ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Further. the Q-bauds secius to exhibit a uegative g.. WhichsugeestsOO frequency dependence.," Further, the Q-bands seems to exhibit a negative $g_*$ , whichsuggests frequency dependence."3assume the optically thin limit. for both ionizing radiaion and photodissociating LW photons.,"assume the optically thin limit, for both ionizing radiation and photodissociating LW photons."4 Both of these approximations clearly fail at points in our simulations. and so it is necessary to understand the nature and implications of this approximaion.," Both of these approximations clearly fail at points in our simulations, and so it is necessary to understand the nature and implications of this approximation."5 For clarity. we discuss ionizing photons and LW photons separately.," For clarity, we discuss ionizing photons and LW photons separately."6 We discuss the impact of radiation hydrodynamic (RHD) effects due to ionizing photons first., We discuss the impact of radiation hydrodynamic (RHD) effects due to ionizing photons first.7 There is now a substanial body of literature on the ionization of primordial gas halos ¢?? and the broad outline of how halos are ionized is ne»w well understood.," There is now a substantial body of literature on the ionization of primordial gas halos \citep{SIR04, WAN04, ISR05, ABS05, SU06, Whalen08, AWB07, WA08} and the broad outline of how halos are ionized is now well understood."8 We begin by noting that the optical depth oftqe halos which are ionized in our simulation box at 2=25r (as shown in Fig. 13).," We begin by noting that the optical depth of the halos which are ionized in our simulation box at $z=25$ (as shown in Fig. \ref{fig:early_profiles}) ),"9 as measured from the virial radius to the center is — at the Lyman limit — well over 100., as measured from the virial radius to the center is – at the Lyman limit – well over 100.10 Therefore. at tirst blush. the optically thin limit seems like a poor approximation.," Therefore, at first blush, the optically thin limit seems like a poor approximation."11 However. this impression is not entirely accurate for two reasons.," However, this impression is not entirely accurate for two reasons."12 First. we are studying the/afer formation of halos in relic HIT regions. and much of the gas that eventually falls into a halo at late times is in the center of halos at reionization.," First, we are studying the formation of halos in relic HII regions, and much of the gas that eventually falls into a halo at late times is in the center of halos at reionization."13 This is the question that ὁ asked: does the excess entropy generated in density gas in relic HIT regions prevent it from forming stars at later times., This is the question that \citet{OH03} asked: does the excess entropy generated in low-density gas in relic HII regions prevent it from forming stars at later times.14 This low density gas has much lower optical depth and so is very likely to be ionized by a nearby Pop III star., This low density gas has much lower optical depth and so is very likely to be ionized by a nearby Pop III star.15"The projected orbital separation. e. measured [rom the light curve. can be related to a combination of the true orbital separation at the time of the event and the orbital inclination: @=αιοοδ(θ]. The value of e,,4 is related to the orbital speed at the time of the event: ο=30km/sxy/(M,M.)CAUεις). The proper motion of the planet can be measured Lom a combination of 4pprance and Tj.","The projected orbital separation, $a,$ measured from the light curve, can be related to a combination of the true orbital separation at the time of the event and the orbital inclination: $a=a_{true} cos(\theta).$ The value of $a_{true}$ is related to the orbital speed at the time of the event: $v=30\, {\rm km/s} \times \sqrt{(M_\ast/M_\odot)\, ({\rm AU}/a_{true})}.$ The proper motion of the planet can be measured from a combination of $\theta_{E,planet}$ and $\tau_E$."16" With D, known. we can estimate the projected value of the planet's orbital velocity. ecos(?). by comparing the values of eyone and o. Combining the equations for e and a. vields a value for the inclination of the orbit."," With $D_L$ known, we can estimate the projected value of the planet's orbital velocity, $v\, cos(\theta),$ by comparing the values of $\omega_{planet}$ and $\omega_{\ast}.