and optical parameters can be found at: $\textunderscore$ $\textunderscore$ $\textunderscore$ $\textunderscore$ $\textunderscore$ $\textunderscore$ v1.0.txt and off the NDWFS homepage (http://www.noao.edu/noao/noaodeep/).518"opt.IR, The best matching eriteria depends on the science to be undertaken and for this reason. we include in this data release all multiply matched sources (with >1% probability of being the correct optical counterpart) as well as information regarding their. optical magnitude. distance to the X-ray source and probability of being the optical counterpart."," The best matching criteria depends on the science to be undertaken and for this reason, we include in this data release all multiply matched sources (with $>$ probability of being the correct optical counterpart) as well as information regarding their optical magnitude, distance to the X-ray source and probability of being the optical counterpart."519 Within our electronic table we include the following columns: (1) Name of X-ray (2) X-ray Right Ascension 2000 shifted to NDWFS astrometric frame (3) X-ray Right Ascension 2000 shifted to NDWFS astrometric frame (4) X-ray Right Ascension 2000 shifted to NDWFS astrometric frame (5) X-ray Declination 2000 shifted to NDWFS astrometric frame (6) X-ray Declination 2000 shifted to NDWFS astrometric frame (7) X-ray Declination 2000 shifted to NDWFS astrometric frame (8) X-ray Right Ascension 2000 shifted. to NDWFS astrometric frame (total (9) X-ray Declination 2000 shifted to NDWFS astrometric frame (total (10) Name of X-ray (11) Probability of X-ray source having an optical (12) Number of optical sources with 156 probability of being associated with the X-ray (13) Optical rank (12most probable in running order to least (14) Bayesian probability of (15) Identification flag (1 — optical ID; -1 — no optical ID., Within our electronic table we include the following columns: (1) Name of X-ray (2) X-ray Right Ascension 2000 shifted to NDWFS astrometric frame (3) X-ray Right Ascension 2000 shifted to NDWFS astrometric frame (4) X-ray Right Ascension 2000 shifted to NDWFS astrometric frame (5) X-ray Declination 2000 shifted to NDWFS astrometric frame (6) X-ray Declination 2000 shifted to NDWFS astrometric frame (7) X-ray Declination 2000 shifted to NDWFS astrometric frame (8) X-ray Right Ascension 2000 shifted to NDWFS astrometric frame (total (9) X-ray Declination 2000 shifted to NDWFS astrometric frame (total (10) Name of X-ray (11) Probability of X-ray source having an optical (12) Number of optical sources with $>$ probability of being associated with the X-ray (13) Optical rank (1=most probable in running order to least (14) Bayesian probability of (15) Identification flag (1 – optical ID; -1 – no optical ID.520 In cases of no optical ID being the most probable identification. the following flag values have been applied manually: -3 — no optical ID. but source obscured by nearby star / missing data: -2 — no optical ID. but X-ray position is close to optically bright galaxy (source is either obscured by or associated with the galaxy): -1 — ‘true’ no optical ID (optical image is truly blank». (," In cases of no optical ID being the most probable identification, the following flag values have been applied manually: -3 – no optical ID, but source obscured by nearby star / missing data; -2 – no optical ID, but X-ray position is close to optically bright galaxy (source is either obscured by or associated with the galaxy); -1 – 'true' no optical ID (optical image is truly blank)). ("52116) NDWFS optical name (Null if no optical (17) Optical (NDWFS) Right Ascension 2000 (hours: Null if no optical (18) Optical (NDWFS) Right Ascension 2000 (minutes: ull if no optical (19) Optical (NDWFS) Right Ascension 2000. (seconds: ull if no optical (20) Optical (NDWFS) Declination 2000 (degrees; Null if 10 optical (21) Optical (NDWFS) Declination 2000 (minutes: Null if 10 optical (22) Optical (NDWFS) Declination 2000 (seconds: Null if 10 optical (23) Optical (NDWFS) Right Ascension 2000 (total,16) NDWFS optical name (Null if no optical (17) Optical (NDWFS) Right Ascension 2000 (hours; Null if no optical (18) Optical (NDWFS) Right Ascension 2000 (minutes; Null if no optical (19) Optical (NDWFS) Right Ascension 2000 (seconds; Null if no optical (20) Optical (NDWFS) Declination 2000 (degrees; Null if no optical (21) Optical (NDWFS) Declination 2000 (minutes; Null if no optical (22) Optical (NDWFS) Declination 2000 (seconds; Null if no optical (23) Optical (NDWFS) Right Ascension 2000 (total522The search for t1ο astrophysical reason of the observed amplitude and phase variability associated: with stellar »ulsation concerns many different. types of stellar pulsators in vastly. cilleren stages of stellar evolution.,The search for the astrophysical reason of the observed amplitude and phase variability associated with stellar pulsation concerns many different types of stellar pulsators in vastly different stages of stellar evolution.523 We refer to his phenomenon as the Blazhko Elect. whieh was noticed »v Blazhko (1907) in the RR Lyrae star RW Dra.," We refer to this phenomenon as the Blazhko Effect, which was noticed by Blazhko (1907) in the RR Lyrae star RW Dra."524 These variations are quie common in RR Όντας stars. e... Szcidl (LOSS) mentions an occurrence of 20 - 30 in the Bltab stars.," These variations are quite common in RR Lyrae stars, e.g., Szeidl (1988) mentions an occurrence of 20 - 30 in the RRab stars."525 We are presently engaged in an extensive programme o examine the Blazhko Effect in RR Lyrae stars., We are presently engaged in an extensive programme to examine the Blazhko Effect in RR Lyrae stars.526 However. he ellect. has also been noticed. among other yvpes of o»ulsators.," However, the effect has also been noticed among other types of pulsators."527 Some examples are: (i) Cepheics: The cepheids with very short periods often show long-term anirlitucle variability., Some examples are: (i) Cepheids: The cepheids with very short periods often show long-term amplitude variability.528 Prorably tie known example is the star V473 Lvr (MIX 7308) with a racial »ulsation period of dd and a Blazhko period. ~ dd. The observed. ampliude variabiitv (by at Cast a actor of 15) during the Blazako evele could not be [lit by <C simple wo-Llrequeney beating model alone (Breecr 1981)., Probably the best-known example is the star V473 Lyr (HR 7308) with a radial pulsation period of d and a Blazhko period $\sim$ d. The observed amplitude variability (by at least a factor of 15) during the Blazhko cycle could not be fit by a simple two-frequency beating model alone (Breger 1981).529 ‘This is also evident from the ‘fact that t1ο amplitude variajons are not svmmetric on t10 Increasing and decreasing xanches (sec also Burki. Mavor Benz 1982).," This is also evident from the fact that the amplitude variations are not symmetric on the increasing and decreasing branches (see also Burki, Mayor Benz 1982)."530 LE beaing is involved. at least three frequencies are recuired.," If beating is involved, at least three frequencies are required."531 Some indications for, Some indications for532a liquid flow between two rotating cylinders.,a liquid flow between two rotating cylinders.533 The latter demonstrate a noulinear instability aud developed turbuleuce (ee. Lukashehuk Predtecheuskii 1981).," The latter demonstrate a nonlinear instability and developed turbulence (e.g., Lukashchuk Predtechenskii 1984)."534 Therefore. we have all the reasons to believe that. for short-wave perturbations. a nonlimear instability is likely to occur.," Therefore, we have all the reasons to believe that, for short-wave perturbations, a nonlinear instability is likely to occur."535 Likewise. in Appendix 3. we show that the dynamics of shortavave incompressible perturbations iu a rotating disk is completely equivalent to that ina plane shear laver.," Likewise, in Appendix 3, we show that the dynamics of short-wave incompressible perturbations in a rotating disk is completely equivalent to that in a plane shear layer."536 This proves the equivalence of the uoulinear instability in a plane shear laver aud iu the situation investigated here., This proves the equivalence of the nonlinear instability in a plane shear layer and in the situation investigated here.537 It is instructive to compare the above instability with that considered by Coldreich Lyuden-Bell (1965) (referred to as ο hereinafter) or à selteravitating. differentially rotating disk.," It is instructive to compare the above instability with that considered by Goldreich Lynden-Bell (1965) (referred to as GLB hereinafter) for a self-gravitating, differentially rotating disk."538 There are two basic differences between our and their situations., There are two basic differences between our and their situations.539 First. differcut branches of erowing perturbations are considered: we deal with the vortex brauch while GLB do with the sounud-eravitational brauch.," First, different branches of growing perturbations are considered: we deal with the vortex branch while GLB do with the sound-gravitational branch."540 Second. the conditions for the erowth of perturbations are different. too.," Second, the conditions for the growth of perturbations are different, too."541 Under couditiou (3.10). the leading vortex perturbations grow. due to the conservation of vorticity. dn an otherwise stable disk.," Under condition (3.10), the leading vortex perturbations grow, due to the conservation of vorticity, in an otherwise stable disk."542 GLB deal with the disk stable or axiallv-svuunetrical perturbations. and the erowth of their non-axiallv-sviunetrcal. long-avave perturbations proceeds due Oa leading[m] role of self-egravitv.," GLB deal with the disk stable for axially-symmetrical perturbations, and the growth of their non-axially-symmetrical, long-wave perturbations proceeds due to a leading role of self-gravity."543C» Toomre (1982) chiisteuec this erowth as “swing amplification”.," Toomre (1982) christened this growth as “swing amplification""."544 It is worth noting that. in our ease. a similar swing amplification occurs for the (vortex) short-wave perturbations aud it does not require selt-eravity.," It is worth noting that, in our case, a similar swing amplification occurs for the (vortex) short-wave perturbations and it does not require self-gravity."545 The growth of perturbations with accounting for viscosity. which is described by Eq. (," The growth of perturbations with accounting for viscosity, which is described by Eq. ("5463.3). is shown in Fig.,"3.3), is shown in Fig."547 l bv the dotted and dashed lines., 1 by the dotted and dashed lines.548" The “stability” described bv the exact solution (3.3) is of very specific kind as em, tends to zero at fo> x."," The “instability"" described by the exact solution (3.3) is of very specific kind as $v_{1r}$ tends to zero at $\tilde t \rightarrow \infty$ ."549 Nevertheless. during a finite time f even by Eq. (," Nevertheless, during a finite time $\tilde t_*$ given by Eq. ("5503.8) the perturbations are in the erowing regine and the amplitude mereases by a factor of kx)E))2(02|1). which can be ss1 if[|πο”...,"3.8) the perturbations are in the growing regime and their amplitude increases by a factor of $k_{\perp}^2551(0)/k_{\perp}^2(-\beta)=(\beta^2+1)$, which can be $\gg1$ if $|\beta|=552|k_r(0)/k_\varphi|\gg 1$."553" Lot us suppose hat by the moment f£=f,--||jH when the amplitude of auv perturbation arrivesat its uaxiun. the viscosity does not play any essential role. M Vel(t.)."," Let us suppose that by the moment $\tilde t =\tilde t_*\equiv \left|\beta554\right|$ when the amplitude of any perturbation arrivesat its maximum, the viscosity does not play any essential role, $\nu\ll\nu _{\rm cr}(\tilde t_*)$ ."555 Though this growth in the amplitude xoceeds during the time interval Af~£f oulv. it could ouset the local turbulence.," Though this growth in the amplitude proceeds during the time interval $\Delta \tilde t \simeq \tilde t_* $ only, it could onset the local turbulence."556 In this case. urbulence can be established everywhere in the disk as a superposition of he spiral perturbations originated iu differeut points of he disk aud on different moments of time: all of them lave oxpericnecd a erowth during AM~f£ ," In this case, turbulence can be established everywhere in the disk as a superposition of the spiral perturbations originated in different points of the disk and on different moments of time; all of them have experienced a growth during $\Delta \tilde t \simeq \tilde t_*$."557The turbulence appeared as a result of the erowth of the perturbations can be characterized by some urbuleut viscosity. which ecucrally is uuch larger than he molecular onc.," The turbulence appeared as a result of the growth of the perturbations can be characterized by some turbulent viscosity, which generally is much larger than the molecular one."558 It is possible that a steady-state regime will emerge in which Tn this regiue. the decay due to Viscosity is strong chough to provide a steady-state level of the turbulence so that the amplitude of the perturbations is kept more or less coustant m time. Substituting Eqs. (," It is possible that a steady-state regime will emerge in which In this regime, the decay due to viscosity is strong enough to provide a steady-state level of the turbulence so that the amplitude of the perturbations is kept more or less constant in time, Substituting Eqs. ("5593.11) aud (3.12) iuto Eq. (,3.11) and (3.12) into Eq. (5603.3) with taking iuto account Eq. (,3.3) with taking into account Eq. (561"3.5) and asstunine that. bv order of magnitude. 42O.? we arrive at the following transcendcutal equation: Taking the logaxitlun of this equation one fiuds: It is straightforward to see that the basic coutributiou iuto the turbuleut viscosity is eiven by the perturbations of the smallest A's: therefore 1444,&0.50(heμήν.","3.5) and assuming that, by order of magnitude, $A\simeq \Omega$, we arrive at the following transcendental equation: Taking the logarithm of this equation one finds: It is straightforward to see that the basic contribution into the turbulent viscosity is given by the perturbations of the smallest $k_{\varphi}$ 's; therefore $\nu_{\rm turb}\simeq 0.5\Omega/(k_{\varphi}^2)_{\rm min}$."562 From Eqs. (, From Eqs. (563"3.2) and (3.12) one has |&.]z|e.[oeht. whence Kos=hhtlhe. By substituting —o,./0 into Eq. (","3.2) and (3.12) one has $\left |k_{\varphi}\right |\simeq \left |k_r\right |\gg564h^{-1}$, whence $\left |k_{\varphi}\right |_{\rm min}\simeq h^{-1}$, By substituting $h=\sigma_v/\Omega$ into Eq. ("5653.15) the latter can be rewritten iu the fori: It is instructive to compare the expression for the Bolin diffusion cocficieut (Dy) with our Eqs. (,3.15) the latter can be rewritten in the form: It is instructive to compare the expression for the Bohm diffusion coefficient $(D_B)_{\rm}$ with our Eqs. (566"3.11) aud (3.105) for vay. A well-known estimation of the Doluu diffusion cocticicnt for a strong turbulence plasma is given by (see e.g. Ikadonitsev. 1961. or a review by orton. 1951): where +, is the maxiunn linear growth rate of the cft iustabilitv. and (A) is the ια wave ΠΙΟ, also from a linear theory.","3.14) and (3.15) for $\nu_{\rm turb}.$ A well-known estimation of the Bohm diffusion coefficient for a strong turbulence plasma is given by (see e.g., Kadomtsev, 1964, or a review by Horton, 1984): where $\gamma_L$ is the maximum linear growth rate of the drift instability, and $(k_\bot)$ is the minimum wave number, also from a linear theory."567" They are uch the same: in our case (tpc0.5© and instead of ky we substitute (heJenincfhi, Kadontsev obtained (Dryas by using the relationship &4p1. where pis the Larmor radius."," They are much the same: in our case $(\gamma_L)_{\rm568 max} \sim569 0.5~ \Omega$ and instead of $k_\bot$ we substitute $(k_\varphi)_{\rm min}570 \simeq h^{-1}.$ Kadomtsev obtained $(D_B)_{\rm max}$ by using the relationship $k_\bot \rho \sim 1,$ where $\rho$ is the Larmor radius."571 At Λιπρ1 Dp has a maxiunun.," At $k_\bot \sim \rho^{-1}$, $D_B$ has a maximum."572 But the Larmor radius in plasina corresponds to the epievelie radius in eraviplysics., But the Larmor radius in plasma corresponds to the epicyclic radius in graviphysics.573 The latter. in fact. is thethickuess of disk. ky=~ht . audthis. acually. is beiug used here.," The latter, in fact, is thethickness of disk, $k_\bot \simeq h^{-1}$ , andthis, actually, is being used here."574 This viscosity whose value is given by Eq. (, This viscosity whose value is given by Eq. (5753.15) or (3.16) was called dy Fridiman Ozernoy (1992),3.15) or (3.16) was called by Fridman Ozernoy (1992)576TT first used the virial theorem to estimate the lius of the Coma clister.,"\citet{zwicky1933,zwicky1937} first used the virial theorem to estimate the mass of the Coma cluster."577 With some modifications. notalblv a correction term for the surface pressure (?).. the virial theorem remains m wide use (e.g.?.audret-erencesthere)...," With some modifications, notably a correction term for the surface pressure \citep{1986AJ.....92.1248T}, the virial theorem remains in wide use \citep[e.g.,][and references578therein]{girardi98}."579" Jeans analysis incorporates the radial dependence of the projected velocity dispersion (οιον,277.andreferencestherein) aud obviates the need for a surface terni."," Jeans analysis incorporates the radial dependence of the projected velocity dispersion \citep[e.g.,][and580references therein]{cye97,2000AJ....119.2038V,bg03} and obviates the need for a surface term."581 Jeans analysis aud the caustic method are closely related., Jeans analysis and the caustic method are closely related.582 Both use the plase space distribution of galaxics to estimate the cluster mass profile., Both use the phase space distribution of galaxies to estimate the cluster mass profile.583 The primary cditfercuce is theue the Jeans method assmmes that the cluster is in dvnamical equilibriun: the caustic method docs not., The primary difference is that the Jeans method assumes that the cluster is in dynamical equilibrium; the caustic method does not.584 The Jeans method depends on the width of the velocity distribution of cluster 1ienibers a a eiven radius. whereas the caustic method calculates the edges of the velocity distribution at a eiven radius.," The Jeans method depends on the width of the velocity distribution of cluster members at a given radius, whereas the caustic method calculates the edges of the velocity distribution at a given radius."585 The caustic method is not independeut of he Jeans imethod. as the D99 method Iniuimizes⋅⋅⋅ -->Leg| within the virial region with radius R (see DOO for a nore detailed discussion).," The caustic method is not independent of the Jeans method, as the D99 method minimizes $|<$$v_{esc}^2$$>_R - 4 <$$v^2$$>_R|$ within the virial region with radius R (see D99 for a more detailed discussion)."586 Mass estimates based on Jeans :alysis this provide a consistency check but not au independent verification of the caustic mass estimates., Mass estimates based on Jeans analysis thus provide a consistency check but not an independent verification of the caustic mass estimates.587 Apaving the Jeans method requires an asstuption about either the amass distribution or the orbital cistrinition., Applying the Jeans method requires an assumption about either the mass distribution or the orbital distribution.588 Typically. oue assumes that light traces mass aud tius that the projected galaxy density is proportional to tle| projected mass ceusity (6.8..7) or one assunies a fuuctional form for the orbital distribution (e.g.?)..," Typically, one assumes that light traces mass and thus that the projected galaxy density is proportional to the projected mass density \citep[e.g.,][]{girardi98}589 or one assumes a functional form for the orbital distribution \citep[e.g.,][]{bg03}."590 Note hat most authors make the implicit assumption that the orατα] distribution of the dark matter can be inferred frou hat of the galaxies., Note that most authors make the implicit assumption that the orbital distribution of the dark matter can be inferred from that of the galaxies.591 Many recent simulations sueecst that ittle (~10%)) or no velocity bias exists on linear and mildly non-linear scales (7??j..," Many recent simulations suggest that little $\sim$ ) or no velocity bias exists on linear and mildly non-linear scales \citep{kauffmann1999a,kauffmann1999b,diemand04,faltenbacher05}."592 ILowwever. galaxies in simulated clusers often have sienificautly dciffereut orbital distributions tian the dark matter (e.g.7T7)..," However, galaxies in simulated clusters often have significantly different orbital distributions than the dark matter \citep[e.g.,][]{1999ApJ...516..530K,dkthesis,faltenbacher05}."593 Dynamical friction shouk produce a sialer velocity dispersion for cluster galaxies than dark mator (2?7).. although. they lav undergo more frequent nicveers (due to their smaller velocities) or tidal disruption. 