$ Combining the equations for $v$ and $a,$ yields a value for the inclination of the orbit."17 This example illustrates that for nearby lenses. orbital solutions can be obtained. even for face-on orbits.," This example illustrates that for nearby lenses, orbital solutions can be obtained, even for face-on orbits."18 Furthermore. there can be enough information to provide independent checks on the values of some physical parameters.," Furthermore, there can be enough information to provide independent checks on the values of some physical parameters."19 Even planets in very. wide orbits can be well studied with lensing. especially if there is a repeating event (DiStelano Scalzo 1999h).," Even planets in very wide orbits can be well studied with lensing, especially if there is a repeating event Stefano Scalzo 1999b)."20 When high-velocity stellar-mass objects are nearby. their Einstein angles are large enough io be measured during the event by measuring the centroid shift in the lensed source.," When high-velocity stellar-mass objects are nearby, their Einstein angles are large enough to be measured during the event by measuring the centroid shift in the lensed source."21" In general. this leaves a clegeneracy between. Dj, and M."," In general, this leaves a degeneracy between $D_L$ and $M$."22 The degeneracy can be resolved if (he lens is detected., The degeneracy can be resolved if the lens is detected.23 Consider. for example. a halo dwarf star with M=0.251. and e=150 km !.," Consider, for example, a halo dwarf star with $M=0.25\, M_\odot$ and $v=180$ km $^{-1}$."24 Lf this lens is 24.8 pe away from us. il can cause an event with Tj—5 days.," If this lens is $34.8$ pc away from us, it can cause an event with $\tau_E=5$ days."25 Assuming that Dy22Dj. The value of &j; would be 7.6 milliareseconds. ancl the astrometric shift induced by the lens could be measured: (he optimal case would be when (he lensed source is a bright blue star.," Assuming that $D_S>>D_L,$ The value of $\theta_E$ would be $7.6$ milliarcseconds, and the astrometric shift induced by the lens could be measured; the optimal case would be when the lensed source is a bright blue star."26 Such a halo chvarl would itself be easily detected alter moving Irom the source position. ancl its proper motion and parallax could be directly measured.," Such a halo dwarf would itself be easily detected after moving from the source position, and its proper motion and parallax could be directly measured."27 Its gravitational mass could therefore be measured to hieh precision., Its gravitational mass could therefore be measured to high precision.28" This lens would travel across the skv with an angular speed of ~1"" vr.|.", This lens would travel across the sky with an angular speed of $\sim 1^{\prime\prime}$ $^{-1}$.29 With such a high angular speed., With such a high angular speed.30" it is very likely that. if the background fiekl is dense. additional lensing events will occur over a (time interval of ~10 νους,"," it is very likely that, if the background field is dense, additional lensing events will occur over a time interval of $\sim 10$ years."31 Decause (he presence of the lens is already known. il is easier to identilv future events with confidence. even if (he angle of closest approach is larger.," Because the presence of the lens is already known, it is easier to identify future events with confidence, even if the angle of closest approach is larger."32 Once a second event is discovered. the general direction of the lens motion is known and future photometric ancl astrometric events are more easily predicted.," Once a second event is discovered, the general direction of the lens motion is known and future photometric and astrometric events are more easily predicted."33 If a sequence of events is detected. the proper motion and parallax can be computed by comparing the locations and times of the events.," If a sequence of events is detected, the proper motion and parallax can be computed by comparing the locations and times of the events."34 This means that even for dark high-speed lenses. mass measurements can be made.," This means that even for dark high-speed lenses, mass measurements can be made."35 When the lens is a neutron star. it may radiate x-ravs as il cools and/or accretes matter [rom the ISM: it may therefore be catalogued as a weak x-ray source.," When the lens is a neutron star, it may radiate x-rays as it cools and/or accretes matter from the ISM; it may therefore be catalogued as a weak x-ray source."36 It is worth noting (hat repeating events have been observed (Skowron et 2009)., It is worth noting that repeating events have been observed (Skowron et 2009).37 Every event of short duration is likely to be associated with an interesting lens: a low-mass object. or a high-velocity mass.," Every event of short duration is likely to be associated with an interesting lens: a low-mass object, or a high-velocity mass."38 These events should (therefore be high-prioritv, These events should therefore be high-priority39"of cosmic rav protons. [NCE,)— N,E,.","of cosmic ray protons, $N(E_p) = K_p E_p^{-s}$."40 In this case the inclusive. cross section for the production. of $7 1s approximately that of π and thus from Eqs.(36- 37)). one finds⋅: where ts)uL264.⋅6510“aelos. ‘and we Iput where Lt follows⋅ that the slope of⋅ the spectum of secondary . . . ⋅ MEN ⊀ . . .⋅⋝⊀ ⋅ ∖∖⊽↓⋯⇍↓⊔↿↓⊳∖⋜↧⊳∖⊳∖⊔⊔↓∢⊾∠⊓↓↥⋜∐∖∖⊽↓↿↓⊔⊔∢⋅⋯↛↓↥↿↓⊔↓⋖⊾−⊳∖↿⋖⊾↓≻↿↓↕⋖⋅⊳∖↓≻⋖⋅≼∼↿↓⋅⊔⊔↓ 1999).," In this case the inclusive cross section for the production of $\pi^\pm$ is approximately that of $\pi^o$ and thus from \ref{qepm2}- \ref{ppi}) ), one finds: where $A(s)=64\times c \times 10^{-27} a^{1-s}$, and we put and where and where the are defined as: and It follows that the slope of the spectum of secondary electrons and positrons is essentially that of the cosmic ray protons in this approximation (e.g., Dermer 1986a; Blasi Colafrancesco 1999)."41⋅↔ In addition.," In addition, Eq."42 Ίσα.⊲⋅ 38. .describes theof : departure⋅ from the. simple power2.4. law shape which is solving. to the increase of⋅ the inclusive cross⊀ section with⊀ thechanges energv of the scattering⊀ protons (e.g... Dermer 1986b).," \ref{qepm_s} describes the slight departure from the simple power law shape which is due to the increase of the inclusive cross section with the energy of the scattering protons (e.g., Dermer 1986b)."43⋅ As shown in Paper L the spectra of protons as allected by the reacceleration are usually not power laws.," As shown in Paper I, the spectra of protons as affected by the reacceleration are usually not power laws."44 Therefore the expressions given here for the case of power law spectra |are in general not applicable.p although in the following? we will DDsometimes. use them. where specified.EN in. order to estimate. orders of magnitudo.," Therefore the expressions given here for the case of power law spectra are in general not applicable, although in the following we will sometimes use them, where specified, in order to estimate orders of magnitude."45. A detailed: modelling of the injection of MIID turbulence Ced clusters and of all the related processes of waveparticle coupling is a very complex matter and. well above the capabilitiesqui of⋅ present numerical. simulations. ancl seni.analytical treatments., A detailed modelling of the injection of MHD turbulence in galaxy clusters and of all the related processes of wave--particle coupling is a very complex matter and well above the capabilities of present numerical simulations and semi--analytical treatments.46 On the other hand. the basies of this process ean be hopefully understood by making use of viable assumptions and simplifications: this is the aim of Sect.45.," On the other hand, the basics of this process can be hopefully understood by making use of viable assumptions and simplifications: this is the aim of Sect.4–5."47 We assume that the injection of turbulence starts in with a merger event. and remains constant [or ο...the duration of such an event., We assume that the injection of turbulence starts in coincidence with a merger event and remains constant for the duration of such an event.48 As a necessary simplification the spectrum. of Huid. turbulence is taken in the form. of a power law (I2q.18)). which