1esultiug iu alarger velocity dispersion of the surviving custer galaxies relative to the dark matter (277).. ," Dynamical friction should produce a smaller velocity dispersion for cluster galaxies than dark matter \citep{1999ApJ...516..530K,2003ApJ...590..654Y,2005MNRAS.361.1203V}, although they may undergo more frequent mergers (due to their smaller velocities) or tidal disruption, resulting in alarger velocity dispersion of the surviving cluster galaxies relative to the dark matter \citep{1999ApJ...523...32C,diemand04,faltenbacher05}. ."594Note iUso that velocity bias may depend on the mass of the cluster (7) or the huninosities of the tracer galaxies (?).. , Note also that velocity bias may depend on the mass of the cluster \citep{berlind03} or the luminosities of the tracer galaxies \citep{2006MNRAS.366.1455S}. .595Aniuportant caveat is that the, Animportant caveat is that the596blazars to be detected by GLAST rouglv matches with the skv density of Hat spectrum radio sources down to 50 παν at 5 GIIz (Padovani2007). and 65 mJv at 8.4 GIIz 200T).,blazars to be detected by GLAST rougly matches with the sky density of flat spectrum radio sources down to 50 mJy at 5 GHz \citep{pad07} and 65 mJy at 8.4 GHz \citep{hea07}.597. However. our results show that a large number of GLAST sources would be detected al even lower radio flux densities if the luminosity relationship we observe for EGRET sources also holds up for GLAST sources.," However, our results show that a large number of GLAST sources would be detected at even lower radio flux densities if the luminosity relationship we observe for EGRET sources also holds up for GLAST sources."598 It is very likely that many new radio observations would be required in a!, It is very likely that many new radio observations would be required in a!599 nv of the cases mentioned above. but especially for cases in w!," ny of the cases mentioned above, but especially for cases in w!"600 hieh the putative radio source may not even be in anv previous catalog., hich the putative radio source may not even be in any previous catalog.601 (Frou a theoretical perspective. confinmation of the previously determined correlation between gammnma-rav and radio huminosities will lead to confirmation of SSC. though the precise agreement would have to be re-analvzed with these new data.," >From a theoretical perspective, confirmation of the previously determined correlation between gamma-ray and radio luminosities will lead to confirmation of SSC, though the precise agreement would have to be re-analyzed with these new data."602 The author thanks M. Lister for many useful discussions aud the anonvimous referee for abundant constructive comments., The author thanks M. Lister for many useful discussions and the anonymous referee for abundant constructive comments.603 S. Bloom would like to acknowledge the generosity of the National Radio Astronomy Observatory (NRAQO) during his stav as a Visiting Scientist ad NRAO IILeadeqiarters in Charlottesville. VÀ.," S. Bloom would like to acknowledge the generosity of the National Radio Astronomy Observatory (NRAO) during his stay as a Visiting Scientist at NRAO Headquarters in Charlottesville, VA."604" ο, Bloom would also like to acknowledge several summer Faculty Fellowship grants from ILunpden-Syduiey. College.", S. Bloom would also like to acknowledge several Summer Faculty Fellowship grants from Hampden-Sydney College.605 This work has also made extensive use of the NASA Extragalactic Database (NED) and NASA's Astrophysics Data Svstem Dibliographie Services (ADS)., This work has also made extensive use of the NASA Extragalactic Database (NED) and NASA's Astrophysics Data System Bibliographic Services (ADS).606Jeckiman 1990a). but are all based on data of much lower quality.,"Beckman 1990a), but are all based on data of much lower quality."607 The error on the fit to the slope is solely the error due to the least-squares fit to the data points., The error on the fit to the slope is solely the error due to the least-squares fit to the data points.608 The size of the bins does not seem to be an important factor in the determination ofthe slope: fitting the slope (over the same range in log L) to the LE constructed with bins of 0.1 gives a=—2.16x0.04., The size of the bins does not seem to be an important factor in the determination of the slope: fitting the slope (over the same range in $\log L$ ) to the LF constructed with bins of 0.1 gives $a=-2.16\pm0.04$.609 Including the rregions in the CNR in the LE. preclictably. lowers the slope oa=1.95x0.04 due to the inclusion of relatively more ueh-L rregions.," Including the regions in the CNR in the LF, predictably, lowers the slope to $a=-1.95\pm0.04$ due to the inclusion of relatively more $L$ regions."610 For all fits to the dise LE. the range over which the it was made (indicated in Fig. 2))," For all fits to the disc LF, the range over which the fit was made (indicated in Fig. \ref{disclf}) )"611 is 37.9<loeL39.3., is $37.9<\log L<39.3$.612 A stecpening of the LE at high £L. and/or a break. or jump in the LE has been observed. in a number of spiral ealaxies. in all cases near logL=38.7 and has »en interpreted in physical terms as a distinction between density and ionization bounded rregions (Beckman et al.," A steepening of the LF at high $L$, and/or a break or jump in the LF has been observed in a number of spiral galaxies, in all cases near $\log613L=38.7$ $^{-1}$, and has been interpreted in physical terms as a distinction between density and ionization bounded regions (Beckman et al."614 1998)., 1998).615 While such an ellect is not immecdiately obvious in the LE as shown in Fig., While such an effect is not immediately obvious in the LF as shown in Fig.616 2. a more detailed discussion of the possible detection in the data set for MIOO is given in Paper LL (Rozas et al..," 2, a more detailed discussion of the possible detection in the data set for M100 is given in Paper II (Rozas et al.,"617 in preparation), in preparation).618 Fie., Fig.619 3 shows the separate LEs for the arm and. interarm parts of the cise of ALLOO., \ref{aialf} shows the separate LFs for the arm and interarm parts of the disc of M100.620 The shapes of both the arm and interarm LE are very similar to that of the eise LE discussed before., The shapes of both the arm and interarm LF are very similar to that of the disc LF discussed before.621 Fits to the slopes ofthe arm and interarm rregion LEs vield a=2.07£0.04 (arm) anda=218+0.21 (interarm). fitting over ranges of 37.9<loeb39.3 and 37.5<logL38.5. respectively.," Fits to the slopes of the arm and interarm region LFs yield $a=-2.07\pm0.04$ (arm) and $a=-2.18\pm0.21$ (interarm), fitting over ranges of $37.9<\log L<39.3$ and $37.5<\log L<38.5$, respectively."622 The arm and interarm LE slopes can thus not be considered. dilferent. given the errors in the fits.," The arm and interarm LF slopes can thus not be considered different, given the errors in the fits."623 Lt is dillicult to determine what range in log Lis best for use in the fitting. especially. for. the interarm LE. but the arm and interarm slopes will not be significantly dillerent. for any reasonable choice οἱ range.," It is difficult to determine what range in $\log624L$ is best for use in the fitting, especially for the interarm LF, but the arm and interarm slopes will not be significantly different for any reasonable choice of range."625 Copa Beckman (1990a) concluded: from fits to Lbs. derived from their list of 456 rregions as catalogued from an iimage of the central 3713/6 part of MIOO. that arm and interarm LE slopes were slightly different.," Cepa Beckman (1990a) concluded from fits to LFs, derived from their list of 456 regions as catalogued from an image of the central $\mind 3.1\times\mind6263.6$ part of M100, that arm and interarm LF slopes were slightly different."627 But they only used less than a quarter of the number of rregions of the present paper. distributed. over a much reclucecl area of the disce.," But they only used less than a quarter of the number of regions of the present paper, distributed over a much reduced area of the disc."628 Furthermore. the errors on their fits. of about 0.3. are large compared to the cilference in slope 2.34 arm. 3.06 interarm).," Furthermore, the errors on their fits, of about $\pm0.3$, are large compared to the difference in slope $-2.34$ arm, $-3.06$ interarm)."629 The conclusion must be al their dillerence is not significant. but does indicate the trend also found in the present paper. that the interarm LE slope is steeper than the arm LP slope.," The conclusion must be that their difference is not significant, but does indicate the trend also found in the present paper, that the interarm LF slope is steeper than the arm LF slope."630 When compared to the arm LE. the interarm LE. is slightly. clisplaced toward the lower left ofthe diagram. i.e.. toward lower numbers and lower luminosities.," When compared to the arm LF, the interarm LF is slightly displaced toward the lower left of the diagram, i.e., toward lower numbers and lower luminosities."631 However. the [act that the arm and interarm: LE slopes are equal is a strong indication that the ppopulations in and between the arms are cillerent (see also Section 6)," However, the fact that the arm and interarm LF slopes are equal is a strong indication that the populations in and between the arms are different (see also Section 6)."632 The CNR in MIOO accounts for about of the total Iline Lux of the complete galaxy (I&napen et al., The CNR in M100 accounts for about of the total line flux of the complete galaxy (Knapen et al.633 19953)., 1995a).634 The comission is organised into a pair of tightly. wound. spiral, The emission is organised into a pair of tightly wound spiral635A dispersion relation has been derived for gravitational instabilities in a medium with cloud collisional cooling bv Elmegreen (1989).,A dispersion relation has been derived for gravitational instabilities in a medium with cloud collisional cooling by Elmegreen (1989).636 The cooling function due to the clouc-eloucd collisions with an isotropic. Maxwellian distribution of cloud velocities is a power-law of the density and the temperature (Elneereen 1987). similar to the form of our cooling rate in (his paper.," The cooling function due to the cloud-cloud collisions with an isotropic, Maxwellian distribution of cloud velocities is a power-law of the density and the temperature (Elmegreen 1987), similar to the form of our cooling rate in this paper."637 Thus. in a cloudy medium without much star formation activily (1e... witout heating). the energy dissipation is given by equation (9).," Thus, in a cloudy medium without much star formation activity (i.e., without heating), the energy dissipation is given by equation (9)."638 Elmegreen showed that (he regions with such conditions will clamp into cloud complexes on a variety of scales., Elmegreen showed that the regions with such conditions will clump into cloud complexes on a variety of scales.639 Since on the largest scales. the rotation and shear of the Galaxy become important. our results describe the general properties of structure formation in such regions.," Since on the largest scales, the rotation and shear of the Galaxy become important, our results describe the general properties of structure formation in such regions."640 This simple model has nevertheless some limitations., This simple model has nevertheless some limitations.641 We have not included explicit healing terms in our energv equation. in order to minimize (he number of parameters.," We have not included explicit heating terms in our energy equation, in order to minimize the number of parameters."642 llowever. we can consider additional terms in the governing equations.," However, we can consider additional terms in the governing equations."643 For example. one could invoke the flow inertia in the momentum equation. or heat conduction in the energy equation.," For example, one could invoke the flow inertia in the momentum equation, or heat conduction in the energy equation."644 Although the similarity indices would be selected in these cases. we can consider only limited. values of the exponents of the cooling function and the viscosity model.," Although the similarity indices would be selected in these cases, we can consider only limited values of the exponents of the cooling function and the viscosity model."645 Also. (he assumption of similarity solutions. could be dropped. although we shoukl not forget the complex nature of the governing partial differential equations.," Also, the assumption of similarity solutions, could be dropped, although we should not forget the complex nature of the governing partial differential equations."646 Also. we assumed a power law for the form of cooling rate and viscosity and the results depend strongly on (he form of these funelions.," Also, we assumed a power law for the form of cooling rate and viscosity and the results depend strongly on the form of these functions."647 However. as we mentioned in SG. it seems (hal we can use piece-wise solutions.," However, as we mentioned in SG, it seems that we can use piece-wise solutions."648 I1 means that for each part of the evolution of the solutions. we can lind the suitable exponents and (hen join one set of solutions to the another one.," It means that for each part of the evolution of the solutions, we can find the suitable exponents and then join one set of solutions to the another one."649 Thus. it will be possible to consider a nich wider range of cooling Dunctüions and viscosity models wilh the same analvtical-tvpe of solution.," Thus, it will be possible to consider a much wider range of cooling functions and viscosity models with the same analytical-type of solution."650 , 651"1979) which gives the radio Ilux from a jet viewed at right angle to the jet axis as Llere z is à coordinate along the conical jet axis of symmetry. (2) is the radius of the jet. j,(2) is the optically thin svnchrotron emissivity for a power law clistribution of electrons over energv. and 7,(2) is the optical depth for a viewing angle perpendicular to the jet axis.","1979) which gives the radio flux from a jet viewed at right angle to the jet axis as Here $z$ is a coordinate along the conical jet axis of symmetry, $R(z)$ is the radius of the jet, $j_{\nu}(z)$ is the optically thin synchrotron emissivity for a power law distribution of electrons over energy and $\tau_{\nu}(z)$ is the optical depth for a viewing angle perpendicular to the jet axis."652 Noting that Tí(2) becomes huge below the shock at the base of the jet. he integral can be taken from z*0 to zx.," Noting that $\tau_{\nu}(z)$ becomes huge below the shock at the base of the jet, the integral can be taken from $z \approx 0$ to $z \rightarrow \infty$."653 Both ως). ancl τος) depend on the magnetic field. ancl density distributions along the jet., Both $j_{\nu}(z)$ and $\tau_{\nu}(z)$ depend on the magnetic field and density distributions along the jet.654" We assume that the magnetic ield will be proportional to 2,,, of eq. (", We assume that the magnetic field will be proportional to $B_m$ of eq. (6559).,9).656 Phe density after xwsage through the jet shock will remain proportional to fh of cq. (, The density after passage through the jet shock will remain proportional to $\rho_m$ of eq. (65710).,10).658 “Phus we assume that D(2)=92f(:)V and p(z)=ο)Ve where f(z) and οί) are distribution ‘unctions along the jet.," Thus we assume that $B(z)=\beta f(z)/\chi_m^3$ and $\rho(z) = g(z)\beta^2/\chi_m^5$, where f(z) and g(z) are distribution functions along the jet."659 In order to evaluate the integral for £5. it is helpful to scale s and A(z) to match the disk radius at the base of he jet nozzle.," In order to evaluate the integral for $F_{\nu}$, it is helpful to scale $z$ and $R(z)$ to match the disk radius at the base of the jet nozzle."660 For this purpose. we define variables scaled ⇂↥≺⋅⊳∖⋜⋯↓≺⋅⋜↧⊳∖∖∶↳⊽∶∶⊔↾∣ry aud Rec)=BG)mτry.," For this purpose, we define variables scaled the same as $\chi$; $\zeta = z \dot{m}^{-2/7}/r_g$ and $R_{\zeta}(\zeta)= R(z)\dot{m}^{-2/7}/r_g$."661" With this scaling.8 Z2;ς can automatically always match ∖αν, at the base of the jet ancl: The integral above has magnetic Ποια and. density dependence only via 4=g/M? in Equations. (9). and (10)."," With this scaling, $R_{\zeta}$ can automatically always match $\chi_m$ at the base of the jet and: The integral above has magnetic field and density dependence only via $\beta = \mu/M^3$ in Equations (9) and (10)."662" For given inner disk radius in units of rj. having D, determined. predominantly by the central object represents a case that was not considered in H803."," For given inner disk radius in units of $r_g$, having $B_m$ determined predominantly by the central object represents a case that was not considered in HS03."663 Nevertheless. using heir method. (and with notation adapted from their eq. (," Nevertheless, using their method (and with notation adapted from their eq. ("6648) o the present case. Og=J and óc:= 7) we obtain o fron a differentiation of the logarithm of the integral with respect o αν).,"8) to the present case, $\phi_B= \beta$ and $\phi_C=\beta^2$ ) we obtain $\alpha$ from a differentiation of the logarithm of the integral with respect to $\ln(\nu)$."665 second. dillerentiation of In(a) with respect to n(m) vields a zero because the MECO magnetic field. and hus 3. is independent of m. thus assuring that there is no ow state spectral evolution as m changes.," A second differentiation of $\ln{(\alpha)}$ with respect to $\ln{(\dot{m})}$ yields a zero because the MECO magnetic field, and thus $\beta$, is independent of $\dot{m}$, thus assuring that there is no low state spectral evolution as $\dot{m}$ changes."666 Further. following 11803. we assume scale invariance of the jet morphology.," Further, following HS03, we assume scale invariance of the jet morphology."667 For given vou. the integral is invariant with respect to nnm.," For given $\chi_m$, the integral is invariant with respect to $\dot{m}$."668 The scaling of B and p satisfies the conditions for applicability ofthe method used ον H803 to obtain their eq. (, The scaling of $B$ and $\rho$ satisfies the conditions for applicability of the method used by HS03 to obtain their eq. (66910a).,10a).670" Then by similar method we obtain the dependence of P, on M and Fox37. where Taking the canonical value ofp—2. we obtain g=(17|)/6 and for the accretion disk-intrinsic magnetic moment interaction and spectral index described by equations. (1) through (14) we find Η oxAMET. as would apply for MECO ACN/GBUC this recovers the ΠΡΟΣ dependence of 4xA106 from their eq. ("," Then by similar method we obtain the dependence of $F_\nu$ on M and $F_{\nu} \propto \beta^q$, where Taking the canonical value of $p=2$, we obtain $q=(17+8\alpha)/6$ and for the accretion disk-intrinsic magnetic moment interaction and spectral index described by equations (1) through (14) we find If $\beta \propto M^{-1/2}$, as would apply for MECO AGN/GBHC this recovers the HS03 dependence of $F_{\nu} \propto M^{(17/12-\alpha /3)}$ from their eq. ("67110a). but for strict scale invariance of the integral. there is no further dependence on m here.,"10a), but for strict scale invariance of the integral, there is no further dependence on $\dot{m}$ here."672 “Phis differs from the ii dependence found. by LISO3 because the dominant magnetic field of the jet originates in the MIECO rather than being generated in the accretion How of the disk., This differs from the $\dot{m}$ dependence found by HS03 because the dominant magnetic field of the jet originates in the MECO rather than being generated in the accretion flow of the disk.673 With gin eq. (, With $\mu$ in eq. (67411) written in terms of 3. a comparison with eq. (,"11) written in terms of $\beta$, a comparison with eq. ("67516) shows the radio Hux to be proportional to E.,16) shows the radio flux to be proportional to $\dot{E}$.676" Thus we can take the integrated. radio πας as luminosity. Ly. to be given by where €, is a constant dependent on the. radio bandwidth."," Thus we can take the integrated radio flux as luminosity, $L_R$, to be given by where $C_o$ is a constant dependent on the radio bandwidth."677 As noted by 11803. there will also be optically thin x-ray emission from the jet.," As noted by HS03, there will also be optically thin x-ray emission from the jet."678 In this case. taking 7<<lin eq.," In this case, taking $\tau_{\nu} << 1$ in eq."679 14. we obtain what is essentially an integral over the jet source volume for the optically thin x-ray emission of the jet.," 14, we obtain what is essentially an integral over the jet source volume for the optically thin x-ray emission of the jet."680 Since fy depends on m in the same way as before. both racdio-infrared and the jet part of the x-ray Huxes are proportional io E.," Since $F_{\nu,x}$ depends on $\dot{m}$ in the same way as before, both radio-infrared and the jet part of the x-ray fluxes are proportional to $\dot{E}$."681 While the base of the jet contributes to the x-ray Lux. its raciiating volume is likely much smaller than that of the ADC. which produces most of the x-ray flux.," While the base of the jet contributes to the x-ray flux, its radiating volume is likely much smaller than that of the ADC, which produces most of the x-ray flux."682 The cutolf of this part of the x-ray Dux and the onset of soft thermal emissions as the inner disk radius pushes inside corotation and the accretion Dow reaches the central object marks the spectral state transition., The cutoff of this part of the x-ray flux and the onset of soft thermal emissions as the inner disk radius pushes inside corotation and the accretion flow reaches the central object marks the spectral state transition.683 The ADC actually grows in the high state (while producing a declining fraction of the x-rav luminosity) as it is cooled by photons from the central object., The ADC actually grows in the high state (while producing a declining fraction of the x-ray luminosity) as it is cooled by photons from the central object.684" Finally, we note that the degree of collimation of a jet actually appears to depend on the scale height. and oessure of the corona (Ixato. Minishige Shibata 2004). out. £s can still be caleulated. for a largely uncollimated outllow: for example. a large angle [ow spreading out from he inner rings of the disk."," Finally, we note that the degree of collimation of a jet actually appears to depend on the scale height and pressure of the corona (Kato, Minishige Shibata 2004), but $F_\nu$ can still be calculated for a largely uncollimated outflow; for example, a large angle flow spreading out from the inner rings of the disk."685 In this case. we would obtain an integral similar to eq.," In this case, we would obtain an integral similar to eq."686 14., 14.687 with ede replaced. hy a column length. parallel to the line of sight looking into the xdasma and integrated over the area of the Dow. projected »rpendiceular to the line of sight.," with $R_\zeta^2 d\zeta$ replaced by a column length parallel to the line of sight looking into the plasma and integrated over the area of the flow, projected perpendicular to the line of sight."688" Fhough there would be differences of numerical factors depending on viewing angle. scale invariance for given rj,ry=vis would still require all coordinates to be scaled in ternis of ry and m'* in the sanie wav as in eq."," Though there would be differences of numerical factors depending on viewing angle, scale invariance for given $r_m/r_g = \chi_m$ would still require all coordinates to be scaled in terms of $r_g$ and $\dot{m}^{2/7}$ in the same way as in eq."689 Lt and we would still obtain £.x£., 14 and we would still obtain $F_\nu \propto \dot{E}$.690 Thus the scaling results we have obtained for magnetospherically driven outllows are very robust. even though there may. be considerable uncertainty about the geometric details of the low.," Thus the scaling results we have obtained for magnetospherically driven outflows are very robust, even though there may be considerable uncertainty about the geometric details of the flow."691" Sincem [£x.pr3 ""and Layxre Jit Oso.is apparent that we should expect radio Luminosity. LgxL5"," Since $\dot{E} \propto r^{-3}$ and $L_d \propto r^{-9/2}$, it is apparent that we should expect radio luminosity, $L_R \propto L_d^{2/3}$."692 [n particular we find where Strictly speaking. Ly should be the bolometric uminositv of the disk. however. the x-ray luminosity over a large energy band is a very substantial fraction of the disk uminositv.," In particular we find where Strictly speaking, $L_d$ should be the bolometric luminosity of the disk, however, the x-ray luminosity over a large energy band is a very substantial fraction of the disk luminosity."693 To compare with the correlation exponent of 2/3 obtained here. recent studies. including noisy data for both GDIIC and AGN have vieldec 0.7140.01 (Gallo. Fender oolev 2003). 0.72 (Alarkoll et al.," To compare with the correlation exponent of 2/3 obtained here, recent studies, including noisy data for both GBHC and AGN have yielded $0.71 \pm 0.01$ (Gallo, Fender Pooley 2003), 0.72 (Markoff et al."694 2003. Faleke. Ixórrding Markoll 2003). 0.60€0.11 (MEIIDO3) ancl 0.64+0.09 (Maccarone. Gallo," 2003, Falcke, Körrding Markoff 2003), $0.60 \pm 0.11$ (MHD03) and $0.64 \pm 0.09$ (Maccarone, Gallo"695The gravitationa waves (CAVs) ciuitted divine the final stages of the coalescence of two merging black holes (BIIs) carry linear LOMA. nuplvine that the center of mass of the system experiences a recoil (Bounor Rotenbere 1961: Peres 1962).,"The gravitational waves (GWs) emitted during the final stages of the coalescence of two merging black holes (BHs) carry linear momentum, implying that the center of mass of the system experiences a recoil (Bonnor Rotenberg 1961; Peres 1962)."696 TI1e resulting recoil velocity had been known to be large .owdth values estimated to be of order cgo1000lans5 (Fitchett 1983).," The resulting recoil velocity had been known to be large, with values estimated to be of order $v_{\rm kick} \sim 1000~{\rm km~s^{-1}}$ (Fitchett 1983)."697 Favata et al. (, Favata et al. (6982001) has recentlv revisited this problem andl coniputed recoil velocities. treating the spin and orbital cwnamics of the imereiue DII. as well as the generation of CAVS in the stroue eravitv regunue.,"2004) has recently revisited this problem and computed recoil velocities, treating the spin and orbital dynamics of the merging BHs, as well as the generation of GWs in the strong gravity regime."699 They have found the range of possilde recoil velocities to be 100kmsSeZOO600καν+. with the exact value depending ou the mass ratio of the mereiue DIIs. their spin. aix orbital parameters.," They have found the range of possible recoil velocities to be $100~{\rm700km~s^{-1}}\lsim v_{\rm kick} \lsim 600~{\rm km~s^{-1}}$, with the exact value depending on the mass ratio of the merging BHs, their spin, and orbital parameters."701 These velocities are large compared to the escape velocities of cawart galaxies. auk of the typical dark matter hedos that existed at the carly epochs of galaxy formation (+2 6).," These velocities are large compared to the escape velocities of dwarf galaxies, and of the typical dark matter halos that existed at the early epochs of galaxy formation $z\gsim 6$ )."702 Iu hierarchica cosinogonics. the SMDIIS that are known ο exist in the ocal universe erew via a conidüuation of accretion aix uecrgeers between holes residing in individual DM. halos.," In hierarchical cosmogonies, the SMBHs that are known to exist in the local universe grew via a combination of accretion and mergers between holes residing in individual DM halos."703 Aleyyitt. et al. (, Merritt et al. (7042001) and. Madau Quataert (2001) recently considered several consequences of a large recoil rat removes a BIT from the «‘enter of its jiost ealaxy.,2004) and Madau Quataert (2004) recently considered several consequences of a large recoil that removes a BH from the center of its host galaxy.705 Iu particular. Merritt et al. (," In particular, Merritt et al. ("7062001) pointec mt that the jection of SMDIIs. from he shallow potentials of D wos at Ligh redshift iuplies a masa redshift at which ιο progenitors of presentdav 8MBUs could lave startec -iergiug (and sticking) with eac1 other.,2004) pointed out that the ejection of SMBHs from the shallow potentials of DM halos at high redshift implies a maximum redshift at which the progenitors of present–day SMBHs could have started merging (and sticking) with each other.707 Tu thisLetter. we cousider the erowth history of SMDIIs lat are in place at 2> Goaad are thought to power ie bright quasars recently dixὈνοος (Fan et al.," In this, we consider the growth history of SMBHs that are in place at $z>6$, and are thought to power the bright quasars recently discovered (Fan et al."708 2000: 2001: 2003) iu the Sloan Dieital Sky Survey (SDSS)., 2000; 2001; 2003) in the Sloan Digital Sky Survey (SDSS).709" As discussed in Hain Loe» (2001: hereafter IILOL). relatively little time is available for the growth of these few. \NL, SMDIIS prior tfo z~6. and their seed BUs mist be present as early as 2~10."," As discussed in Haiman Loeb (2001; hereafter HL01), relatively little time is available for the growth of these few $\times10^9~{\rm M_\odot}$ SMBHs prior to $z\sim 6$, and their seed BHs must be present as early as $z\sim 10$."710 A model in which stellar seed DIIS appear iu small progenitor DM. halos is consistent with the presence of a ~L«10?AL. SMBII at 210. provided that cach seed BIL can erow at least at the Eddingtonlimited expoucutial rate. aud that the progenitor halos cau form seed DITs suticicutly cary on.," A model in which stellar seed BHs appear in small progenitor DM halos is consistent with the presence of a $\sim 4\times10^9~{\rm M_\odot}$ SMBH at $z\sim 10$, provided that each seed BH can grow at least at the Eddington–limited exponential rate, and that the progenitor halos can form seed BHs sufficiently eary on."711 The ejection of a mergerproduct SAIBIT from its host halo severely lits the ability of massive SMDIIS to grow at 2>6. by disrupting the early stages of growth.," The ejection of a merger–product SMBH from its host halo severely limits the ability of massive SMBHs to grow at $z>6$, by disrupting the early stages of growth."712 Iu thisLetter. as au example. we model the growth of the SMDBII powenrug the most distaut SDSS quasar. SDSS 105111021 at redshift +=6.13. with au inferred DII mass of ~L«10?AL...," In this, as an example, we model the growth of the SMBH powering the most distant SDSS quasar, SDSS 1054+1024 at redshift $z=6.43$, with an inferred BH mass of $\sim7134\times 10^9~{\rm M_\odot}$."714 Under the assiiuption that progenitor holes are ejected from DAL halos with velocity dispersious 0<Mgaf2. and do not contribute to the final BIT mass. we fud that typical recoil velocities niust either be below the value eua=LOOkins+ found by Favata et ab.," Under the assumption that progenitor holes are ejected from DM halos with velocity dispersions $\sigma<v_{\rm kick}/2$, and do not contribute to the final BH mass, we find that typical recoil velocities must either be below the value $v_{\rm kick}= 100~{\rm km~s^{-1}}$ found by Favata et al.,"715 or else this SMDIT must wave had a phase during which it eaimed mass siguificautv amore rapidly than the Eddinetonlimited exponential erowth rate would imply., or else this SMBH must have had a phase during which it gained mass significantly more rapidly than the Eddington–limited exponential growth rate would imply.716 The rest of thisLetter is orgauzed as follows., The rest of this is organized as follows.717 Iu 2. we discuss the interred values of the relevant parameters (halo aud BIT mass) of SDSS 105111021.," In \ref{sec:quasar}, we discuss the inferred values of the relevant parameters (halo and BH mass) of SDSS 1054+1024."718 In 23. we describe the method we use mode the growth of the SMDIT by accretion aud mergers.," In \ref{sec:model}, we describe the method we use model the growth of the SMBH by accretion and mergers."719 Iu l.. we present our main result. showing that excluding seed Ες from lowmass progenitor halos necessitates a fasterthan Eddington erowth rate.," In \ref{sec:results}, we present our main result, showing that excluding seed BHs from low–mass progenitor halos necessitates a faster–than Eddington growth rate."720 In 5.. we discuss various uucertaiuties about our results.," In \ref{sec:discuss}, we discuss various uncertainties about our results."721 Iu 6.. we sununuarize the iaplicatious of this work and offer our The starting point for the constraints we derive below," In \ref{sec:conclude}, we summarize the implications of this work and offer our The starting point for the constraints we derive below"722detector [oil before and after etching.,detector foil before and after etching.723 The etchecl detectors were measured with an automatic image analyzer system [1H].., The etched detectors were measured with an automatic image analyzer system \cite{noll}.724 The tracking was performed using the front faces of two or more sheets for calibrations and for fragmentation studies [15].., The tracking was performed using the front faces of two or more sheets for calibrations and for fragmentation studies \cite{dekhissi}.725 The first strange event candidate in the LI CR39 laver (top face) in module 7408. is shown in Fig. l..," The first strange event candidate in the L1 CR39 layer (top face) in module 7408, is shown in Fig. \ref{fig:tracce}."726 Two tracks [rom this event are also shown in Fig., Two tracks from this event are also shown in Fig.727 3. bottom., \ref{fig:micro} bottom.728 The tracks have strange shapes and seem {ο be made up of several prongs wilh some tracks ending (heir range normally while others have sharp cones at their endings., The tracks have strange shapes and seem to be made up of several prongs with some tracks ending their range normally while others have sharp cones at their endings.729 There were no tracks in the L3 and LG CR39 sheets nor in the Makrolol L2. L4. L5 sheets.," There were no tracks in the L3 and L6 CR39 sheets nor in the Makrofol L2, L4, L5 sheets."730ancl negative. suggesting that the protoplanet would undergo a random walk rather than monotonic. inward migration.,"and negative, suggesting that the protoplanet would undergo a random walk rather than monotonic, inward migration."731 We note. however. that as the protoplanet mass increases. and the spiral waves excited increase in amplitude to become comparable or larger that the turbulent density wakes. the torques due to the inner and outer disc begin to separate.," We note, however, that as the protoplanet mass increases, and the spiral waves excited increase in amplitude to become comparable or larger that the turbulent density wakes, the torques due to the inner and outer disc begin to separate."732 This can be observed by comparing figures τι. 13.. ancl 19.. which show the torques from the inner and outer discs becoming progressively distinguishable from each other as the planet mass increases.," This can be observed by comparing figures \ref{fig8}, , \ref{fig14}, , and \ref{fig20}, which show the torques from the inner and outer discs becoming progressively distinguishable from each other as the planet mass increases."733 This is also accompanied by a Louction in the relative torque Iuctuation noise level., This is also accompanied by a reduction in the relative torque fluctuation noise level.734 ligure 20 shows the running time average of the torques »er unit mass for run G3., Figure \ref{fig21} shows the running time average of the torques per unit mass for run G3.735 The straight line in this figure is the time averaged. total torque per unit mass obtained in the equivalent laminar dise run., The straight line in this figure is the time averaged total torque per unit mass obtained in the equivalent laminar disc run.736 As in runs Cl and 2. he runningὃν time averageo of the total torquei per unit mass ails to converge for the run time considered here.," As in runs G1 and G2, the running time average of the total torque per unit mass fails to converge for the run time considered here."737 However. he relative Ductuation amplitudes are smaller in this case eading to a smaller anticipated time for convergence.," However, the relative fluctuation amplitudes are smaller in this case leading to a smaller anticipated time for convergence."738 This is part of the trend for larger mass protoplanets to produce arecr amplitude perturbations that are more dillicult for he turbulence to allect., This is part of the trend for larger mass protoplanets to produce larger amplitude perturbations that are more difficult for the turbulence to affect.739" Η we consider the running mean of the total torque in igure 20. we can reasonably take a value of Tc—6 "".", If we consider the running mean of the total torque in figure \ref{fig21} we can reasonably take a value of ${\overline T} \simeq - 6 \times 10^{-6}$ .740 A byeve inspection of figure 19. indicates that the evel of Huctuation in the torques is opc10., A by–eye inspection of figure \ref{fig20} indicates that the level of fluctuation in the torques is $\sigma_T \simeq 4 \times 10^{-5}$.741 The xecdieted run time for convergence of the running mean from equation G is then =20. 30 planetary. orbits. which is shorter than for Gl or G2 and is comparable to the tine for which the simulation has been run.," The predicted run time for convergence of the running mean from equation \ref{T_av3} is then $\simeq 20$ – $30$ planetary orbits, which is shorter than for G1 or G2 and is comparable to the time for which the simulation has been run."742 Although it always corresponds to inward. migration. the non convergence of the running mean toward a well defined. value suggests that a simple picture of local turbulence in the vicinity of the planet. in which the state variables have well defined. mean values on top of which are superposed Buctuations with a well defined. Ciaussian spectrum. is not accurate.," Although it always corresponds to inward migration, the non convergence of the running mean toward a well defined value suggests that a simple picture of local turbulence in the vicinity of the planet, in which the state variables have well defined mean values on top of which are superposed fluctuations with a well defined Gaussian spectrum, is not accurate."743 Instead. it appears that the global nature of the disc plavs an important role in continuously mocdifving the local structure of the cise and turbulence.," Instead, it appears that the global nature of the disc plays an important role in continuously modifying the local structure of the disc and turbulence."744 Communication. between dillerent. regions of the cise can allect the local. properties such as the mean density. the amplitude. spatial. and temporal distribution of density anc velocity Ductuations over long time scales. such that a local running mean is problematic to define.," Communication between different regions of the disc can affect the local properties such as the mean density, the amplitude, spatial, and temporal distribution of density and velocity fluctuations over long time scales, such that a local running mean is problematic to define."745 An examination of the ¢obal properties of a turbulent. disc model. such as the global magnetic energy. (see c.g. papers LLL) show that there are short and longer time scale variations in the turbulence that reflect modifications to the local and global turbulence. and by implication the local dise structure.," An examination of the global properties of a turbulent disc model, such as the global magnetic energy (see e.g. papers I–III) show that there are short and longer time scale variations in the turbulence that reflect modifications to the local and global turbulence, and by implication the local disc structure."746 The results presented. in section 3.6. for the local shearing box simulations show smaller relative fluctuations and greater convergence of the mean torques toward the expected value. indicating that the global properties of turbulent. disces nmav play an important role by inducing longer time scale modilication to the local state of thediscin the vicinity of an embecdcded: protoplanet.," The results presented in section \ref{box-res}747 for the local shearing box simulations show smaller relative fluctuations and greater convergence of the mean torques toward the expected value, indicating that the global properties of turbulent discs may play an important role by inducing longer time scale modification to the local state of thediscin the vicinity of an embedded protoplanet."748then the radio torus aud the tail eud of the recent outburst experience the same cceree of shock deflection since both structures can be reearded as passive tracers of the post-sloclk velocity fied and hence provide a natural explanation for tle appzwent connectivity of both structures.,then the radio torus and the tail end of the recent outburst experience the same degree of shock deflection since both structures can be regarded as passive tracers of the post-shock velocity field and hence provide a natural explanation for the apparent connectivity of both structures.749 With this idea 1n nuid. we sketch a schematic of the time evolution 1n our nio delin Figure I..," With this idea in mind, we sketch a schematic of the time evolution in our model in Figure \ref{fig1}."750" The reason for the transformation of à plasmabub""n into a toroidal vortex ring cai beeasiest seen in the vest frame of the shock. where the rani pressure of the pre-shock gas balances the thermul pressure iu the post-shock regime."," The reason for the transformation of a plasma bubble into a toroidal vortex ring can be easiest seen in the rest frame of the shock, where the ram pressure of the pre-shock gas balances the thermal pressure in the post-shock regime."751 The bubbleis aled wit1i hot (velativistic) and more dilute plasma compared to the stromuding ICAL., The bubble is filled with hot (relativistic) and more dilute plasma compared to the surrounding ICM.752 Once the dilute radio plasima of thebubble comes iuto contact with the sliock surface. tle rain pressure ds reduced at this point of coutact ¢lue to he smaller deusity inside thebubble (?)..," Once the dilute radio plasma of the bubble comes into contact with the shock surface, the ram pressure is reduced at this point of contact due to the smaller density inside the bubble \citep{2002MNRAS.331.1011E}."753 The shock aid the post-shoc- eas expand into thebubble aru propagate with a faster velocity compared to the iucklent shock in the ICM., The shock and the post-shock gas expand into the bubble and propagate with a faster velocity compared to the incident shock in the ICM.754 Owing to svuunetry. the ambierit eas peuetrates the ux through the ceuter of the bubbe first and has a smaller velocity for larger napact paraiuecters.," Owing to symmetry, the ambient gas penetrates the line through the center of the bubble first and has a smaller velocity for larger impact parameters."755 This difference 1 propagation velocities 1uplies a shear flow aud evetually causes a vortex flow 1wound he newly foriucc torus which stabilizes it as it πιωνος row with the pos-shocX velocity field., This difference in propagation velocities implies a shear flow and eventually causes a vortex flow around the newly formed torus which stabilizes it as it moves now with the post-shock velocity field.756 To stuv the timescale on whicl this transformation happens. we the onuc-dieisonal BRicuaun problemli of: eshock passage through a upbuljble exactly iu Appendix D..," To study the timescale on which this transformation happens, we solve the one-dimensional (1D) Riemann problem of a shock passage through a bubble exactly in Appendix \ref{sec:Riemann}."757 These caleulatious are complemented ]o» a ste of two-dimensional (2D) axisviunietric slulations usine à code that euplovs an upwind. tota variation diminishing scheme to solve the lydrodvuamical equations of motion (7)..," These calculations are complemented by a suite of two-dimensional (2D) axisymmetric simulations using a code that employs an upwind, total variation diminishing scheme to solve the hydrodynamical equations of motion \citep{1998ApJ...509..244R}."758 To map out space. We varieL the Mach umuber aud initialparsmetorbubbleΤΟM. density coiitrast (see Figure 2. for one realization).," To map out parameter space, we varied the Mach number and initial bubble/ICM density contrast (see Figure \ref{fig:images} for one realization)."759 As a result. we Bud that an initially spheroidal bubbde will then evolve iuto a torus on a timescale Tori tiat is determined by the crossing time of the original 1ibbleICM. contact discontinuity (CD) through the bub|ble.," As a result, we find that an initially spheroidal bubble will then evolve into a torus on a timescale $\tau_\rmn{form}$ that is determined by the crossing time of the original bubble–ICM contact discontinuity (CD) through the bubble."760" For typical uuubers. Tg,21Pyy (Equation (D7)))."," For typical numbers, $\tau_\rmn{form}\simeq 1.4\times 10^8\,\rmn{yr}$ (Equation \ref{eq:tau_form}) ))."761 As we will «ce iu Section 5.. this is much faster than απ trausverse shear ou the scale of the bubble or DeyΌλα can act to distort it.," As we will see in Section \ref{sec:model}, this is much faster than any transverse shear on the scale of the bubble or beyond can act to distort it."762 The morpleogv of the radio torus is consistent witli AID simulations of this effect that assuue strong shocks (chFigs9andLOi| 7). ," The morphology of the radio torus is consistent with MHD simulations of this effect that assume strong shocks \citep[cf. Figs.~9 and 10763in][]{2002MNRAS.331.1011E}. ."764The relativistic plasma within the bubble οxperiences an adiabatic compresslon bv a C that increases the Loreitz factor of the relativis iccJectrous as TxCt5m aud tjo Tins luaenetic ποια as BXC?3, The relativistic plasma within the bubble experiences an adiabatic compression by a $C$ that increases the Lorentz factor of the relativistic electrons as $\Gamma\propto C^{1/3}$ and the rms magnetic field as $B\propto C^{2/3}$.765 Ileuce the radio ciΠο of a cooled electrou pomulation icreases aS Maux*BY?xci!3; aud illuninites a previously unobservade radio plasia (Ty. ," Hence the radio cutoff of a cooled electron population increases as $\nu_\rmn{max}\propto B \Gamma^2\propto766C^{4/3}$ and illuminates a previously unobservable radio plasma \citep{2001A&A...366...26E}. ."767"Sviclirotron and inverse Compton aging develops a steep spectim with spectral index a~2 aud a low surface Damifuess S5,xva", Synchrotron and inverse Compton aging develops a steep spectrum with spectral index $\alpha\sim2$ and a low surface brightness $S_\nu\propto\nu^{-\alpha}$.768 The ealaxv itself reinaius on a ballistic orbit that is unaffectec |]»* the shock passage that likely trigecrs a new outflow that is now seen as a head-tail radio elulss10n wih the jets being beut by the ram pressure wiud., The galaxy itself remains on a ballistic orbit that is unaffected by the shock passage that likely triggers a new outflow that is now seen as a head-tail radio emission with the jets being bent by the ram pressure wind.769 The asociated. compression wave propagating the iutersellar medium could have triggered ongbar-like iusabitv in the πιο aceretion disk that rabled efficieut aneular monieutuun transport outward id accretion outo he supermassiveblack hole (SMDIT) which was res»ouside for launching the spectraljet., The associated compression wave propagating through the interstellar medium could have triggered a bar-like instability in the inner accretion disk that enabled efficient angular momentum transport outward and accretion onto the super-massive black hole (SMBH) which was responsible for launching the jet.770 This iodel ex]aus the observed steepeniug of the heac-tail radio galaxy of Aa0.5 due to radiative cooπιο along the bright partof the tail., This model explains the observed spectral steepening of the head-tail radio galaxy of $\Delta \alpha \simeq 0.5$ due to radiative cooling along the bright partof the tail.771 Iun particular.Olr model nuaturallv accounts for the observed. sudCll steepeuimg of the spectral iudex aud," In particular,our model naturally accounts for the observed sudden steepening of the spectral index and"772wwas observed with Chandra in 2007 March 4—5 with the Advanced CCD Imaging Spectrometer (ACIS) using a frame time of 3.2 s. We utilized the whole ACIS-I CCD array to obtain an image of the remnant.,was observed with Chandra in 2007 March $4-5$ with the Advanced CCD Imaging Spectrometer (ACIS) using a frame time of 3.2 s. We utilized the whole ACIS-I CCD array to obtain an image of the remnant.773 The data were reprocessed on 2007 August 7 in order to correct for a systematic aspect offset of ~0.47. possibly caused by a changing thermalvironment!.," The data were reprocessed on 2007 August 7 in order to correct for a systematic aspect offset of $\sim0.4""$, possibly caused by a changing thermal."774. The total observing time on source was ~29 ks., The total observing time on source was $\sim29$ ks.775 Examining the data for times of high background we noticed that the observation was affected by soft-proton flares., Examining the data for times of high background we noticed that the observation was affected by soft-proton flares.776 Cleaning the data by removing these flares from the data led to an effective exposure time of ~2] ks., Cleaning the data by removing these flares from the data led to an effective exposure time of $\sim21$ ks.777 The analysis was performed in the 0.5—8 keV energy band., The analysis was performed in the $0.5-8$ keV energy band.778 A false color image of the ACIS-I data of iis displayed in Figure 2., A false color image of the ACIS-I data of is displayed in Figure 2.779 Comparing the X-ray image with the radio contours obtained from the 1.4 GHz NVSS data (Condon et al., Comparing the X-ray image with the radio contours obtained from the 1.4 GHz NVSS data (Condon et al.780 1998) shows that the X-ray emission is entirely enclosed in the radio are-like structure (see Figure 3)., 1998) shows that the X-ray emission is entirely enclosed in the radio arc-like structure (see Figure 3).781 The center-filled X-ray emission and the radio shell-like morphology suggest bbelongs to the category of “mixed-morphology™ SNRs (Rho Petre 1998).," The center-filled X-ray emission and the radio shell-like morphology suggest belongs to the category of “mixed-morphology"" SNRs (Rho Petre 1998)."782 We have searched for the point sources in the whole ACIS- data by means of the wavelet source detection algorithm and found 36 sources., We have searched for the point sources in the whole ACIS-I data by means of the wavelet source detection algorithm and found 36 sources.783 These sources are marked by circles in Figure 2., These sources are marked by circles in Figure 2.784 The limiting count rate of the search was 1077 ets/s. The source positions. positional errors. signal-to- ratios as well as the estimates of extent of all these 36 sources are given in Table |.," The limiting count rate of the search was $2\times10^{-4}$ cts/s. The source positions, positional errors, signal-to-noise ratios as well as the estimates of extent of all these 36 sources are given in Table 1."785 Cross-correlating these sources with the SIMBAD and NED databases did not result in any identification withir a search radius of 5 aresec around each source., Cross-correlating these sources with the SIMBAD and NED databases did not result in any identification within a search radius of 5 arcsec around each source.786 Twelve of these newly detected sources are located within the supernova remnant., Twelve of these newly detected sources are located within the supernova remnant.787 