basically means that there is roughly a single driving scale.," As a necessary simplification the spectrum of fluid turbulence is taken in the form of a power law \ref{wfluid}) ), which basically means that there is roughly a single driving scale."49 Phe turbulence that is injected is only fluid turbulence. while the MID turbulence is eveloped later as a consequence of theLighthilf mechanism.," The turbulence that is injected is only fluid turbulence, while the MHD turbulence is developed later as a consequence of the mechanism."50 We assume that the physical conditions in the ICM (namely magnetic field strength. temperature and number density of the thermal particles) do not change significantly curing the ime in which the turbulence is injected.," We assume that the physical conditions in the ICM (namely magnetic field strength, temperature and number density of the thermal particles) do not change significantly during the time in which the turbulence is injected."51 We also assume that there is no spatial dilfusion. of re particles during the period of injection of the. [uid turbulence. and. ignore the elect of the mixing. processes which may take place cluring cluster merger events.," We also assume that there is no spatial diffusion of the particles during the period of injection of the fluid turbulence, and ignore the effect of the mixing processes which may take place during cluster merger events."52 1n acicition2. we assume that the [uid. turbulence ane the ALD turbulence are isotropic and that the magnetic field is tangled enough to ensure that also the clistribution of the accelerated. particles is isotropic in pitch angle., In addition we assume that the fluid turbulence and the MHD turbulence are isotropic and that the magnetic field is tangled enough to ensure that also the distribution of the accelerated particles is isotropic in pitch angle.53 With these assumptions the interaction between waves ancl particles can be investigated: by solving the set. of coupled differential equations Eqs. 10.. I1..," With these assumptions the interaction between waves and particles can be investigated by solving the set of coupled differential equations Eqs. \ref{elettroni}, \ref{protoni},"54 and. 12.., and \ref{turbulence}.55 We consider situations in which the amount of energy injected in the form of turbulence is typically much. smaller. than the thermal οποίον of the ICM. ancl thus the thermal distributions⋠⋠⋠ of⋅ electrons. and protons are. treated: as stationary.," We consider situations in which the amount of energy injected in the form of turbulence is typically much smaller than the thermal energy of the ICM, and thus the thermal distributions of electrons and protons are treated as stationary."56. Since» the time. scale of⋅ damping. and. cascacing. are much shorter than the particle acceleration time scale. ⋅. ⋖⋅⇂∢⋅≼∙↥↓⋅∪⊔≱∖⋜⋯∠⇂↓≻∪≱∖⊔↓⋅∪⊔≱∖↓⊳∖∢⊾⊳∖⊳∖⋖⋅⊔↿↓⋜↧∐∙∖⇁⇂↓⋯∣∪⇂↿↓↥∢⊾≼∼∪⊳∖⊔↓⊔⇍↓⋅⋜↧∙∖⇁ . uu ↓≻↓⋅∪⋯⊔⊳∖↓⊔↿↓⊔⊳∖⋜↧↓≻↓≻↓⋅∪⇀∖↓⊔↓⋜⊔↓∪⊔↿∖∢⋅⊓∙≟↣∐⋖⋅↓⋅⊔↓∢⊾↓⋅↓≤⋗↖∖↻⋜↧∶⊥≻↓⋜↧⊳∖↓⊾∖↽. . the. waves approaches a stationary solution. (obtained.. by. Colafr," Since the time scale of damping and cascading are much shorter than the particle acceleration time scale, following Paper I we adopt a, in which it is assumed that within each time-step the spectrum of the waves approaches a stationary solution (obtained by solving Eq."57ancesco Eq.. 12.. with 0M∙⊽∙ Yer.=0) and that this solution. slight. with time. due. to the evolution of. the spectrum of due the accelerated. electrons and. protons., \ref{turbulence} with $\partial W/ \partial t =0$ ) and that this solution changes with time due to the evolution of the spectrum of the accelerated electrons and protons.58" As discussed. in. Paper lL. Alfvénn⋅∕ waves channel most. ο the energy into. relativistic""MN protons. therefore⋅ subtracting MNi from⋅ the electron component which Dasis on the other haux responsible for the observed: radiations."," As discussed in Paper I, Alfvénn waves channel most of the energy into relativistic protons, therefore subtracting it from the electron component which is on the other hand responsible for the observed radiations."59 Ht follows that if protons are too abundant in the ICM. the AULD turbulence is too