Four point-like sources. labeled in Figure 2 with the numbers #99. #110. #111 and #335 are located within. ~1.5 aremin of the geometrical remnant center.," Four point-like sources, labeled in Figure 2 with the numbers 9, 10, 11 and 35 are located within $\sim1.5$ arcmin of the geometrical remnant center."788 Source 7111 is the brightest among them., Source 11 is the brightest among them.789 Hereafter. we designate this source asCXOU195422.," Hereafter, we designate this source as."79097+312902.1.. It is also interesting to notice a trail-like radio feature close to the remnant center which has one end apparently coincide with source #110 (cf., It is also interesting to notice a trail-like radio feature close to the remnant center which has one end apparently coincide with source 10 (cf.791 Figure 3)., Figure 3).792 We designate it asCXOU195424., We designate it as.793754+312824.9.. This source appears to be slightly extended. which is also suggested by the ratio between its extent and the estimated PSF size (cf.," This source appears to be slightly extended, which is also suggested by the ratio between its extent and the estimated PSF size (cf."794 Table 1)., Table 1).795 However. the low significance level of the detection and the patchy envirnoment of the remnant emission do not allow one to determine if iis intrinsically extended.," However, the low significance level of the detection and the patchy envirnoment of the remnant emission do not allow one to determine if is intrinsically extended."796 In the false colour image. source #335 appears to have the hardest X-ray emission among these four central point sources (see Figure 2).," In the false colour image, source 35 appears to have the hardest X-ray emission among these four central point sources (see Figure 2)."797 We designate this source as hhereafter., We designate this source as hereafter.798 Before we have extracted the remnant spectra. all point-like sources were removed.," Before we have extracted the remnant spectra, all point-like sources were removed."799 The spectra were then extracted from the elliptical-shaped regions illustrated in Figure 4., The spectra were then extracted from the elliptical-shaped regions illustrated in Figure 4.800 These regions cover both the northern and the southern radio shells., These regions cover both the northern and the southern radio shells.801 The background spectra for the corresponding CCD chips were extracted from the boxed regions marked in Figure 4., The background spectra for the corresponding CCD chips were extracted from the boxed regions marked in Figure 4.802 We utilized the tool SPECEXTRACT in the data reduction package CIAO 3.4.1 with the calibration data CALDB 3.4.1 to extract the spectra and to compute the response files., We utilized the tool SPECEXTRACT in the data reduction package CIAO 3.4.1 with the calibration data CALDB 3.4.1 to extract the spectra and to compute the response files.803 After background subtraction there are 1028 and 610 net counts avaliable for the spectral analysis of the northern rim (1.e.the sum of two northern elliptical regions) and southern rim (i.e. the sum of two southern elliptical regions). respectively.," After background subtraction there are 1028 and 610 net counts avaliable for the spectral analysis of the northern rim (i.e.the sum of two northern elliptical regions) and southern rim (i.e. the sum of two southern elliptical regions), respectively."804 The background contributions are found to be ~60% in both. the northern and," The background contributions are found to be $\sim60\%$ in both, the northern and"805spectrum for KK2000-06 measured with the Effelsberg 100-m radio telescope (7) suggests a heliocentric velocity of ~2250kkmss~!.,spectrum for KK2000-06 measured with the Effelsberg 100-m radio telescope \citep{huchtmeier01} suggests a heliocentric velocity of $\sim$ $^{-1}$.806 Therefore it is possible that KK2000-04 is a plate flaw and KK2000-06 is a distant galaxy unrelated to NGC1313., Therefore it is possible that KK2000-04 is a plate flaw and KK2000-06 is a distant galaxy unrelated to NGC1313.807 The extremely low surface brightness dwarf galaxy NGC2784 DWI was first detected by ?.., The extremely low surface brightness dwarf galaxy NGC2784 DW1 was first detected by \cite{parodi02}.808" It is located between the SO galaxy NGC2784 and the nucleated early-type dwarf KK98-73 on the sky and due to its morphology its size and location, ? suggest it is likely to be (dE),satellite of NGC2784."," It is located between the S0 galaxy NGC2784 and the nucleated early-type dwarf KK98-73 on the sky and due to its morphology (dE), its size and location, \cite{parodi02} suggest it is likely to be a satellite of NGC2784."809 ? give NGC2784 DW1 a membershipa distance and include it in the census of galaxies within 10 Mpc., \cite{karachentsev04} give NGC2784 DW1 a membership distance and include it in the census of galaxies within 10 Mpc.810" However, it is important to note that no independent distance measurement has been obtained to date."," However, it is important to note that no independent distance measurement has been obtained to date."811" Our deep near-IR observation detected the faint galaxy KK98-73, while NGC2784 DW1 is barely visible as expected from the recorded mean effective surface brightness of (u)egg©25mmagaarcsec ? and Treff© 20aarcsec in the B-band."," Our deep near-IR observation detected the faint galaxy KK98-73, while NGC2784 DW1 is barely visible as expected from the recorded mean effective surface brightness of $\langle \mu\rangle_{eff}\approx25$ $^{-2}$ and $r_{eff}\approx 20$ arcsec in the $B$ -band."812 It is instructive to see how galaxies can change their appearance when going from 2MASS to the deeper LSI observations., It is instructive to see how galaxies can change their appearance when going from 2MASS to the deeper LSI observations.813" For example, our image of the barred Sc galaxy NGC2835 (Fig. [12))"," For example, our image of the barred Sc galaxy NGC2835 (Fig. \ref{fig:2mass}) )"814 reveals the rich near-IR morphology and extent of this spiral galaxy for the first time., reveals the rich near-IR morphology and extent of this spiral galaxy for the first time.815" The almost face-on view presents a well-ordered 4 or 5-arm spiral pattern outlined by the star-dominated Population II disk, which closely traces the gas-dominated Population I disk morphology observed in the B-band "," The almost face-on view presents a well-ordered 4 or 5-arm spiral pattern outlined by the star-dominated Population II disk, which closely traces the gas-dominated Population I disk morphology observed in the $B$ -band \citep{sandage94}."816The 2MASS image for the irregular Sculptor group (?).galaxy ESO473-G024 shows qualitatively the limitation of that survey to study dwarf galaxies., The 2MASS image for the irregular Sculptor group galaxy ESO473-G024 shows qualitatively the limitation of that survey to study dwarf galaxies.817" With a central H-band surface brightness of ~20.5 aarcsec~*, ESO473-G024 remains effectively undetected in 2MASS (Fig. "," With a central $H$ -band surface brightness of $\approx 20.5$ $^{-2}$, ESO473-G024 remains effectively undetected in 2MASS (Fig. \ref{fig:2mass}) )."818"Our image uncovers a smooth, dE-like morphology [I2)).with little evidence of irregularity."," Our image uncovers a smooth, dE-like morphology with little evidence of irregularity."819 T'his stands in stark contrast to the B-band image that is dominated by a number of prominent regions and dust features., This stands in stark contrast to the $B$ -band image that is dominated by a number of prominent regions and dust features.820" It has been previously pointed out by ? that the short integration time of 2M failed to detect most of the lower surface brightness ASS(dwarf) galaxies and that, if they were detected, fluxes were underestimated by as much as 70 percent."," It has been previously pointed out by \cite{andreon02} that the short integration time of 2MASS failed to detect most of the lower surface brightness (dwarf) galaxies and that, if they were detected, fluxes were underestimated by as much as 70 percent."821" To investigate this issue further, we plot in Figure the difference between our total extrapolated apparent magnitudes (m,oys—Am; Table 3, col."," To investigate this issue further, we plot in Figure \ref{fig:comp} the difference between our total extrapolated apparent magnitudes $m_{H,obs}-\Delta m$; Table 3, col."822" 2 and Table 4, col 6) and the total magnitudes from the 2MASS All-Sky Extended Source Catalog for 21 galaxies we have in common, as a function of mean effective surface brightness ((ugr)e; Table 3, col."," 2 and Table 4, col 6) and the total magnitudes from the 2MASS All-Sky Extended Source Catalog for 21 galaxies we have in common, as a function of mean effective surface brightness $\langle\mu_H \rangle_{eff}$; Table 3, col."823 4)., 4).824 LSI galaxies with a surface brightness rs;fainter than wy=18 magaarcsec are affected at different levels with the missing flux ?in the range between 0.2 and mmag., LSI galaxies with a surface brightness fainter than $\mu_{H}=18$ ${}^{-2}$ are affected at different levels with the missing flux in the range between 0.2 and mag.825 Even in the cases of the luminous galaxies NGC2784 and NGC3115 our analysis finds that their 2MASS H-band magnitudes are mmag too faint., Even in the cases of the luminous galaxies NGC2784 and NGC3115 our analysis finds that their 2MASS $H$ -band magnitudes are mag too faint.826 'To demonstrate that the disparity between the 2MASS and our H-band magnitudes is not caused by differences in the measuring procedure we analysed 2MASS images using our method., To demonstrate that the disparity between the 2MASS and our $H$ -band magnitudes is not caused by differences in the measuring procedure we analysed 2MASS images using our method.827" The photometric parameters listed in the 2MASS Extended Source Catalog, as well as the surface brightness profiles, were reproduced within the quoted uncertainties."," The photometric parameters listed in the 2MASS Extended Source Catalog, as well as the surface brightness profiles, were reproduced within the quoted uncertainties."828 It should be noted that the 2MASS Large Galaxy Atlas (?) has employed two different methods for recovering the flux below the sky background, It should be noted that the 2MASS Large Galaxy Atlas \citep{jarrett03} has employed two different methods for recovering the flux below the sky background829"Observations of many star-forming galaxies show that a common mode of star formation involves the production of voung massive star clusters (or ""super star clusters”). which mieht have masses [ewx10?AZ. with hall-mass radii of slew pe (e.g.. van den Bergh 1971 and numerous subsequent papers; see Mafzz-Appellánniz 2001 for a review of the structural parameters of such clusters).","Observations of many star-forming galaxies show that a common mode of star formation involves the production of young massive star clusters (or “super star clusters""), which might have masses $\sim$ $\times83010^5\,M_\odot$ with half-mass radii of $\sim$ few pc (e.g., van den Bergh 1971 and numerous subsequent papers; see Maízz-Appellánniz 2001 for a review of the structural parameters of such clusters)."831 According to recent N-bocly simulations (Ebisuzaki et al., According to recent N-body simulations (Ebisuzaki et al.832 2001: Portegies Zwart, 2001; Portegies Zwart833with aud The matter power spectrmn. P(A). can be defined via the two-point correlation function im Fourier space as where 85 is the 3-dimensional Dirac delta fuuction.,"with and The matter power spectrum, $P(k)$, can be defined via the two-point correlation function in Fourier space as where $\delta_D$ is the 3-dimensional Dirac delta function."834 In linear perturbation theory. it is usually assumed that iuflatiou laid down an initial spectrum of the form ην where ny is the scalar spectral iudex (assunued to be 0.96 in this work).," In linear perturbation theory, it is usually assumed that inflation laid down an initial spectrum of the form $k^{n_s}$, where $n_s$ is the scalar spectral index (assumed to be 0.96 in this work)."835 Physical processes which evolve P(A) through the various cosmological epochs cau simply be condensed ito the equation where PG)x, Physical processes which evolve $P(k)$ through the various cosmological epochs can simply be condensed into the equation where $P_\phi(k)\propto k^{n_s-4}$.836VI Tis also common to define the dimensionless power spectrum P(A) as Cousequeutly. the variance of deusitv fiuctuatious snoothed ou scale R can be written as 5odose Daepees ecwhereto .. Iu our numerical work. we shall uoxinalise P(A) so that The most widely studied type of is the ‘local’ type parametrized. at lowest orders. bv fxp aud gxr. which are the coefficients in the Taylor expansion of the non-linear Newtouian potential. 9. in terms of the linear. Gaussian field. o. Pi(x))= This form of nou-Caussianity arises insimple models of suele aud multiπαα inflation (277) as well as some curvaton models (27)..," It is also common to define the dimensionless power spectrum $\mc{P}(k)$ as Consequently, the variance of density fluctuations smoothed on scale $R$ can be written as ^2_R= A^2(k) where A(k)= ^2 W(kR) D(0) In our numerical work, we shall normalise $\mc{P}(k)$ so that The most widely studied type of is the `local' type parametrized, at lowest orders, by $\fnl$ and $\gnl$, which are the coefficients in the Taylor expansion of the non-linear Newtonian potential, $\Phi$, in terms of the linear, Gaussian field, $\phi$, )= This form of non-Gaussianity arises insimple models of single and multi-field inflation \citep{bartolo,rigopoulos,byrnes} as well as some curvaton models \citep{bartolo2,sasaki}."837 In this work. we shall assuuie non-Caussianity only of this form.," In this work, we shall assume non-Gaussianity only of this form."838 In ecueral. it is possible that nou-Cassiaty may be non-local.," In general, it is possible that non-Gaussianity may be non-local."839 Mechanisiis such as DBI inflation (7). or inflation with a non-standard Lagrangian (?7) are known to generate primarily non-local non-Causssianity.," Mechanisms such as DBI inflation \citep{alishahiha} or inflation with a non-standard Lagrangian \citep{arkani-hamed,chen3} are known to generate primarily non-local non-Gausssianity."840 We coment on these possibilities later. but leave a full investigation for future work.," We comment on these possibilities later, but leave a full investigation for future work."841 We adopt the ‘larec-scale-structire’ couvention in which d is extrapolated to += 0., We adopt the `large-scale-structure' convention in which $\Phi$ is extrapolated to $z=0$ .842 We also take fxj and gxp to be constant. although it is conceivable that they may be scale dependent (see ?? for constraints on the runuiug of fxp).," We also take $\fnl$ and $\gnl$ to be constant, although it is conceivable that they may be scale dependent (see \cite{sefusatti,cayon} for constraints on the `running' of $\fnl$ )."843" In this section. we investigate how this form of is related to the reduced eiunuulauts. S,. defined by "," In this section, we investigate how this form of is related to the reduced cumulants, $S_n$ , defined by (R)"844" can still radiate, though in it contributes little to the gasoverall emission due to the large practiceradial velocities it develops.","gas can still radiate, though in practice it contributes little to the overall emission due to the large radial velocities it develops."845" In the case of the thermal the radial structure was taken from ?,, and the vertical quantitiesstructure was determined by that the disk is to p."," In the case of the thermal quantities the radial structure was taken from \citet{Yuan-Quat-Nara:03}, and the vertical structure was determined by assuming that the disk height is comparable to $\rho$."846 Note that all of the assumingmodels we employ heightnecessarily have comparablethe spin aligned with the orbital momentum of the accretion flow., Note that all of the models we employ necessarily have the spin aligned with the orbital angular momentum of the accretion flow.847" For the regions that angulardominate the mm emission, this assumption is well due to disk and viscous torques, though it may be justifiedviolated at large precessiondistances."," For the regions that dominate the $\mm$ emission, this assumption is well justified due to disk precession and viscous torques, though it may be violated at large distances."848 Thermal electrons alone are incapable of the nearly-flat spectrum of Sgr A* below 43GHz.," Thermal electrons alone are incapable of reproducing the nearly-flat spectrum of Sgr A* below $43\,\GHz$."849 Thus reproducingit is necessary to also include a nonthermal component., Thus it is necessary to also include a nonthermal component.850" As with the thermal components, we adopt a self-similar model for a population of nonthermal electrons, with a power-law distribution corresponding to a spectral index of 1.25 and cut off below Lorentz factors of 10? (consistentwith?).."," As with the thermal components, we adopt a self-similar model for a population of nonthermal electrons, with a power-law distribution corresponding to a spectral index of $1.25$ and cut off below Lorentz factors of $10^2$ \citep[consistent with851][]{Yuan-Quat-Nara:03}."852" The radial power-law index was chosen to reproduce the low frequency spectrum of Sgr A*, and is insensitive to the black hole properties due to the distant location of the long-wavelength emission."," The radial power-law index was chosen to reproduce the low frequency spectrum of Sgr A*, and is insensitive to the black hole properties due to the distant location of the long-wavelength emission."853 The primary emission mechanism at the wavelengths of, The primary emission mechanism at the wavelengths of854"runs at Το»10? K. Thus baryonic infall onto newly formed halos can commence when T,z10? K. Since the IGM is cooler in the rrun, gas there gets a “head-start” in accreting onto DM halos.","runs at $T\sim10^3$ K. Thus baryonic infall onto newly formed halos can commence when $\Tvir \gsim 10^3$ K. Since the IGM is cooler in the run, gas there gets a “head-start” in accreting onto DM halos."855" However, as is evident in the figure, the enhanced H» cooling channel in the rrun allows the gas to quickly catch-up and surpass its twin in the rrun."," However, as is evident in the figure, the enhanced $_2$ cooling channel in the run allows the gas to quickly catch-up and surpass its twin in the run."856" Thus by redshift z—14, the halo has formed CD gas in the rrun, but not in the rrun."," Thus by redshift $z=14$, the halo has formed CD gas in the run, but not in the run."857 How does adding a LWB impact this positive feedback?, How does adding a LWB impact this positive feedback?858" From Fig. 4,,"," From Fig. \ref{fig:LW_delta},"859" we have already surmised that a background intensity of JANνὰ10” can offset these trends by decreasing the enhanced Hg fraction in 3,relic HII regions."," we have already surmised that a background intensity of $\Jlwb\gsim10^{-3}$, can offset these trends by decreasing the enhanced $_2$ fraction in relic HII regions."860" In Fig. 8,,"," In Fig. \ref{fig:LW3NoUVB_vs_LW3Heat},"861 we plot profiles from the same halo in the curves) and curves)., we plot profiles from the same halo in the ) and ).862 By comparing the solid curves from Fig., By comparing the solid curves from Fig.863" 7 to the dashed curves from Fig. 8,,"," \ref{fig:NoUVB_vs_Heat} to the dashed curves from Fig. \ref{fig:LW3NoUVB_vs_LW3Heat},"864 one confirms that a LWB with JEN~10 effectively neutralizes the positive feedback from the transient UVB., one confirms that a LWB with $\Jlwb\sim10^{-3}$ effectively neutralizes the positive feedback from the transient UVB.865? Thus at z=14 the halo core has a similar gas profile and cooling time in the aand rruns., Thus at $z=14$ the halo core has a similar gas profile and cooling time in the and runs.866" By comparing the two profiles at z=14 in Fig. δ.,"," By comparing the two profiles at $z=14$ in Fig. \ref{fig:LW3NoUVB_vs_LW3Heat},"867" we see that the transient UVB still stimulates positive feedback,but the effect is not nearly as dramatic."," we see that the transient UVB still stimulates positive feedback,but the effect is not nearly as dramatic."868" Specifically, in the halo core at z—14 the density is enhanced and the cooling time is lowered (both by a factor of ~ 2) in the rrun compared to the rrun."," Specifically, in the halo core at $z=14$ the density is enhanced and the cooling time is lowered (both by a factor of $\sim2$ ) in the run compared to the run."869" This level of positive3 feedback is much more modest compared with the case with no LWB, where the equivalent density enhancement was a factor of ~50 and the cooling time was lower by a factor of ~15 (see Fig. 7))."," This level of positive feedback is much more modest compared with the case with no LWB, where the equivalent density enhancement was a factor of $\sim50$ and the cooling time was lower by a factor of $\sim15$ (see Fig. \ref{fig:NoUVB_vs_Heat}) )."870 Does this trend continue as we increasethe strength of the UVB?, Does this trend continue as we increasethe strength of the UVB?871" In Fig. 9,"," In Fig. \ref{fig:LW2NoUVB_vs_LW2Heat},"872" the solid and dashed curves correspond to the aand rruns at z=14, _Heat0.8respectively; similarly in Fig. 10,,"," the solid and dashed curves correspond to the and runs at $z=14$, respectively; similarly in Fig. \ref{fig:LW1NoUVB_vs_LW1Heat},"873" the solid and dashed curves correspond to the aand rruns at z—14, respectively."," the solid and dashed curves correspond to the and runs at $z=14$, respectively."874" Here we see that the core density in the rrun is lower than in the rrun, but the cooling time islower by the same factor of seen in Fig. 8,,"," Here we see that the core density in the run is lower than in the run, but the cooling time is by the same factor of $\sim2$ seen in Fig. \ref{fig:LW3NoUVB_vs_LW3Heat},"875 sourced by the enhanced He fraction., sourced by the enhanced $_2$ fraction.876" In fact, from higher redshift output and the previous figures, we see that the density is still “catching up"" as time progresses; namely, the dashed density curve keeps getting closer to the solid density curve."," In fact, from higher redshift output and the previous figures, we see that the density is still “catching up” as time progresses; namely, the dashed density curve keeps getting closer to the solid density curve."877 Thus we see thathalo., Thus we see that.878" It is important to note that in this regime where a strong LWB dominates the overall feedback, star formation is likely to be substantially delayed."," It is important to note that in this regime where a strong LWB dominates the overall feedback, star formation is likely to be substantially delayed."879" This delay can be long enough to allow the halo to be photoevaporated during reionization, before it had a chance to host additional stars."," This delay can be long enough to allow the halo to be photoevaporated during reionization, before it had a chance to host additional stars."880" Thus if one is only concerned with the fate of those minihalos contributing their ionizing photons to the progress of reionization, it is possible that the sole persistent feedback mechanism is positive."," Thus if one is only concerned with the fate of those minihalos contributing their ionizing photons to the progress of reionization, it is possible that the sole feedback mechanism is ."881" As we have noted a number of times in this paper, our simulations"," As we have noted a number of times in this paper, our simulations"882non-linear outcome of the iustabilitv could iustead lead to strong Comptonization of the disk 2001).,non-linear outcome of the instability could instead lead to strong Comptonization of the disk .883.. Nonetheless. the aremmeuts above preclude an alpha type stress. at least below 7~0.5. vet the very high state is indeed secu in the same range m bununositv as the disk dominated state2006).," Nonetheless, the arguments above preclude an alpha type stress, at least below $l\sim 0.5$, yet the very high state is indeed seen in the same range in luminosity as the disk dominated state."884". At higher luuinosities2001).. there is a limit evele observed in GRS1915|LOL which could be the reumant of this radiation pressure instability frou, a mmareinally stable stress such as predicted with the mean disk2006)."," At higher luminosities, there is a limit cycle observed in GRS1915+104 which could be the remnant of this radiation pressure instability from a marginally stable stress such as predicted with the mean disk."885. Tlowever. this hint evele behavior could alternatively be from other mstabilifies to do with the super Eddington flows.," However, this limit cycle behavior could alternatively be from other instabilities to do with the super Eddington flows."886 This is au important distinction. as the classic radiation pressure instability is not scale invariant with mass. but is triggered at /x(6.17.," This is an important distinction, as the classic radiation pressure instability is not scale invariant with mass, but is triggered at $l\propto m^{-1/8}$."887" Thus even if the disk is stable in stellar mmass black holes up to P~0.5. it can be unstable at 120.09 for a 10*AF, ACN,"," Thus even if the disk is stable in stellar mass black holes up to $l\sim 0.5$, it can be unstable at $l\gtrsim 0.09$ for a $10^7 \msun$ AGN."888" Iu this case the instability could play a role iu producing he puzzling. soft excess’ seen in high mass accretion rate AGN, predominantly Narrow Line Sevfert Ls2002)."," In this case the instability could play a role in producing the puzzling, 'soft excess' seen in high mass accretion rate AGN, predominantly Narrow Line Seyfert 1's."889. ITowever. there are uultiple similaritics between the very high state and Narrow Line Sevfert 1 spectra to make it more likely that here is a similar explanation for both types of object.," However, there are multiple similarities between the very high state and Narrow Line Seyfert 1 spectra to make it more likely that there is a similar explanation for both types of object."890 Siuiluly. those properties of super Eddington flows which likewise depend ou the alpha stress are also xobablv not a realistic description of these disks.," Similarly, those properties of super Eddington flows which likewise depend on the alpha stress are also probably not a realistic description of these disks."891 Radiation trapping is a generic feature of anv of the stress prescriptions1991).. resulting in optically thick advection of energv especially in the disk anidplane2001).," Radiation trapping is a generic feature of any of the stress prescriptions, resulting in optically thick advection of energy especially in the disk midplane."892. Ilowever. the denser disks which result from the alternative stress prescriptions are less likely to become effectively optically thin to the escaping radiation. so are unlikely to show the very large color-temperature correction which can arise from overheating of alpha disks2003).," However, the denser disks which result from the alternative stress prescriptions are less likely to become effectively optically thin to the escaping radiation, so are unlikely to show the very large color-temperature correction which can arise from overheating of alpha disks."893. We caution that fitting such models to hieh mass accretion rate spectra from ULN aud NELSIs may not be appropriate., We caution that fitting such models to high mass accretion rate spectra from ULX and NLS1's may not be appropriate.894 So what then are the caveats to using disk spectra as an estimator for black hole spin?, So what then are the caveats to using disk spectra as an estimator for black hole spin?895 The first is that the spectramist be disk dominated., The first is that the spectra be disk dominated.896 The disk radius cau be under or overestimated when a substantial fraction of the dissipation goes instead into a corona. either in the very high or low/harcd state (GDPOS).," The disk radius can be under – or overestimated when a substantial fraction of the dissipation goes instead into a corona, either in the very high or low/hard state (GDP08)."897 This may be the origin of the discrepancy in spin determination by disk spectral fitting in GRS 1915|1012006)., This may be the origin of the discrepancy in spin determination by disk spectral fitting in GRS 1915+104.898. The spectra ofCRS 1915|10 παν well be more complex than the disk dominated spectra seen frou. DIID due to its higher πιουναν200L).. perhaps powerluge strong winds (see below).," The spectra of GRS 1915+104 may well be more complex than the disk dominated spectra seen from BHB due to its higher luminosity, perhaps powering strong winds (see below)."899 It seclus premature to apply the wncertaintics from this one wathological object to other sub-Ecddinetou BOB2008)., It seems premature to apply the uncertainties from this one pathological object to other sub-Eddington BHB.900. Secoudly. the value of the color-teniperature correction is robust for all of the dense disk stress prescriptions. mt varies with bandpass aud also varies with the detailed disk model used to fit the spectra.," Secondly, the value of the color-temperature correction is robust for all of the dense disk stress prescriptions, but varies with bandpass and also varies with the detailed disk model used to fit the spectra."901 We caution hat differences in spectral shape between the models neaus that the same color-teniperature correction actorscannot bo simply| applied to aud fits., We caution that differences in spectral shape between the models means that the same color-temperature correction factors be simply applied to and fits.902 Ironically. for both the ecneric proportional counter and CCD bancdpasses. the fits eive a siupler (approxiuatelv coustant color teniperaturo) represcutation of the cata.," Ironically, for both the generic proportional counter and CCD bandpasses, the fits give a simpler (approximately constant color temperature) representation of the data."903 Thirdly. the structure of the disk as 7»1 is not well modeled by this code.," Thirdly, the structure of the disk as $l\to 1$ is not well modeled by this code."904 We neglect optically thick advection. and changes in the scale height of the disk witli radius which may lead to self shiclding for highly inclined objects2005).. but these are uulikely to have much. effect for 7<0.5. where the majority of DIID data are taken.," We neglect optically thick advection, and changes in the scale height of the disk with radius which may lead to self shielding for highly inclined objects, but these are unlikely to have much effect for $l<0.5$, where the majority of BHB data are taken."905 However. disks at high buninosities are likely to," However, disks at high luminosities are likely to"906hundred vears ago. but is svaumetrie now. the OII and [sO observations could be reconciled with the intrinsic asvinmeltry scenario.,"hundred years ago, but is symmetric now, the OH and $_2$ O observations could be reconciled with the intrinsic asymmetry scenario."907 One possible explanation lor a change in the distribution of water vapor over such a relatively short timescale involves the time dependence of (he stellar mass loss rate., One possible explanation for a change in the distribution of water vapor over such a relatively short timescale involves the time dependence of the stellar mass loss rate.908 The circumstellar envelope of IRC+10216 contains multiple dust shells which are the result of episodic mass loss., The circumstellar envelope of IRC+10216 contains multiple dust shells which are the result of episodic mass loss.909 Detailed images of these shells by AManuron Lueeis (1999. 2000). show that the shells are incomplete - they are arcs rather than rings.," Detailed images of these shells by Mauron Huggins (1999, 2000), show that the shells are incomplete - they are arcs rather than rings."910" Additionally. the dust distribution in the innermost regions of the envelope (7<15"") is an extremely asvmmetric bipolar outflow."," Additionally, the dust distribution in the innermost regions of the envelope $r\lesssim 15^{\prime \prime}$ ) is an extremely asymmetric bipolar outflow."911 The timescale on which these dust shells are produced is of order a few hundred vears., The timescale on which these dust shells are produced is of order a few hundred years.912 A new mass loss study by Fong. Meisner Shah (2003) demonstrates that mass loss in IRC+10216 has been ongoing for at least 7000 vears and that mass loss occurred in aclumnpy and asymmetric fashion.," A new mass loss study by Fong, Meixner Shah (2003) demonstrates that mass loss in IRC+10216 has been ongoing for at least $7000\,$ years and that mass loss occurred in a clumpy and asymmetric fashion."913 Rapicl variations in (he mass loss rate are also possible: recent. high-resolution IR images show dust distribution asvnunetries on size scales as small as tens of milliarcseconcds and imply mass loss variations on timescales of vears (Tuthill et al., Rapid variations in the mass loss rate are also possible; recent high-resolution IR images show dust distribution asymmetries on size scales as small as tens of milliarcseconds and imply mass loss variations on timescales of years (Tuthill et al.914 2000: Weigelt et al., 2000; Weigelt et al.915 2002: Menshehikov. Hofmann Weigelt 2002).," 2002; Men'shchikov, Hofmann Weigelt 2002)."916 Ford Neuleld (2001) showed that the vaporization of water [rom iev bodies orbiting IRC+10216 is sensitively dependent on the stellar flux. impinging on an 1ον body., Ford Neufeld (2001) showed that the vaporization of water from icy bodies orbiting IRC+10216 is sensitively dependent on the stellar flux impinging on an icy body.917" Since the dust distribution is highly asvnunetric. the luminosity of the central star will ""leak"" ont in an asvinmetric and probably quite patchy pattern. after multiple scatterings and dust absorption ancl"," Since the dust distribution is highly asymmetric, the luminosity of the central star will “leak” out in an asymmetric and probably quite patchy pattern, after multiple scatterings and dust absorption and re-emission."918 Thus. the flix iupingine on different icy bodies at (he same astrocentric radius will nol be necessarily be the same: it will depend on (he particular geometry of radiation leakage through the circumstellar dust.," Thus, the flux impinging on different icy bodies at the same astrocentric radius will not be necessarily be the same; it will depend on the particular geometry of radiation leakage through the circumstellar dust."919 Therefore. the water vaporization rate [from the surlace of a particular ον body. (ancl the distribution of water vapor in the circeumstellar outflow) will depend very substantially on the time varving dust distribution in the circumstellar outflow.," Therefore, the water vaporization rate from the surface of a particular icy body (and the distribution of water vapor in the circumstellar outflow) will depend very substantially on the time varying dust distribution in the circumstellar outflow."920 Note that (his scenario is still capable of producing the water line profile observed by Melnick et al. (, Note that this scenario is still capable of producing the water line profile observed by Melnick et al. (9212001).,2001).922 1Η (he water vapor is more or less off to one side of the star (Irom a terrestrial observers perspective). there will be roughly equal amounts of material coming toward us and moving away [from us. still vielding a roughly svannmetrice profile.," If the water vapor is more or less off to one side of the star (from a terrestrial observer's perspective), there will be roughly equal amounts of material coming toward us and moving away from us, still yielding a roughly symmetric profile."923 Additionally. since the water line is optically thick. it is probable that some clumpiness or patchiness in the water distribution would be smoothed out in the line prolile.," Additionally, since the water line is optically thick, it is probable that some clumpiness or patchiness in the water distribution would be smoothed out in the line profile."924 We have detected the 1665 and 1667 MIIz lines of OIL in emission towards the AGB star IRC+10216.," We have detected the $1665$ and $1667\,$ MHz lines of OH in emission towards the carbon-rich AGB star IRC+10216."925 This detection supports the identification of the 556.936 GIIz emission detected toward IRC+10216 by Melniek et al. (," This detection supports the identification of the $556.936\,$ GHz emission detected toward IRC+10216 by Melnick et al. ("926"2001) with the 144—Ip, transition of",2001) with the $1_{10}-1_{01}$ transition of927frequency expected in the knots and iu the inter-knot regions of the jet.,frequency expected in the knots and in the inter-knot regions of the jet.928 Although the main aim of this work was to give a physical description of how the diffusive acceleration miechanisni can work in a Welvin-Uehuboltz unstable jet. we could also derive the treuds of the above described observational quantities with the position along the jet axis. and this was achieved translating our results iu time iuto behavior with space.," Although the main aim of this work was to give a physical description of how the diffusive acceleration mechanism can work in a Kelvin-Helmholtz unstable jet, we could also derive the trends of the above described observational quantities with the position along the jet axis, and this was achieved translating our results in time into behavior with space."929 It is necessary to keep it into account when we refer for example to Fig., It is necessary to keep it into account when we refer for example to Fig.930 7: the plots iu Fig., 7: the plots in Fig.931 Ta and 7h are not snapshots of the jet at a certain time. but are obtained following a parcel of the jet material as it moves downstream. thus evolving both in space and in tine.," 7a and 7b are not snapshots of the jet at a certain time, but are obtained following a parcel of the jet material as it moves downstream, thus evolving both in space and in time."932 For a more realistic application to observational data of he mechanisin described in this paper. a ‘spatial’ analysis of the evolution of a je propagating iu a nediuu with decreasing density is required. in order o obtain snapshots of the whole (non-cvliudrical) jet a selected times: this nuplies he adoption of large grids (seo for exaniple Micouo et al.," For a more realistic application to observational data of the mechanism described in this paper, a `spatial' analysis of the evolution of a jet propagating in a medium with decreasing density is required, in order to obtain snapshots of the whole (non-cylindrical) jet at selected times; this implies the adoption of large grids (see for example Micono et al.,"933 1998) and consequently of a large uunuber of Lagrangian particles. to cover with a good. statistic the whole jet body: in this wav we could also obtain indications on the variaion of the density of the Lagrangian particles iu different jet zones. aud thus ou their relative brightuess.," 1998) and consequently of a large number of Lagrangian particles, to cover with a good statistic the whole jet body; in this way we could also obtain indications on the variation of the density of the Lagrangian particles in different jet zones, and thus on their relative brightness."934 This study will be the subject of a future work., This study will be the subject of a future work.935 Achterbere. A.. 1990.Plasmas. Whover Academic Publishers. 67 Dell. A.L.. 1978.182. 117 Dicknell. C.V.. Beechnan. ALC... 1996.ApJ467. 597 Diretta. J.À.. Zhou. F.. Owen. E.N.. 1995.ApJ447. 582 Birkinshaw.lad AL. 1991.Astrophysics. P.A. IIughes ed..," Achterberg, A., 1990, Kluwer Academic Publishers, 67 Bell, A.L., 1978,, 147 Bicknell, G.V., Begelman, M.C., 1996,, 597 Biretta, J.A., Zhou, F., Owen, F.N., 1995,, 582 Birkinshaw, M., 1991, P.A. Hughes ed.,"936" Cambridge University Dress. 278 Disuovatvi-lkoeau. G.S.. Lovelace. R.V.E.. 1995.296. L19 Dlaudford. R.D. aud Eicheler. D.. 1987.154. 1 Blandford. R.D.. aud Ostriker. J.D.. 1980.ApJ237. Dodo. G.. Massaclia. S.. Ferri. Αν, Trussoui. E.. 1991.283. 655 Bridle. AIL. Perlev. R.A. δι.22. 319 Burns. J.O.. Feigelson. E.D.. Schacier. E.J.. 1983.273. 125 Colella. P.. Woodward. P.R.. 1981.54. 171 De Pater. L. Perley. R.À.. 1983.273. 61 Diy. L. OC. 1983.A6. 973 Ferrari. A.. Trussoni. E.. Zaninetti. L.. 1978.64. Ferrari. A.. Melrose. D.B. 1997.68. 171 Frais-Buruct. D.. Golombeck. D.. Macchetto. F.D.. Nieto. J.L.. Leliewre. C... Perrvinan. ALA.C.. Di Serego Aliehieri. S.. 1991a.4.7101. ὃς. Fraix-Durnet. D.. Colombeck. D... Macchetto.. F.D.. 1991.AF102. 562 ILudee P.E.. Norman M.L.. 1988a.ApJ334. 70 Tardee P.E.. Norman M.L.. 1988b.ApJ334. 80 Ieaveus. A.F.. Dru. L.OC... 1988.235. 907 Jones. TA. Ryu. D.. Eugcl. A.. 1999.4pJ512. 105 Kardashev N.S.. 1962.6. 317 Kirk. J.C... Schucider. P.. 1987.αρ.315. 125 Kirk. JA... 1991.Astrophysics. Saas-Foe Advanced Course 21 (Lecture Notes 1991). Verlag. Berlin. 225 Lesch. IL. Birk. G.T.. 1998.ApJ499. 167 Li. IL. Miller. J.A.. Colgate. S.A... 1997.ACNs, Proceedings of the Tuternational Confereuce. 162 Mack. IIL. Wein. U.. ODoa. C.D.. Willis. A.C.. Saripalli. L.. 1998.329. 112 Massaelia. ον, Bodo. αν, Ferrari. À.. Bossi. P.. 1996.Nuclei; Proceedings ofa Workshop Ueld at Dad Iounef (3-7 July 1995). 275 news, A.P... Scheuer. PLA... 1990.242. rews. A.P.. Scheuer. PLAC... 1990.242. AMeisenhenuer. Rosser. H.-J.. Schlóttelburg. AL. 1996.Nuclei. Proceedings of a Workshop Ποια at Dad Tounet (3-7 July 1995). 231 AMeiscuheiuer. I. Newman. AL. Rosser. IT.-J.. 1996.307. 61 AMeiseuhenuer. I. Newman. M. Rosser. IT.-J.. 1996.307. 61 Melrose. D.B.. Pope. ALI. 1993.10. 222 Micono. AL. Massaglia. ον, Bodo ων Rossi. P.. Ferrari. AL. 1998.333. 989 Ostrowsky. NL. 1990.238. 135 Ostrowsky. NL. 1998."," Cambridge University Press, 278 Bisnovatyi-Kogan, G.S., Lovelace, R.V.E., 1995,, L19 Blandford, R.D., and Eicheler, D., 1987,, 1 Blandford, R.D., and Ostriker, J.P., 1980,, 793 Bodo, G., Massaglia, S., Ferrari, A., Trussoni, E., 1994,, 655 Bridle, A.H., Perley, R.A., 1984,, 319 Burns, J.O., Feigelson, E.D., Schreier, E.J., 1983,, 128 Colella, P., Woodward, P.R., 1984,, 174 De Pater, I., Perley, R.A., 1983,, 64 Drury, L. O'C. 1983,, 973 Ferrari, A., Trussoni, E., Zaninetti, L., 1978,, 43 Ferrari, A., Melrose, D.B. 1997,, 171 Fraix-Burnet, D., Golombeck, D., Macchetto, F.D., Nieto, J.L., Lelievre, G., Perryman, M.A.C., Di Serego Alighieri, S., 1991a,, 88, Fraix-Burnet, D., Golombeck, D., Macchetto, F.D., 1991,, 562 Hardee P.E., Norman M.L., 1988a,, 70 Hardee P.E., Norman M.L., 1988b,, 80 Heavens, A.F., Drury, L.O'C., 1988,, 997 Jones, T.W., Ryu, D., Engel, A., 1999,, 105 Kardashev N.S., 1962,, 317 Kirk, J.G., Schneider, P., 1987,, 425 Kirk, J.G., 1994, Saas-Fee Advanced Course 24 (Lecture Notes 1994), Springer--Verlag, Berlin, 225 Lesch, H., Birk, G.T., 1998,, 167 Li, H., Miller, J.A., Colgate, S.A., 1997, Proceedings of the International Conference, 162 Mack, K.H., Klein, U., O'Dea, C.P., Willis, A.G., Saripalli, L., 1998,, 442 Massaglia, S., Bodo, G., Ferrari, A., Rossi, P., 1996, Proceedings of a Workshop Held at Bad Honnef (3-7 July 1995), 275 Matthews, A.P., Scheuer, P.A.G., 1990,, 616 Matthews, A.P., Scheuer, P.A.G., 1990,, 623 Meisenheimer, Rösser, H.-J., Schlöttelburg, M., 1996, Proceedings of a Workshop Held at Bad Honnef (3-7 July 1995), 231 Meisenheimer, K., Neumann, M., Rösser, H.-J., 1996,, 61 Meisenheimer, K., Neumann, M., Rösser, H.-J., 1996,, 61 Melrose, D.B., Pope, M.H., 1993,, 222 Micono, M., Massaglia, S., Bodo G., Rossi, P., Ferrari, A., 1998,, 989 Ostrowsky, M., 1990,, 435 Ostrowsky, M., 1998,"937here.,here.938 The physical state of a rotating. fluid (strengthless) body depends on the angular momentum and distribution of matter.," The physical state of a rotating, fluid (strengthless) body depends on the angular momentum and distribution of matter."939 Non- or slowly-rotating Πα bodies are generally spherical., Non- or slowly-rotating fluid bodies are generally spherical.940 Moderate rotation produces a Maclaurin spheroid in which &=bc. and faster rotation results in a (triaxial Jacobian ellipsoid in which «>b=ec.," Moderate rotation produces a Maclaurin spheroid in which $a=b\gtrsim c$, and faster rotation results in a triaxial Jacobian ellipsoid in which $a>b\gtrsim c$."941 Hubbard. defines the dimensionless rotation rate ο) as where w is the angular rotation rate and p is the bulk density of the body: in this formalism. the transition from Maclaurin to Jacobian bodiesoccurs at the bifurcation point Q?=0.19.," Hubbard defines the dimensionless rotation rate $\Omega$ as where $\omega$ is the angular rotation rate and $\rho$ is the bulk density of the body; in this formalism, the transition from Maclaurin to Jacobian bodiesoccurs at the bifurcation point $\Omega^2=0.19$."942 The maximum value lor the dimensionless rotation rate (£2) is reached at the bifburcation point., The maximum value for the dimensionless rotation rate $\Omega$ ) is reached at the bifurcation point.943 Thus. the minimum density for a [Iud iis 0.67 ο ? for a rotation period of 7.5 hours.," Thus, the minimum density for a fluid is 0.67 g $^{-3}$ for a rotation period of 7.5 hours."944 All densities greater than this produce two theoretically viable solutions. one representing (he Jacobian ellipsoid branch of solutions aud one the the Maclaurin spheroid branch.," All densities greater than this produce two theoretically viable solutions, one representing the Jacobian ellipsoid branch of solutions and one the the Maclaurin spheroid branch."945 Here we consider each branch in turn., Here we consider each branch in turn.946 If we assume that the observed ]liehteurve is derived from the gross shape of the body. then we require the branch of solutions corresponding (to a (riaxial Jacobian ellipsoid where «>5.," If we assume that the observed lightcurve is derived from the gross shape of the body, then we require the branch of solutions corresponding to a triaxial Jacobian ellipsoid where $a>b$."947 The rotation period must be 7.5 hours: if the best-fit solution of 7.5 hours is used. its double-peaked nature implies that it is a complete rotation period. whereas if the second-best-lit solution of 3.79 hours is used. ils single peak implies (hat 3.79 hours corresponds to only a half period (since the lighteurve is shaped-cerived for a Jacobian body).," The rotation period must be 7.5 hours: if the best-fit solution of 7.5 hours is used, its double-peaked nature implies that it is a complete rotation period, whereas if the second-best-fit solution of 3.79 hours is used, its single peak implies that 3.79 hours corresponds to only a half period (since the lightcurve is shaped-derived for a Jacobian body)."948 Hence. we know w (the angular rotation rate).," Hence, we know $\omega$ (the angular rotation rate)."949 Tassoul introduces 7. which describes the energy state of a rotating body and which is the ratio of rotational kinetic energy (Ix) to the absolute value of the gravitational potential energv (W): r=K/|Wl|. where 7 issmall for nearly spherical bodies and increases for bodies with increasing asphericities (Figure 5)).," Tassoul introduces $\tau$, which describes the energy state of a rotating body and which is the ratio of rotational kinetic energy (K) to the absolute value of the gravitational potential energy (W): $\tau=K/|W|$, where $\tau$ issmall for nearly spherical bodies and increases for bodies with increasing asphericities (Figure \ref{fvfig}) )."950 Tassoul shows the relationship between 0? and 7: from Equation 1. and our knowledge of w. we convert this relationship to p as a function of 7.," Tassoul shows the relationship between $\Omega^2$ and $\tau$; from Equation \ref{hubbeqn} and our knowledge of $\omega$, we convert this relationship to $\rho$ as a function of $\tau$."951 This result bulkdensity as a function of the energy state of the body [or a Jacobian ellipsoid isshown in Figure 5. as the red line on the right half of the plot., This result — bulkdensity as a function of the energy state of the body for a Jacobian ellipsoid— isshown in Figure \ref{fvfig} as the red line on the right half of the plot.952 Chandrasekhar(1969) tabulates the relationship between b/a. e/a and o7>(πρ) (what Chandrasekhar writes as Q we write here as w. the angular rotation rate).," \citet{chandra} tabulates the relationship between$b/a$ , $c/a$ and $\omega^2/(\pi G \rho)$ (what Chandrasekhar writes as $\Omega$ we write here as $\omega$ , the angular rotation rate)."953 We therefore can derive the relationship between b/a. ef/a. and p. andconsequently between θα. e/a. and," We therefore can derive the relationship between $b/a$ , $c/a$ , and $\rho$ , andconsequently between $b/a$ , $c/a$ , and"954The period covers all of solar evele 21 (May. 1976- July 1986). evcle 22 (August 1986- March 1996). and evcle 23(Àxil 1996- May. 2008).,"The period covers all of solar cycle 21 (May 1976- July 1986), cycle 22 (August 1986- March 1996), and cycle 23 (April 1996- May 2008)."955" The mouthly flare uuubers of CH‘lass. M-clasx, aud N-class fares have obvious 20110:ical variability as well as suuspot numbers (see he."," The monthly flare numbers of C-class, M-class, and X-class flares have obvious periodical variability as well as sunspot numbers (see fig."956 1)., 1).957 Ilowever. different flares have different poak intensities of soft N-rav flux.," However, different flares have different peak intensities of soft X-ray flux."958 For iustauce. the peak flux ο| nan N30 fiare is LOO times larecr than that of C3.0 fiares.," For instance, the peak flux of an X3.0 flare is 100 times larger than that of C3.0 flares."959 For M-class flares. the difference of the pea- flux is about 10 times from MI.O to M9.9.," For M-class flares, the difference of the peak flux is about 10 times from M1.0 to M9.9."960 Considering he pliysics. we snuned the monthly peak fluxes of all he sb-class flames of the same type flares.," Considering the physics, we summed the monthly peak fluxes of all the sub-class flares of the same type flares."961 Detailed calcultions can |© seen from the equations in section 2., Detailed calculations can be seen from the equations in section 2.962 Frou table 1. t1e uunibers of C-class flares are larger han that of M-class and N-class flares in each cycle.," From table 1, the numbers of C-class flares are larger than that of M-class and X-class flares in each cycle."963 However. the total peak fluxes of the C-class flares are ower than those of M-class flares in cycles 21 anc 22.," However, the total peak fluxes of the C-class flares are lower than those of M-class flares in cycles 21 and 22."964 Figs., Figs.965" δα. hb. ο, d show that the monthly peak fluxcs of the C-class. M-class; A-class flares aud total peal. Huxes of the three types of flares (blue lines) from Max 1976 to Mav 2008 and their 13-poimt smoothed values superimposed (red dues)."," 2a, b, c, d show that the monthly peak fluxes of the C-class, M-class, X-class flares and total peak fluxes of the three types of flares (blue lines) from May 1976 to May 2008 and their 13-point smoothed values superimposed (red lines)."966 The monthly pea- fluxes of CH‘lass. Meelass. and N-class flares have obvious periodical variability as well as the change of iiouthlily SunsMt onunnbers (Fig.," The monthly peak fluxes of C-class, M-class, and X-class flares have obvious periodical variability as well as the change of monthly sunspot numbers (Fig."967 2e)., 2e).968 To show the systematic time-lag (or time-lead) between the mouthly peak fluxes of C«‘lass. Meclass A-class flares and the mouthly SunsMt ΠΠΟΟΤΣ in a cycle. we have done a correlation analvsis of the two time series.," To show the systematic time-lag (or time-lead) between the monthly peak fluxes of C-class, M-class, X-class flares and the monthly sunspot numbers in a cycle, we have done a correlation analysis of the two time series."969" In order to climinate the iuypact that large. active flare-productive regions exert simultancously to sunspot aud flare uuubers. we adoptexd the 13-p.«iut smoothed monthly peak fluxes of C-class. \L-class, N-class flares aud sunspot uuuboers ) calculute the correlation coefficient. ancl plase relation between them."," In order to eliminate the impact that large, active flare-productive regions exert simultaneously to sunspot and flare numbers, we adopted the 13-point smoothed monthly peak fluxes of C-class, M-class, X-class flares and sunspot numbers to calculate the correlation coefficient and phase relation between them."970" The| smoother| imouthlv peak fluxes of σας», ALcelass anc N-class flares have positive correlation cocfficleuts with t16 smoothed mouthly sunspot wuubersf (seen from table 2)."," The smoothed monthly peak fluxes of C-class, M-class and X-class flares have positive correlation coefficients with the smoothed monthly sunspot numbers (seen from table 2)."971 The correlation coefficients of M-class aud A-class flares and sunspot umubers are higher in cvele 22 than trose in cvcles 21 and 23., The correlation coefficients of M-class and X-class flares and sunspot numbers are higher in cycle 22 than those in cycles 21 and 23.972 Furthermore. he coirelation coefficicuts of the smoothed peak fluxes )etween the tbie Kinds of soft N-rav flares in evcle 22 are lieher than rose In and 23.," Furthermore, the correlation coefficients of the smoothed peak fluxes between the three kinds of soft X-ray flares in cycle 22 are higher than those in and 23."973 The correlation cocfficicuts betw«vn the smoothed monthly sunspot mmbers aud the smoothed mouthly peak fluxes of C-class. Meclass. and X-class flares can be seen in figure 3.," The correlation coefficients between the smoothed monthly sunspot numbers and the smoothed monthly peak fluxes of C-class, M-class, and X-class flares can be seen in figure 3."974 The abscissa indicates the shift of the smoothed uouthlv sunspot numbers pertaining to the smoothed uouthlv peak fluxes of C-class; M-class aud X-class dares. with negative values represcuting backwards shifts.," The abscissa indicates the shift of the smoothed monthly sunspot numbers pertaining to the smoothed monthly peak fluxes of C-class, M-class and X-class flares, with negative values representing backwards shifts."975 It is found that the mouthly peak fiuxes of C-class. M-class. ancl N-class flares have a very noticeable time lag of 13. 8. aneLS mouths respectively iu cycle 2] with respect to suispot nunibers.," It is found that the monthly peak fluxes of C-class, M-class, and X-class flares have a very noticeable time lag of 13, 8, and 8 months respectively in cycle 21 with respect to sunspot numbers."976 There is no time lag between the suuspot wmubers and M-class flares iu eveles 22., There is no time lag between the sunspot numbers and M-class flares in cycles 22.977 However. tlrere is a one-nmonth time lag for C-class flare and a one-month time lead for N-class flare with respect to sunspot nuubers iu evcle 22.," However, there is a one-month time lag for C-class flare and a one-month time lead for X-class flare with respect to sunspot numbers in cycle 22."978" Moreover. the smoothed mouths"" peak fiuxes of C-class; Meclass. and N-class flares have a very noticeale tine lag of one mouth. 5 mouths. and 21 ποιές respectively with respect to the sinoothed mouthly sunspot numbers iu evele 23."," Moreover, the smoothed monthly peak fluxes of C-class, M-class, and X-class flares have a very noticeable time lag of one month, 5 months, and 21 months respectively with respect to the smoothed monthly sunspot numbers in cycle 23."979 If we take tlie three types of flares together. there is an obvious tin1ο lag of 9 months in cycle 21. πο time lag iu cvcle 22 aud a characteristic time lag of 5 mouths in evele 23 with respect to sunspot uunuboers.," If we take the three types of flares together, there is an obvious time lag of 9 months in cycle 21, no time lag in cycle 22 and a characteristic time lag of 5 months in cycle 23 with respect to sunspot numbers."980 Tn this paper. we preseut a statistical study on three types of soft N-rav flares from May. 1976 to Alay 2008.," In this paper, we present a statistical study on three types of soft X-ray flares from May 1976 to May 2008."981 We use the data of the smoothed mouthly peak fluxcs of C-class. M-class. ane| X-class flares aud the simootled mouthily suuspot numbers," We use the data of the smoothed monthly peak fluxes of C-class, M-class, and X-class flares and the smoothed monthly sunspot numbers."982 The main results are as follows: 1l., The main results are as follows: 1.983 The simeothed 1aouthlv peak fluxes of C-class. ALclass. aud. N-class flares have a very. noticeable time lag of 13. 8. aud 8 months respectivolv with respect to the s1uioothed monthly suspot ummmbers in cvcele 21.," The smoothed monthly peak fluxes of C-class, M-class, and X-class flares have a very noticeable time lag of 13, 8, and 8 months respectively with respect to the smoothed monthly sunspot numbers in cycle 21."984" 2,", 2.985 There is a onc-uionth time lag for the simootled uouthlv peal fiuxes ο: C-class flares. a oneAnonthl time σας for the smootliec monthlv peak fluxes of N-class fares and no time lag for the smoothed monthly peak fixes of Meclass flare swith respect to the smoothed uouthlv sunspot nuuCrs In cvcle 22.," There is a one-month time lag for the smoothed monthly peak fluxes of C-class flares, a one-month time lead for the smoothed monthly peak fluxes of X-class flares and no time lag for the smoothed monthly peak fluxes of M-class flares with respect to the smoothed monthly sunspot numbers in cycle 22."986 3., 3.987 The smoothed ταιouthlv peak fluxes of C-class. M-class. and N-class flares have a verv noticeable time ag of one month. 5 nouths. and 21 mouths in evcle 23 respectively with respect to the smoothed monthly sunspot mmubers.," The smoothed monthly peak fluxes of C-class, M-class, and X-class flares have a very noticeable time lag of one month, 5 months, and 21 months in cycle 23 respectively with respect to the smoothed monthly sunspot numbers."988 ., 4.989 I£ we take the twee types of flares together. we fud that the soft N-rav flares have an obvious time lag of 9 mouths iu cvcle 21. no time lag in evele 22 aud a characteristic time ag of 5 months iun evele 23 with respect to the snoothed monthly sunspot nuubers.," If we take the three types of flares together, we find that the soft X-ray flares have an obvious time lag of 9 months in cycle 21, no time lag in cycle 22 and a characteristic time lag of 5 months in cycle 23 with respect to the smoothed monthly sunspot numbers."990 5., 5.991 The correlation coefiicients of the smoothed imonthlv peak fiuxes «Mf M-class aud N-class flares aud the simoothed iionuthlv sunspot nunibers are higher iu evele 22 than those in evcles 21 aud 23., The correlation coefficients of the smoothed monthly peak fluxes of M-class and X-class flares and the smoothed monthly sunspot numbers are higher in cycle 22 than those in cycles 21 and 23.992 6., 6.993 The correlation cocficients between the threc kinds of soft ταν flares m cvele 22 are higher tha- those in aud 23., The correlation coefficients between the three kinds of soft X-ray flares in cycle 22 are higher than those in and 23.994 Iu this paper. we adopted the method developed by Autalové (1996) aud1wed the smoothed 1ionthlly. pea-," In this paper, we adopted the method developed by $\acute{a}$ (1996) and used the smoothed monthly peak"995There is a nother object which shows all the properties of the z=0.89 high luminosity cluster of ealaxies LWGA. J1226.9+3332.,There is a nother object which shows all the properties of the $z=0.89$ high luminosity cluster of galaxies 1WGA $+$ 3332.996 In particular both for this object aud for LWGOA J1226.9+3332 there is an IR bright (xy~15.8) red (B-Ix—5.2) galaxy in the X-ray. error circle aud a stroug (>To at 1-15) excess of extendecl aud red. (R-W>1.5) sources., In particular both for this object and for 1WGA $+$ 3332 there is an IR bright $\sim 15.8$ ) red $\sim 5.2$ ) galaxy in the X-ray error circle and a strong $> 7\sigma$ at K=18) excess of extended and red $\geq 4.5$ ) sources.997 HIC this galaxy. were a first ranked cluster ellipticals with My=—26.7£0.5 (assuming negligible IX-correctiou. gy=0.5 and. Hp=50 km ! loas in Collins Mann. 1998). we would have a limit on the redshift: 2=0.85noe for the candidate cluster (2=0.68(i5 from the K=15.5 galaxy in 1WGA J1226.9+3332 field of view).," If this galaxy were a first ranked cluster ellipticals with $M_K =-26.7 \pm 0.5$ (assuming negligible K-correction, $q_0 =0.5$ and, $_0$ =50 km $^{-1}$ $^{-1}$ as in Collins Mann, 1998), we would have a limit on the redshift: $z=0.85^{+0.40}_{-0.25}$ for the candidate cluster $z=0.68^{+0.30}_{-0.19}$ from the K=15.5 galaxy in 1WGA $+$ 3332 field of view)."998 This galaxy. is extremely red (2—Aον5.140.5 lor the candidate cluster aud 5.1£0.3 for LWOA J1226.94+3332). as expected for and high z clusters oL galaxies.," This galaxy is extremely red $R-K \sim 5.1 \pm 0.5$ for the candidate cluster and $5.1 \pm 0.3$ for 1WGA $+$ 3332), as expected for and high z clusters of galaxies."999 Only. au unevolviug elliptical galaxy at 0.7«z« 1.1 or a Sbe galaxy at Z21.2 cau have such red color (Coleman. Woo Weedimanu. 1980).," Only an unevolving elliptical galaxy at $0.7<$ $<1.1$ or a Sbc galaxy at $>1.2$ can have such red color (Coleman, Woo Weedman, 1980)."1000 (0.75«21.0 are the limits for the hieh z cluster LWCGA J1226.9+3332)., $0.75 < z < 1.0$ are the limits for the high z cluster 1WGA $+$ 3332).1001 This observational evidence strongly support the identification of this object with a high redshift (0.5€pz 1.0) cluster of galaxies., This observational evidence strongly support the identification of this object with a high redshift $0.5 \leq z \leq 1.0$ ) cluster of galaxies.1002 Thanks to the large area saiupled aud with two high redshift ἐς=0.15 aud z=0.59) clusters of galaxies and one more caudidate out of the 16 selected sources. the selection of bright aud extremely X-ray loud sources(ROSAT blank fiekl sources) proved to be the most efficient methocl for fincing highly luminous aud high recdshilt clusters of galaxies.," Thanks to the large area sampled and with two high redshift $z=0.45$ and $z=0.89$ ) clusters of galaxies and one more candidate out of the 16 selected sources, the selection of bright and extremely X-ray loud sources blank field sources) proved to be the most efficient method for finding highly luminous and high redshift clusters of galaxies."1003 LC. would like to thank the organizers of the meeting for the financial support., I.C. would like to thank the organizers of the meeting for the financial support.1004 This work was supported by NASA eraut. GO 0-1086X. αμα by the Italian MURST (IC and AC)., This work was supported by NASA grant GO 0-1086X and by the Italian MURST (IC and AC).1005 P.M. acknowledges an ESA fellowship., P.M. acknowledges an ESA fellowship.1006systems and populations of NS-NS binaries using different networks of advanced GW detectors.,systems and populations of NS–NS binaries using different networks of advanced GW detectors.1007" For the majority of optimally oriented NS-NS binaries examined, we show good agreement of our MCMC derived errors with the error ellipses obtained from analytical timing accuracy and Fisher matrix formulae."," For the majority of optimally oriented NS–NS binaries examined, we show good agreement of our MCMC derived errors with the error ellipses obtained from analytical timing accuracy and Fisher matrix formulae."1008" However, for a handful of SNR signals at threshold particular with the standard geometrically degenerate(in LIGO-Virgo network), we show that sky error regions can be non-ellipsoidal and non-contiguous, show multimodal distributions, and the best-fits can be shifted away from their true values."," However, for a handful of SNR signals at threshold (in particular with the standard geometrically degenerate LIGO--Virgo network), we show that sky error regions can be non-ellipsoidal and non-contiguous, show multimodal distributions, and the best-fits can be shifted away from their true values."1009" Of particular relevance, our results show that the inclusion of LIGO-Australia in a worldwide GW detector network improves localization errors both for individual and populations of binaries up to a factor of ~ 5, reducing the appearance of multimodal islands."," Of particular relevance, our results show that the inclusion of LIGO-Australia in a worldwide GW detector network improves localization errors both for individual and populations of binaries up to a factor of $\sim$ 5, reducing the appearance of multimodal islands."1010" Finally, the number of detected binaries increases with the number of detectors in a network."," Finally, the number of detected binaries increases with the number of detectors in a network."1011 A natural extension of this paper is to include astrophysically realistic populations of NS-NS and spin-precessing NS-BH binaries., A natural extension of this paper is to include astrophysically realistic populations of NS–NS and spin-precessing NS–BH binaries.1012 Outstanding questions that are yet to be addressed are the implications of our findings for observational EM follow up., Outstanding questions that are yet to be addressed are the implications of our findings for observational EM follow up.1013 Our results show that measurements of astrophysical populations of GW events result in error areas of ~10deg?.," Our results show that measurements of astrophysical populations of GW events result in error areas of $\sim 10\,1014\mbox{deg}^2$."1015" In the optical, cross-correlating localization error areas >10deg? with as complete as possible galaxy catalogs, such as the “Local Universe"" census proposed by Kulkarni&Kasliwal (2009), should aid EM search strategies (Kasliwaletal. 2011))."," In the optical, cross-correlating localization error areas $> 10 \, \mbox{deg}^2$ with as complete as possible galaxy catalogs, such as the “Local Universe” census proposed by \cite{kk09}, should aid EM search strategies \citealt{Kasliwal:2011}) )."1016" As recent observations indicate, a small number ( five at present) of SHBs appear to be located several tens of kpc away from their host galaxies (e.g., Berger2010;Fongetal. 2010))."," As recent observations indicate, a small number $\sim$ five at present) of SHBs appear to be located several tens of kpc away from their host galaxies (e.g., \citealt{Berger:2010,Fong:2010}) )."1017" Thus, search strategies will need to include the possibility of such effects when looking for transients of NS binary mergers."," Thus, search strategies will need to include the possibility of such effects when looking for transients of NS binary mergers."1018" Moreover, time-domain surveys provide an estimate of the false-positive rate of dynamic galactic (foreground) and extragalactic (background) transients."," Moreover, time-domain surveys provide an estimate of the false-positive rate of dynamic galactic (foreground) and extragalactic (background) transients."1019 Currently operating and future optical and radio EM facilities are thus capable of preparing for and performing follow-up of GW events., Currently operating and future optical and radio EM facilities are thus capable of preparing for and performing follow-up of GW events.1020" We are grateful to Josh Bloom, Scott Hughes, Sterl Phinney, Bangalore Sathyaprakash and Michele"," We are grateful to Josh Bloom, Scott Hughes, Sterl Phinney, Bangalore Sathyaprakash and Michele"1021momenta diffusion prevails upon advection.,momenta diffusion prevails upon advection.1022 In a qualitative way one could describe this effect bv wriüng.r—ust+ΟΠΠ and repeat (he argument above., In a qualitative way one could describe this effect by writing $x=u_{2}t + \sqrt{2D(p)t}$ and repeat the argument above.1023 The result is not completely analvlical but it requires (he numerical integration of a simple differential equation which results in the dotted thin lines shown in the right panel of Fig. 4.., The result is not completely analytical but it requires the numerical integration of a simple differential equation which results in the dotted thin lines shown in the right panel of Fig. \ref{fig:space7_bohm}.1024 These qualitative results show how the bumps in fact are expected for r>4 and for low enough momenta. while thev disappear for pZPinar:," These qualitative results show how the bumps in fact are expected for $r>4$ and for low enough momenta, while they disappear for $p\gtrsim p_{max}$."1025 In Fig., In Fig.1026 5 we plot the spectrum of accelerated particles at different distances upstream (left panel) aud downstream (right panel) for Bohm diffusion., \ref{fig:spectradistance} we plot the spectrum of accelerated particles at different distances upstream (left panel) and downstream (right panel) for Bohm diffusion.1027" In the left panel the spectrum is plotted at.=—0.1L4,,,4, (solid line). c=ανω (dashed line) and 0=—2£4,,4, dotted line). where ιν=D(p,,,,)/u4."," In the left panel the spectrum is plotted at $x=-0.1L_{1,max}$ (solid line), $x=-L_{1,max}$ (dashed line) and $x=-2 L_{1,max}$ (dash-dotted line), where $L_{1,max}=D(p_{max})/u_{1}$."1028 In the upstream plasma we can see (he expected {rend of lower οποίον particles to be confined closer to the shock surface., In the upstream plasma we can see the expected trend of lower energy particles to be confined closer to the shock surface.1029 At increasingly larger distances from the shock only hieh energy particles are present., At increasingly larger distances from the shock only high energy particles are present.1030" On the other hand at ppae, energy losses become important and the absolute number of particles drops down.", On the other hand at $p>p_{max}$ energy losses become important and the absolute number of particles drops down.1031 In the right panel (he spectrum is plotted at =0.1Lee» (solid lime). à=ο (dashed line) and ar=ομως (dash-dotted line) with Loja=Τρ(puo).," In the right panel the spectrum is plotted at $x=0.1L_{2,max}$ (solid line), $x=L_{2,max}$ (dashed line) and $x=2 L_{2,max}$ (dash-dotted line) with $L_{2,max}=u_{2}\tau_{loss}(p_{max})$."1032 In the downstream plasma the main effect to be noticed is that the spectrum is truncated at lower energies while moving further downstream. as a result of svnchrotron energy losses (hat eut out high enerev particles [rom the spectrum.," In the downstream plasma the main effect to be noticed is that the spectrum is truncated at lower energies while moving further downstream, as a result of synchrotron energy losses that cut out high energy particles from the spectrum."1033ol the gererating source. not the position at which the sidelobe is measured.,"of the generating source, not the position at which the sidelobe is measured."1034 This respouse is noclulatec by the antena gain so sources outside the primary beam will be suppressed. Lowever wieght poijt sources. aud patches of diffuse emission. will still display polarized sidelobes ac“OSS he itlages. these will generate apparent polarized signal where none exists.," This response is modulated by the antenna gain so sources outside the primary beam will be suppressed, however bright point sources, and patches of diffuse emission, will still display polarized sidelobes across the images, these will generate apparent polarized signal where none exists."1035 This produces au eTOL in the Stoses conversion even if the array is perfectly calibrated., This produces an error in the Stokes conversion even if the array is perfectly calibrated.1036 This is the prevailiug polarizecd signal lu images of the simulated sky aud is wo doubt also present in the images of the true sky. but he signifiant [requeucy svuthesis over the 30MHz bandwidth: mitigates the effect and. there‘ore calibration errors dominate those images.," This is the prevailing polarized signal in images of the simulated sky and is no doubt also present in the images of the true sky, but the significant frequency synthesis over the 30MHz bandwidth mitigates the effect and therefore calibration errors dominate those images."1037 This effect will severely limit the polarization fidelity of integrated images unless ai accuule model of tie radio sky can be obtained., This effect will severely limit the polarization fidelity of integrated images unless an accurate model of the radio sky can be obtained.1038 A significant project is underway with the MWA to obalu an initial uodel of the sky through an all-sky. survey. project that will be continually. improved through tle lifetime of the instrument., A significant project is underway with the MWA to obtain an initial model of the sky through an all-sky survey project that will be continually improved through the lifetime of the instrument.1039 We have clemoustated the pe‘formance of a 'eal-tine calibratjon aud nagging pipeine for the MWA-32T. Wide-field polarimetri¢ linaging |as successfully beet performed via the integraljon of warped. aud weighed suapshios.," We have demonstrated the performance of a real-time calibration and imaging pipeline for the MWA-32T. Wide–field polarimetric imaging has successfully been performed via the integration of warped, and weighted snapshots."1040 The sinilalous indicate theuo the calibration ad imageug pipeline works with st[Iicieut. ficlelity 00 remove 1istrumental pola‘ization [rol a simialed point source population., The simulations indicate that the calibration and imaging pipeline works with sufficient fidelity to remove instrumental polarization from a simulated point source population.1041 Bu the observec point souve »opulation displays residial polariZulion. in the worst case. at the < level anc iu general :ul le uw level: tus is likely due to a mm»erfect calibration.," But the observed point source population displays residual polarization, in the worst case, at the $<$ level and in general at the $<$ level; this is likely due to an imperfect calibration."1042 Calibratio1 precision is united by OW sunapsliot sensitivity aud the [act In we Cannot account or the dilleriug primary beam shapes of array elemeuts., Calibration precision is limited by low snapshot sensitivity and the fact that we cannot account for the differing primary beam shapes of array elements.1043 The simulations aso indicate that a imajor component of measu‘ecL polaózed emission fron this and other wide-ljeld-of-view instrunmeus will be clue to the polaized sidelobes of bright ui»olarized features observed off-axis: necessitaing the construction of compreliersive sky moclels aj»plicable to these instrunents., The simulations also indicate that a major component of measured polarized emission from this and other wide-field-of-view instruments will be due to the polarized sidelobes of bright unpolarized features observed off-axis; necessitating the construction of comprehensive sky models applicable to these instruments.1044 The removal ¢X which. preferably in the visibility domaiu. or via a iterative forward mocleing scheme beiug recured to limit this instruuental poarizatlou.," The removal of which, preferably in the visibility domain, or via an iterative forward modeling scheme being required to limit this instrumental polarization."1045 The IWA elements are crossed dipoles on a eround-plae. electrically plasecl to a pointiug rection aud have. considerable lustruleal polarization {p to. 100 %)).," The MWA elements are crossed dipoles on a ground-plane, electrically phased to a pointing direction and have considerable instrumental polarization (up to 100 )."1046 We hav'e removed ---15161tal polarization down to “in real titje: with limied seusitivity aud a coumon scaled --ioclel for each ar‘ay element resyouse., We have removed instrumental polarization down to $<$ 5 in real time; with limited sensitivity and a common scaled model for each array element response.1047 The 512 tile MWA. with better constγαμος. iucividual ile respo1505 aud muuch greater siapshot seusitiviy shotId perform substantialy better.," The 512 tile MWA, with better constrained, individual tile responses and much greater snapshot sensitivity should perform substantially better."1048 The key ---uprovement lies lot simply in iuproviug sensitivity bit accounting for the «illerent. direction epeuden. polaritjetric responses of the constitueαἱ antelnias.," The key improvement lies not simply in improving sensitivity but accounting for the different, direction dependent, polarimetric responses of the constituent antennas."1049 Subsequent ptblicatious in this series will aim to perorm point source subt‘action [rom these ---hages. axd others like them at different frequencies. iu order to obtain spectral iudex informatio: and to coustralu t1ο behaviour of the MIWA antenna bea11.," Subsequent publications in this series will aim to perform point source subtraction from these images, and others like them at different frequencies, in order to obtain spectral index information; and to constrain the behaviour of the MWA antenna beam."1050"power-law model with two additional Gaussian lines fits the data well. with an appropriate Ny, for SN 1006. and a power-law index consistent with fits to a nearby reeion of the bright shock.","power-law model with two additional Gaussian lines fits the data well, with an appropriate $N_{H}$ for SN 1006, and a power-law index consistent with fits to a nearby region of the bright shock."1051 The addition of two Cassia lines for He-like aud. D-like ο is supported by au Ftest at the significance level., The addition of two Gaussian lines for He-like and H-like O is supported by an Ftest at the significance level.1052 Alternatively. following the SE model of Mechetal.(2009).. the data are fit equally well with a svuchrotron aud non-equilibrimm ionization thermal component.," Alternatively, following the SE model of \citet{miceli09}, the data are fit equally well with a synchrotron and non-equilibrium ionization thermal component."1053" In this ft we allowed oulv the normalizatious. powerlaw index 5. temperature AT. ancl ionization timescale b,f to vary."," In this fit we allowed only the normalizations, powerlaw index $\gamma$, temperature $kT$ , and ionization timescale $n_{e}t$ to vary."1054 Their analysis vielded a super-solar oxvecu abundance which matches our spectrum well. the only difference being the best-fit ionization timescale for the 3 features is nomiually lower than that of the shocked region as a whole (at la. but not at 39).," Their analysis yielded a super-solar oxygen abundance which matches our spectrum well, the only difference being the best-fit ionization timescale for the 3 features is nominally lower than that of the shocked region as a whole (at $\sigma$, but not at $\sigma$ )."1055 The iost rolevaut observed characteristics of the three pre-hock features are the generic size-scale of ~dos d0D€un a contimuun that is consisteut with the svuchrotron enuüsson from the bright shock. aud the presence of He-like aud ILlike ο lines that iniply ur ionization age of ~Όταν«105 ? x This --ouization age. comparable to the remuaut lifetime eiven the ambient deusitv of SN 1006. argues against au oeiterpretation of the features as the deuser portious of a CR precursor.," The most relevant observed characteristics of the three pre-shock features are the generic size-scale of $\sim 4\times 10^{18}$ cm, a continuum that is consistent with the synchrotron emission from the bright shock, and the presence of He-like and H-like O lines that imply an ionization age of $\sim 5.7^{+24}_{-3.1}\times 10^8$ $^{-3}$ s. This ionization age, comparable to the remnant lifetime given the ambient density of SN 1006, argues against an interpretation of the features as the denser portions of a CR precursor."1056 The likely supersolar abundances with a svuchrotron dominated continua. relative brightucss of the preshock features. and sinall radius of curvature also support the idea that these are ejecta fluecrs that have breached the shock frout.," The likely supersolar abundances with a synchrotron dominated continuum, relative brightness of the preshock features, and small radius of curvature also support the idea that these are ejecta fingers that have breached the shock front."1057 Ilereafter. πο discuss possible origius for the spacing of the pre-shock features. (," Hereafter, we discuss possible origins for the spacing of the pre-shock features. ("10581) Anomalous viscosity ceternuues the preferred RT waveleneth. (,1) Anomalous viscosity determines the preferred RT wavelength. (10592) The saturated state of nouresonaut imaguetic feld auplification creates cavities and higher density regions at a particular scale. (,2) The saturated state of nonresonant magnetic field amplification creates cavities and higher density regions at a particular scale. (10603) The ejecta flugers originate m the explosion itself.,3) The ejecta fingers originate in the explosion itself.1061 If the preshock features seen are the extension of the ejecta fingers themselves (Cassau-Chenaiotal.2008) then the spacing between them may reflect the wavelength of the R-T instability., If the preshock features seen are the extension of the ejecta fingers themselves \citep{cassam08} then the spacing between them may reflect the wavelength of the R-T instability.1062 In the absence of a periodic perturbation. this depends on the kinematic viscosity (the product of the sound speed aud largest eddy size: v= Iun ," In the absence of a periodic perturbation, this depends on the kinematic viscosity (the product of the sound speed and largest eddy size: $\nu = c_{sound}l_{eddy}$ )."1063"stationaryτομ). incompressible inedia the Ravleigh- linear erowth rate is approximately TO=vk|gkvk? which las a maxinuun at mode waveuunber k=(gay""42 (Plesset&Whipple1971). where g~0.0019 c ? for SN 1006 is the deceleration of the plasiua (estimatedfromtheSNRdy-namicsusingTrnelove&Αανου 1999).. and the ejecta density is assumed much evcater than that of the shocked Exponential erowth goes over to power law erowtli as displaved in Bloudiu&Ellison(2001) when expansion is iucluded."," In stationary incompressible media the Rayleigh-Taylor linear growth rate is approximately $\Gamma = \sqrt{\nu ^2k^4+gk}-\nu k^2$ which has a maximum at mode wavenumber $k=\left(g/\nu ^2\right)^{1/3}/2$ \citep{plesset74}, where $g\simeq 0.0049$ cm $^{-2}$ for SN 1006 is the deceleration of the plasma \citep[estimated from the SNR dynamics using][]{truelove99}, and the ejecta density is assumed much greater than that of the shocked Exponential growth goes over to power law growth as displayed in \citet{blondinellison01} when expansion is included."1064" Taking the observed wavelength of ιν1075 em. we find vy~107) exs78 * and a maximo linear erowth vate οον~6ς101H 1,"," Taking the observed wavelength of $4\times 10^{18}$ cm, we find $\nu\sim 10^{25}$ $^2$ $^{-1}$ and a maximum linear growth rate $g^{2/3}/2\nu1065^{1/3}\sim 6\times 10^{-11}$ $^{-1}$."1066 This is slow. allowing ouly 2 c-folding times during the 1000 vr age of SN 1006.," This is slow, allowing only 2 e-folding times during the 1000 yr age of SN 1006."1067 Additional vorticity is probably needed to speed up the process., Additional vorticity is probably needed to speed up the process.1068" We can compare this to an estimate of the viscosity frou, the product of the sound speed inthe shocked iuterstellar wedi (about |<105 ems 1) anda Ieneth scale determined by the separation between the forward shock and contact discontinuity (about 1 pc) to find pod (Bell2001.2005).."," We can compare this to an estimate of the viscosity from the product of the sound speed inthe shocked interstellar medium (about $4\times 10^8$ cm $^{-1}$ ) and a length scale determined by the separation between the forward shock and contact discontinuity (about 1 pc) to find $\nu\sim 10^{27}$ \citep{bell04,bell05}."1069The dotted line is the “Kennicutt-Schmidt™ law (Kennicutt(1998):: eqn.,The dotted line is the ”Kennicutt–Schmidt” law \citet{ken98}; eqn.1070 | above). with the bold solid portion of the line lying above the lowest estimated of the threshold density listed in 1989).," \ref{eqn:law} above), with the bold solid portion of the line lying above the lowest estimated of the threshold density listed in \citep{ken89}."1071. For most galaxies. the scatter plot has a flat portion at low where the density is constant. followed by an approximately power-law increase In wwith.," For most galaxies, the scatter plot has a flat portion at low where the density is constant, followed by an approximately power-law increase in with."1072. The horizontal dotted line in each panel corresponds to be sensitivity level of the images: us can be seen the flat portion of the scatter plot basically corresponds to the region where falls below the level that can be measured from the current data., The horizontal dotted line in each panel corresponds to be sensitivity level of the images; as can be seen the flat portion of the scatter plot basically corresponds to the region where falls below the level that can be measured from the current data.1073 A straight line was fitted to the binned data iteratively. considering only those points which lie above the FUV sensitivity limit and above the surface gas density value where the straight line meets the FUV sensitivity limit line. starting with an initial guess.," A straight line was fitted to the binned data iteratively, considering only those points which lie above the FUV sensitivity limit and above the surface gas density value where the straight line meets the FUV sensitivity limit line, starting with an initial guess."1074" For some ""deviant"" galaxies (viz.", For some ”deviant” galaxies (viz.1075 E321-014. UGC 6541. UGC 5209. KK 14 and DDO 43) this procedure did not converge.," E321-014, UGC 6541, UGC 5209, KK 14 and DDO 43) this procedure did not converge."1076 For these galaxies 18 HI and FUV peaks can be seen in Figure |. to be offset. making it natural that the scatter plot shows deviations from a simple power aw relation.," For these galaxies the HI and FUV peaks can be seen in Figure \ref{fig:olay} to be offset, making it natural that the scatter plot shows deviations from a simple power law relation."1077 It is worth noting that the galaxy with the smallest HI mass (see Table 43). viz.," It is worth noting that the galaxy with the smallest HI mass (see Table \ref{tab:res}) ), viz."1078 E321-014 is the most deviant. with ye FUV emission being considerably offset from the HI emission.," E321-014 is the most deviant, with the FUV emission being considerably offset from the HI emission."1079 This galaxy (along with UGC 6541) were also outliers in the global relation (Fig. 91)., This galaxy (along with UGC 6541) were also outliers in the global relation (Fig. \ref{fig:tot}) ).1080 Another interesting feature seen in Figure Al is iat while the observed ggenerally lies below that predicted by the fiducial Kennicutt(1998) relation. at high gas column densities. the observed bbegins to approach the predicted rate.," Another interesting feature seen in Figure \ref{fig:plots} is that while the observed generally lies below that predicted by the fiducial \cite{ken98} relation, at high gas column densities, the observed begins to approach the predicted rate."1081 The fact that, The fact that1082Although SDSS reaches r magnitudes up to 23.5. we avoicl stars fainter than 22.5.,"Although SDSS reaches $r$ magnitudes up to 23.5, we avoid stars fainter than 22.5."1083 This conservative limit is set to avoid any complications due to miss-classification of stars ancl galaxies., This conservative limit is set to avoid any complications due to miss-classification of stars and galaxies.1084 was built using a circular region around the center of Palomar 5 with a 07.13 radius., was built using a circular region around the center of Palomar 5 with a $0^\circ.13$ radius.1085 Figure 3aa shows the re(grn) Hess diagram constructed using the stars located inside this circular region., Figure \ref{fcl_pal}a a shows the $r \times (g-r)$ Hess diagram constructed using the stars located inside this circular region.1086 Some of the expected features of a typical GC are visible: a main-sequence (MS). ALS turn-oll (AISTO). Hed Giant Branch (ROB). and Horizontal Branch (1112).," Some of the expected features of a typical GC are visible: a main-sequence (MS), MS turn-off (MSTO), Red Giant Branch (RGB), and Horizontal Branch (HB)."1087 The choice of contour levels of Figure 3. is such that the Asyimptotie Ciant Branch (ACB). and the Blue Stragelers (BS) are not visible despite being present in this cluster.," The choice of contour levels of Figure \ref{fcl_pal} is such that the Asymptotic Giant Branch (AGB), and the Blue Stragglers (BS) are not visible despite being present in this cluster."1088 To avoid minor contributions of background. stars in the region where was built. we only used. stars that occupy the loci expected for à GC population.," To avoid minor contributions of background stars in the region where was built, we only used stars that occupy the loci expected for a GC population."1089 As discussed on previous sections. is expected o vary over large scales.," As discussed on previous sections, is expected to vary over large scales."1090 To accommodate some of this variation. we follow the prescriptions of Rockosietal(2002) and take the average Less diagram of four 3deg Ποιο απ away [rom Palomar 5.," To accommodate some of this variation, we follow the prescriptions of \citet{rock} and take the average Hess diagram of four $3~ deg^2$ fields far away from Palomar 5."1091 The fields. used. are. centred. in same coordinates as in Rockosietal. (2002)..., The fields used are centred in same coordinates as in \citet{rock}. .1092 Phe resulting lless diagram is shown in Figure 3bb. This approach to 1e Construction of is such that the spatial dependency ga1ould be reduced. hence simplifving the solution of equation (7)).," The resulting Hess diagram is shown in Figure \ref{fcl_pal}b b. This approach to the construction of is such that the spatial dependency should be reduced, hence simplifying the solution of equation \ref{nc}) )."1093 We thus apply the ME. under the assumption. that 1 background term does not vary with position., We thus apply the MF under the assumption that the background term does not vary with position.1094 The =neasured background is. ofH 0.51ercemin.27., The measured background is of $0.51 \; arcmin^{-2}$.1095 Figureae 4. shows 1e smoothed (0.1deg Gaussian smoothing) distribution of gaas consistent with Palomar 5 stellar population., Figure \ref{pal_den} shows the smoothed $0.1 \;deg$ Gaussian smoothing) distribution of stars consistent with Palomar 5 stellar population.1096 Having and properly constructed. we nav retrieve the best estimate of the density of stars consistent with in any region of the sky. where well describes the Galaxy field star population.," Having and properly constructed, we may retrieve the best estimate of the density of stars consistent with in any region of the sky where well describes the Galaxy field star population."1097 We applied the lilter to a region 2267«Rel231 and. LL«Dee< 1.17. which was divided in a grid of 0.030.09deg bins.," We applied the matched-filter to a region $226^\circ < RA < 231^\circ$ and $-1.1^\circ < Dec < 1.1^\circ$ , which was divided in a grid of $0.03 \times 0.03 \; deg$ bins."1098 Figure 4. shows the results of the matched-filter as a stellar surface density of Palomar 5 like stars overlaid on a residual contribution by background. stars (ie. the last term on equation 7))., Figure \ref{pal_den} shows the results of the matched-filter as a stellar surface density of Palomar 5 like stars overlaid on a residual contribution by background stars (i.e. the last term on equation \ref{nc}) ).1099 The extra-tidal structure recovered. for Palomar 5 closely resembles the one found in. previous works using the AIP technique., The extra-tidal structure recovered for Palomar 5 closely resembles the one found in previous works using the MF technique.1100 The peak of density along the tail is expected to be of ~0.2aremin7ο according to Odenkirchenetal. (2003)., The peak of density along the tail is expected to be of $\sim 0.2 \; arcmin^{-2}$ according to \citet{oden}. .1101. In this work we find a maximum density of ~0.27iarcemin2 using a cillerent set. of colours. and magnituces., In this work we find a maximum density of $\sim 0.27 \; arcmin^{-2}$ using a different set of colours and magnitudes.1102 The recovered. Palomar 5 tail extends. throughout Lsdeg. ending at the edge of the analysed. field. which sugeests a tail that extends much further. as depicted. by Odenkirchenetal.(2003).," The recovered Palomar 5 tail extends throughout $1.8 ~ deg$, ending at the edge of the analysed field, which suggests a tail that extends much further, as depicted by \citet{oden}."1103. Several density. Ductuations are found along the tail., Several density fluctuations are found along the tail.1104 Most. of these were also found on these previous studies., Most of these were also found on these previous studies.1105 The fluctuations are expected. even for the simplest. of the orbits such as circular. orbits on a axisymmetric potential (Ixüpperetal.2010:Ixüpper.MacLeod.&Leeeic 2008).," The fluctuations are expected even for the simplest of the orbits such as circular orbits on a axisymmetric potential \citep{kupper10,kupper08}."1106. NGC 2298 (also designated by ESO 366-SC 022) is located at?=2457.63. 6=101.01. therefore projected towards the Galactic anti-centre.," NGC 2298 (also designated by ESO 366-SC 022) is located at $l = 245^\circ .63$, $b = -16^\circ .01$, therefore projected towards the Galactic anti-centre."1107 Its position places it near the Galactic disk., Its position places it near the Galactic disk.1108 Lt is thus superimposed on to the thin and thick disks. besides the halo.," It is thus superimposed on to the thin and thick disks, besides the halo."1109" Structural parameters were found by DeMarchi&Pulone (2007)... such as core radius r,=0.29 and tical radius à;28.0 leading to a concentration parameter of e=ος,£r.)L44."," Structural parameters were found by \citet{marchi2298}, such as core radius $r_c = 0\arcmin .29$ and tidal radius $r_t = 8\arcmin .0$ leading to a concentration parameter of $c = log(r_t/r_c) = 1.44$."1110 Phe distance and metallicity taken from Harris(1996) are d—10.80kpe and. Fe/H]=1.85.," The distance and metallicity taken from \citet{harris} are $d = 10.80\, kpc$ and $[Fe/H] = -1.85$."1111 Vhe analysis of the LIST/AC'S CALL from those authors also vielded an extinction of £(D.V)=0.15 towardsthe cluster., The analysis of the HST/ACS CMD from those authors also yielded an extinction of $E(B-V)=0.15$ towardsthe cluster.1112 We here describe a first attempt. to detect an extra-structure around. NGC. 2298. using a field of 2+ sq.," We here describe a first attempt to detect an extra-tidalstructure around NGC 2298, using a field of $\simeq 4$ sq."1113 deg around the cluster., deg around the cluster.1114 Is location towards a dense stellar, Its location towards a dense stellar1115On 5-6 June 2012. Venus will be transiting the Sun as seen from the Earth. for the last time until 2117.,"On 5–6 June 2012, Venus will be transiting the Sun as seen from the Earth, for the last time until 2117."1116 This rare astronomical event was previously observed and reported in the literature six times only., This rare astronomical event was previously observed and reported in the literature six times only.1117 The first detection. of the atmosphere of Venus (the cytherean atmosphere) is traditionally attributed to Lomonosov. who observed the 26 May 1761 transit from the observatory of Saint-Petersburg (?)..," The first detection of the atmosphere of Venus (the cytherean atmosphere) is traditionally attributed to Lomonosov, who observed the 26 May 1761 transit from the observatory of Saint-Petersburg \citep{Marov:2005}."1118 Today. modern approaches are used to detect the atmospheres of transiting exoplanets.," Today, modern approaches are used to detect the atmospheres of transiting exoplanets."1119" Several studies ustig the transmission spectroscopy technique have provided significant insights into the atmospheric composition. structure. aid dynamics of hot giant exoplanets (e.g..2222) This techniqte is now attempted on Neptune-mass exoplanets (??) and on ""super-earths"" (1—10Ma: ??2).."," Several studies using the transmission spectroscopy technique have provided significant insights into the atmospheric composition, structure, and dynamics of hot giant exoplanets \citep[e.g.,][]{Charbonneau:2002,Vidal-Madjar:2003,Vidal-Madjar:2011,Snellen:2010}1120 This technique is now attempted on Neptune-mass exoplanets \citep{Stevenson:2010,Knutson:2011} and on “super-earths"" \citep[1--10~\Mearth;][]{Bean:2010,Bean:2011,Desert:2011a}."1121 The next step. characterisi5 the atmospheres of Earth-mass planets with transmissio1 spectroscopy. is extremely challenging because of the small spatial extent of these gas envelopes: photometric precisiois of the order of 0.1 ppm should be reached for that purpose (??)..," The next step, characterising the atmospheres of Earth-mass planets with transmission spectroscopy, is extremely challenging because of the small spatial extent of these gas envelopes: photometric precisions of the order of 0.1 ppm should be reached for that purpose \citep{Ehrenreich:2006b, Kaltenegger:2009a}."1122 The class of Earth-mass planets includes tellurie -— planets such as the Earth. Venus. or Corot-7b (?) andso-called planets” (?).. possibly such as GJ 1214b (?)..," The class of Earth-mass planets includes telluric – planets such as the Earth, Venus, or Corot-7b \citep{Leger:2011} andso-called ``ocean-planets'' \citep{Leger:2004}, possibly such as GJ 1214b \citep{Charbonneau:2009}."1123 Among planets in this mass range. the atmospheres of telluric exoplanets are the most challenging to characterise because these dense planets have small atmospheric scale heights. and thus compact atmospheres (?)..," Among planets in this mass range, the atmospheres of telluric exoplanets are the most challenging to characterise because these dense planets have small atmospheric scale heights, and thus compact atmospheres \citep{Ehrenreich:2006b}."1124 In this context. Venus can provide an essential proxy for a telluric exoplanet.," In this context, Venus can provide an essential proxy for a telluric exoplanet."1125 Obtaining its transmission spectrum during a transit across the Sun will serve both as a comparison basis for transiting Earth-mass exoplanets to be observed in the future. and a proof of feasibility that such observations can effectively probe the atmospheres of exoplanets in this mass range.," Obtaining its transmission spectrum during a transit across the Sun will serve both as a comparison basis for transiting Earth-mass exoplanets to be observed in the future, and a proof of feasibility that such observations can effectively probe the atmospheres of exoplanets in this mass range."1126 In addition. transit observations of Venus can brinisi precious information about how the atmosphere of a non-habitable world — observed as an exoplanet — differ from that of a habitable planet. the Earth. also observed as an exoplanet in transit during Lunar eclipses (?)..," In addition, transit observations of Venus can bring precious information about how the atmosphere of a non-habitable world – observed as an exoplanet – differ from that of a habitable planet, the Earth, also observed as an exoplanet in transit during Lunar eclipses \citep{Vidal-Madjar:2010}."1127 The previous transit of Venus in 2004 was the first to be scrutinised with modern instrumentation. from space (??) and from the ground (??)..," The previous transit of Venus in 2004 was the first to be scrutinised with modern instrumentation, from space \citep{Schneider:2006a,Pasachoff:2011} and from the ground \citep{Hedelt:2011,Tanga:2011}."1128 This letter aims at providing a theoretical transmission spectrum of the atmosphere of Venus. from the ultraviolet to the infrared. as it could be observed during the transit of June 2012.," This letter aims at providing a theoretical transmission spectrum of the atmosphere of Venus, from the ultraviolet to the infrared, as it could be observed during the transit of June 2012."1129 Transmission spectroscopy probes the atmospheric limb of the transiting planet., Transmission spectroscopy probes the atmospheric limb of the transiting planet.1130 In the following. we consider an unidimensional atmospheric model. only varying with respect to the altitude and ignoring latitudinal and. longitudinal variations in atmospheric structure and composition.," In the following, we consider an unidimensional atmospheric model, only varying with respect to the altitude and ignoring latitudinal and longitudinal variations in atmospheric structure and composition."1131 Although latitudinal variation observations are well documented (e.g.. in the atmospheric density and temperature. cloud top altitude. etc.).," Although latitudinal variation observations are well documented (e.g., in the atmospheric density and temperature, cloud top altitude, etc.),"1132 this simplification is correct considering the geometry of the experiment and the lack of spatial resolution: the latitudinal variations are averaged in the transmission spectrum of the whole limb., this simplification is correct considering the geometry of the experiment and the lack of spatial resolution: the latitudinal variations are averaged in the transmission spectrum of the whole limb.1133 We consider an altitude range comprising the troposphere (0-60 km). the mesosphere (60-100 km). and the upper atmosphere (>100 km) of Venus. up to 400 km in altitude.," We consider an altitude range comprising the troposphere (0–60 km), the mesosphere (60–100 km), and the upper atmosphere $>100$ km) of Venus, up to 400 km in altitude."1134 ? measure the mesospheric temperature profile Τίς) with radio sounding from the VeRa instrument onExpress., \citet{Patzold:2007} measure the mesospheric temperature profile $T(z)$ with radio sounding from the VeRa instrument on.1135 We use their profile assuming an upper boundary temperature of 200 K at 100 km., We use their profile assuming an upper boundary temperature of 200 K at 100 km.1136 The tropospheric temperature profile is extrapolated from the tropopause (220 K at 61 km) down to the surface assuming a constant temperature lapse rate of +8.5 K km!. yielding a surface temperature of 740 K. Above 100 km. the temperature profile corresponds to the neutral component of the ionosphere and follow those used by ?.. initially calculated by ?..," The tropospheric temperature profile is extrapolated from the tropopause (220 K at 61 km) down to the surface assuming a constant temperature lapse rate of +8.5 K $^{-1}$, yielding a surface temperature of 740 K. Above 100 km, the temperature profile corresponds to the neutral component of the ionosphere and follow those used by \citet{Gronoff:2008}, initially calculated by \citet{Hedin:1983}."1137 The pressure profile p(z) is caleulated across the whole altitude range (0-400 km) assuming the atmosphere behaves as a perfect gas at hydrostatic equilibrium. PAD)=poexpf where po=93 bar is the surface pressure and H(z)|-2aiiiΚρΤ[pog] is the atmospheric scale," The pressure profile $p(z)$ is calculated across the whole altitude range (0–400 km) assuming the atmosphere behaves as a perfect gas at hydrostatic equilibrium, $p(z) = p_0 \exp\left[{-\int{{\d z}/{H(z)}}}\right]$ , where $p_0 = 93$ bar is the surface pressure and $H(z) = k_B T(z) / [\mu(z) g(z)]$ is the atmospheric scale"1138are more directly related to cluster mergers (Enlin ct al.,are more directly related to cluster mergers lin et al.1139 1998. Hoettiger et al.," 1998, Roettiger et al."1140 1999. Venturi et al.," 1999, Venturi et al."1141 1999... EnBlin CGopal-Ixrishna. 2001)..," 1999, lin Gopal-Krishna \nocite{1998AA...332..395E,1999ApJ...518..603R,1999dtrp.conf..27V,2001A&A...366...26E}."1142 They are also extended: racio sources with a steep spectrum., They are also extended radio sources with a steep spectrum.1143 In the literature radio relies are often. confused with radio halos even though several distinctive properties exist., In the literature radio relics are often confused with radio halos even though several distinctive properties exist.1144 Cluster racio relies are typically located near the periphery of the cluster: they often exhibit sharp emission edges anc many of them show strong racio polarisation., Cluster radio relics are typically located near the periphery of the cluster; they often exhibit sharp emission edges and many of them show strong radio polarisation.1145 In several cases it could be shown that shock waves are present at the locations of the relies., In several cases it could be shown that shock waves are present at the locations of the relics.1146 In Abell 2256 and Abell 1367 temperature substructures of the hot IGM could be detected (Briel Lenry 1994. Donnelly et al.," In Abell 2256 and Abell 1367 temperature substructures of the hot IGM could be detected (Briel Henry 1994, Donnelly et al."1147 which points towards the presence of shock waves at the location of the cluster relics in these clusters.," \nocite{1994Natur.372..439B,1998ApJ...500..138D} which points towards the presence of shock waves at the location of the cluster relics in these clusters."1148 For Abell 754 (1toettiger at al., For Abell 754 (Roettiger at al.1149 1998: ]xassim et al. 2001)..," 1998; Kassim et al. \nocite{1998ApJ...493...62R,kassim2001a},"1150 Abell 2256 (Itoettiger et al. 1995)..," Abell 2256 (Roettiger et al. \nocite{1995ApJ...453..634R},"1151 Abell 3667 (IXoettiger et al., Abell 3667 (Roettiger et al.1152 and also the Coma cluster (Burns et al., \nocite{1999ApJ...518..603R} and also the Coma cluster (Burns et al.1153 numerical simulations of mergers were fitted to the X-ray data., \nocite{1994ApJ...427L..87B} numerical simulations of mergers were fitted to the X-ray data.1154 These simulations predict. shock waves at locations of observed cluster racio relies., These simulations predict shock waves at locations of observed cluster radio relics.1155 The eluster racio relic 1253]275 in the Coma cluster shows a morphological connection to the nearby racio galaxy NGC 4789 (Ciovannini. Feretti Stanehellini 1991)).," The cluster radio relic 1253+275 in the Coma cluster shows a morphological connection to the nearby radio galaxy NGC 4789 (Giovannini, Feretti Stanghellini \nocite{1991A&A...252..528G}) )."1156 This sugeests that radio relies may be fossil radio plasma that has been revived by a shock., This suggests that radio relics may be fossil radio plasma that has been revived by a shock.1157 Fossil radio plasma is the former outflow of a radio galaxy in which the high-cnerey radio emitting electrons have lost their energy., Fossil radio plasma is the former outflow of a radio galaxy in which the high-energy radio emitting electrons have lost their energy.1158 Due to their invisibility in the radio these cocoons are also calledghosts (I5nBlin 1999)., Due to their invisibility in the radio these cocoons are also called lin \nocite{1999dtrp.conf..275E}.1159 The first. relic formation models considered: dillusive shock acceleration (Fermi 1) as the process producing the radio emitting electrons (enBlin ct al., The first relic formation models considered diffusive shock acceleration (Fermi I) as the process producing the radio emitting electrons lin et al.1160 1905. Rocttiger et al.," 1998, Roettiger et al."1161 1999. Venturi οἱ al. 1999).. Llo," 1999, Venturi et al. \nocite{1998AA...332..395E,1999ApJ...518..603R,1999dtrp.conf..27V}."1162wever. when a fossil raclio cocoon is passed by a cluster merger shock wave. with a vpical velocity of a few 1000 kin/s. the cocoon is compressed adiabatically and not shocked. because of the much higher sound speed within it.," However, when a fossil radio cocoon is passed by a cluster merger shock wave, with a typical velocity of a few 1000 km/s, the cocoon is compressed adiabatically and not shocked because of the much higher sound speed within it."1163 Therefore. shock acceleration cannot x the mechanism that re-energises the relativistic electron ;»pulation.," Therefore, shock acceleration cannot be the mechanism that re-energises the relativistic electron population."1164 But the energv gained during the adiabatic compression Combined with the increase in the magnetic ields strength: can cause the fossil radio cocoon to emit radio waves again., But the energy gained during the adiabatic compression combined with the increase in the magnetic fields strength can cause the fossil radio cocoon to emit radio waves again.1165 One prerequisite for this is that. the electron. population is not older than 0.2 2 Gyr (EnBlin CGopal-Ixrishna. 2001))., One prerequisite for this is that the electron population is not older than 0.2 - 2 Gyr lin Gopal-Krishna \nocite{2001A&A...366...26E}) ).1166 The timescale depends on the conditions in the surroundings. mainlv the external pressure.," The timescale depends on the conditions in the surroundings, mainly the external pressure."1167 In high-pressure environments. such as in cluster cores. the svnehrotron. losses are expected. to be much higher. due to the higher internal magnetic fields of pressure-confined radio plasma.," In high-pressure environments, such as in cluster cores, the synchrotron losses are expected to be much higher due to the higher internal magnetic fields of pressure-confined radio plasma."1168" ""This leads to a shorter maximum age for 10 fossil radio plasma if it is to be revived.", This leads to a shorter maximum age for the fossil radio plasma if it is to be revived.1169 Therefore. relies are found preferentially at the periphery of clusters =vhere the pressure is lower.," Therefore, relics are found preferentially at the periphery of clusters where the pressure is lower."1170 Moreover. numerical simulations garow that merger shocks are [found more [frequently in ee»vipheral cluster regions than in the denser cores (Quilis. xubez. Saez 1998: Miniati et al. 20002).," Moreover, numerical simulations show that merger shocks are found more frequently in peripheral cluster regions than in the denser cores (Quilis, Ibanez, Saez \nocite{1998ApJ...502..518Q}; Miniati et al. \nocite{2000ApJ...542..608M}) )."1171 Both effects. —1e longer time for radio plasma to be revivable. ancl the —ugher frequency of gashock waves could explain why cluster madio relics are more frequently observed at the outskirts of ‘lusters than in more central regions.," Both effects, the longer time for radio plasma to be revivable, and the higher frequency of shock waves could explain why cluster radio relics are more frequently observed at the outskirts of clusters than in more central regions."1172 EnBlin CGopal-Ixrishna. showed. that. the μα»ectral properties of cluster racio relies are well reproduce w this scenario., lin Gopal-Krishna \nocite{2001A&A...366...26E} showed that the spectral properties of cluster radio relics are well reproduced by this scenario.1173 Here. we demonstrate that the observe =rorphologics and polarisation patterns are reproduced. by js model as well.," Here, we demonstrate that the observed morphologies and polarisation patterns are reproduced by this model as well."1174 This is done with the help of the firs 3-dimensional magneto-hydrodyvnamiucal (ATID) simulations of a fossil radio cocoon that is passed by a shock wave., This is done with the help of the first 3-dimensional magneto-hydrodynamical (MHD) simulations of a fossil radio cocoon that is passed by a shock wave.1175 We xoduce artifical radio maps that can be compared directly o high-resolution racio maps of relies., We produce artifical radio maps that can be compared directly to high-resolution radio maps of relics.1176 The magneto-hvdrodvnamical simulations were obtained using the ZEUS-3D code which was developed: especially, The magneto-hydrodynamical simulations were obtained using the ZEUS-3D code which was developed especially1177where /(a.b:.r) is given in equation (16)).,"where $I(a,b;x)$ is given in equation \ref{rel:vfvi}) )."1178" This relation is compared with the data of rotation velocity Vi. and absolute magnitude V, of spiral galaxies in the I band taken from the table of Mathewson.Ford&Buchhorn(1992). and the results are shown in Figure 6 for ανω= 2and in Figure 7 for Ανω=4. together with the data."," This relation is compared with the data of rotation velocity $V_{rot}$ and absolute magnitude $M_{\rm I}$ of spiral galaxies in the I band taken from the table of \citet{mfb92}, and the results are shown in Figure \ref{fig:tfr-nfw-alpha2} for $\alpha_{hot}=2$ and in Figure \ref{fig:tfr-nfw-alpha4} for $\alpha_{hot}=4$, together with the data."1179 In each of these figures the left and right panels are for the impulsive and adiabatic mass losses. respectively.," In each of these figures the left and right panels are for the impulsive and adiabatic mass losses, respectively."1180" Here. assuming a constant baryonic mass to I-band light ratio ALL, and equating V; to the observed rotation velocity 1,,, for bright galaxies. we have set the power index =3 in equation (31)) by adjusting the Vy0M, relation along the horizontal axis in Figures 6 and 7. to fit to the observed TFR in the bright end."," Here, assuming a constant baryonic mass to I-band light ratio $M_i/L_{\rm I}$ and equating $V_i$ to the observed rotation velocity $V_{rot}$ for bright galaxies, we have set the power index $\gamma=3$ in equation \ref{eq:sn-mimf}) ) by adjusting the $V_f-M_f$ relation along the horizontal axis in Figures \ref{fig:tfr-nfw-alpha2} and \ref{fig:tfr-nfw-alpha4} to fit to the observed TFR in the bright end."1181 Our setting of ~=3 is consistent with the scaling relation of dark haloes obtained by A’-body CDM simulations (Navarro.Frenk&White1997) as well as the scaling relation of spiral galaxies obtained by A’-body/SPH CDM simulations (Steinmetz&Navarro 1999)., Our setting of $\gamma=3$ is consistent with the scaling relation of dark haloes obtained by $N$ -body CDM simulations \citep{nfw} as well as the scaling relation of spiral galaxies obtained by $N$ -body/SPH CDM simulations \citep{sn99}.1182. We see from these figures that the οMy relations with no dynamical response and with no dark halo deviate signiticantly from the faint data. while the dynamical response with dark halo improves the fit to the data.," We see from these figures that the $V_f-M_f$ relations with no dynamical response and with no dark halo deviate significantly from the faint data, while the dynamical response with dark halo improves the fit to the data."1183" In particular. the VyM; relations that well agree with the data over the full range of 1, observed are those of 2;=0.2 and à,=2.4 for the impulsive mass loss. and those of z;—0.1. 0.2and à,= 2as well as z;=0.2 and O5,= 4forthe adiabatic mass loss."," In particular, the $V_f-M_f$ relations that well agree with the data over the full range of $M_{\rm I}$ observed are those of $z_i=0.2$ and $\alpha_{hot}=2-4$ for the impulsive mass loss, and those of $z_i=0.1-0.2$ and $\alpha_{hot}=2$ as well as $z_i=0.2$ and $\alpha_{hot}=4$ for the adiabatic mass loss."1184 Theoretical dise size versus magnitude relation or the ryMy relation is obtained by a set of the following equations:, Theoretical disc size versus magnitude relation or the $r_f-M_f$ relation is obtained by a set of the following equations:1185o emerge from the cise and its position relative to the disc surface may remain approximately unchanged for some time.,to emerge from the disc and its position relative to the disc surface may remain approximately unchanged for some time.1186 Thus we make the assumption that the flare is confined by he magnetic field and corotates with the dise and possesses ixecl Bover-Lindquist coordinates 7 and 0., Thus we make the assumption that the flare is confined by the magnetic field and corotates with the disc and possesses fixed Boyer-Lindquist coordinates $r$ and $\theta$.1187 We also assume hat: the flaring region is point-like. has a finite life-time and that photons propagate freely. to either the observer. o the black hole. to the disc or escape to infinity once emitted by the blob.," We also assume that: the flaring region is point-like, has a finite life-time and that photons propagate freely to either the observer, to the black hole, to the disc or escape to infinity once emitted by the blob."1188 Vhis means that the corona above the accretion disc is optically thin., This means that the corona above the accretion disc is optically thin.1189 TFhis is a generalization of the considerations presented by IYDE99 who model X-ray [are asad. like impulse and aclelitionally assume that radiation is produced in the locally non-rotating frame of reference., This is a generalization of the considerations presented by RYBF99 who model X-ray flare as a $\delta-$ like impulse and additionally assume that radiation is produced in the locally non-rotating frame of reference.1190 In order to numerically integrate the photon trajectory from hecorotatiug lare we first analvticallv derive appropriate constants of motion to propagate photons through the Ixerr metric., In order to numerically integrate the photon trajectory from the flare we first analytically derive appropriate constants of motion to propagate photons through the Kerr metric.1191 ALL the necessary. formulae are given in Appenclix D.2 where we express the constants of motion in terms of volar and azimuthal angles in the local rest. [rame of the »oint-like source.," All the necessary formulae are given in Appendix B, where we express the constants of motion in terms of polar and azimuthal angles in the local rest frame of the point-like source."1192 “Thus we can easily. model the isotropic clistribution of radiation in the emitter's frame by a Monte Carlo method., Thus we can easily model the isotropic distribution of radiation in the emitter's frame by a Monte Carlo method.1193 This enables us to calculate the illuminating lux as a function of time and energy in the rest frame of the corotating disc material taking into account all the general relativistic effects. including: previously neglected. Doppler roosting from the moving flare.," This enables us to calculate the illuminating flux as a function of time and energy in the rest frame of the corotating disc material taking into account all the general relativistic effects, including previously neglected Doppler boosting from the moving flare."1194 In the implementation of he algorithm we used the formula (see Appendix C): where we additionally assume that the [lare emits a power law spectrum. with energy index a., In the implementation of the algorithm we used the formula (see Appendix C): where we additionally assume that the flare emits a power law spectrum with energy index $\alpha$.1195 The factor far. which is the ratio of the number of photons intersecting a small patch on the cise (defined by do and dr) to the total number of emitted photons. was calculated by means of the Monte Carlo method.," The factor $f_{sd}$, which is the ratio of the number of photons intersecting a small patch on the disc (defined by $d\phi$ and $dr$ ) to the total number of emitted photons, was calculated by means of the Monte Carlo method."1196 In the above formula £5; is the time it takes for photon emitted from the source to reach the disc element and > is the Lorentz factor for the relative motion of the disc clement and the locally non-rotating observer., In the above formula $\tilde{t}_{sd}$ is the time it takes for photon emitted from the source to reach the disc element and $\gamma$ is the Lorentz factor for the relative motion of the disc element and the locally non-rotating observer.1197" goa is the redshift factor given by where pa, and ps, are the photon lour-momenta at the cise ancl source respectively,", $g_{sd}$ is the redshift factor given by where $p_{d\mu}$ and $p_{s\mu}$ are the photon four-momenta at the disc and source respectively.1198" We follow the lines of reasoning of Cunningham (1975) and split the velocity field of the accretion disc n, into the region outside the radius of marginal stability. where matter follows circular orbits. and the region within the innermost stable orbit where the matter has a negative radial component ancl spirals towards the black hole."," We follow the lines of reasoning of Cunningham (1975) and split the velocity field of the accretion disc $u_{d}$ into the region outside the radius of marginal stability, where matter follows circular orbits, and the region within the innermost stable orbit where the matter has a negative radial component and spirals towards the black hole."1199 The formulae for the are velocity field at! are collected in Appendix D. The radiation. which impinges upon the disc surface is reprocessed απ rellected., The formulae for the flare velocity field $u^{\mu}_{s}$ are collected in Appendix B. The radiation which impinges upon the disc surface is reprocessed and reflected.1200 The shape of the reflected spectrum depends upon many factors. the most important being the cise structure and ionization state of the accretion disc.," The shape of the reflected spectrum depends upon many factors, the most important being the disc structure and ionization state of the accretion disc."

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