ellicientlv. clamped and the acceleration of electrons is suppressed.," It follows that if protons are too abundant in the ICM, the MHD turbulence is too efficiently damped and the acceleration of electrons is suppressed."60 This process is in fact quite complex. since i," This process is in fact quite complex, since it"613C 273 is the well-known quasar at the redshift 2=0.158. discovered together with its famous large-scale jel al (he very. beeinning of quasar optical researches (seeareviewCourvoisier L998).,"3C 273 is the well-known quasar at the redshift $z = 0.158$, discovered together with its famous large-scale jet at the very beginning of quasar optical researches \citep[see a review by][]{cou98}."62. At radio frequencies it appears as the one-sided. core-dominated source of non-thermal radiation. with the radio jel extended up to a lew tens of kpe trom the core. similarly (o ils optical counterpart.," At radio frequencies it appears as the one-sided, core-dominated source of non-thermal radiation, with the radio jet extended up to a few tens of kpc from the core, similarly to its optical counterpart."63 The jet is also prominent al X-ray lrequencies. although the origin of this radiation is still being debated Gn contrast with the raclio-to- emission. whose svuchrotvon nature is surely established).," The jet is also prominent at X-ray frequencies, although the origin of this radiation is still being debated (in contrast with the radio-to-optical emission, whose synchrotron nature is surely established)."64 Until now. neither (he jet," Until now, neither the jet"65", I weshowtheFRcolour− −∁∘∅⋯⊤⊤∊∅⊄∐⋚∅∎∘∏≼≼∊∘∕↕∘∘⋟∁↥⊟∐∁↥≼↕∠↨⊖∕↕⊖⊖⋟∁↺∁∃∣∁∐∣⊟↥∁⊂↥ for silicate and graphite.",", we show the FIR colour--colour relation $(60/100)_\mathrm{cl}$ and $(140/100)_\mathrm{cl}$ ) calculated for silicate and graphite."66 We observe that the FIR colours of the BCD sample can be reproduced with x~ 30-300 except for the lowest data point (II Zw 71)., We observe that the FIR colours of the BCD sample can be reproduced with $\chi\sim 30$ –300 except for the lowest data point (II Zw 71).67" This is consistent with the conclusion in HO8 that the ISRF (especially the UV ISRF, which contributes most to the dust heating) in BCDs can be 100 times higher than the Galactic ISRF in the solar neighbourhood."," This is consistent with the conclusion in H08 that the ISRF (especially the UV ISRF, which contributes most to the dust heating) in BCDs can be 100 times higher than the Galactic ISRF in the solar neighbourhood."68" Our results not only confirm the warm Satellite)) 60 µπι-100 1m colours of BCDs (Hoffmanetal.1989),, but also show high temperatures of dust contributing to the emission at A>100 um. A few Virgo Cluster BCDs observed by Observatory)) show relatively cold 170 µπι--100 jum colours (Popescuetal.2002),, indicating that the presence of warm dust is not necessarily the case at least in cluster environments."," Our results not only confirm the warm ) 60 $\mu$ m–100 $\mu$ m colours of BCDs \citep{hoffman89}, but also show high temperatures of dust contributing to the emission at $\lambda >100~\mu$ m. A few Virgo Cluster BCDs observed by ) show relatively cold 170 $\mu$ m--100 $\mu$ m colours \citep{popescu02}, indicating that the presence of warm dust is not necessarily the case at least in cluster environments."69 We also find that the calculated FIR colours cover the area between the main correlation and the subcorrelation., We also find that the calculated FIR colours cover the area between the main correlation and the subcorrelation.70" With x<10, the colours trace the main correlation, which is appropriate for the Milky Way, the LMC and the SMC."," With $\chi\la 10$, the colours trace the main correlation, which is appropriate for the Milky Way, the LMC and the SMC."71" On the other hand, the FIR colours are rather similar to the subcorrelation for x2100."," On the other hand, the FIR colours are rather similar to the subcorrelation for $\chi\ga 100$."72" While Hibietal.(2006) and HHS07 claimed that the subcorrelation can be reproduced with dust emission with multiple temperature components, we see here that the upper part of the subcorrelation can be explained with a single temperature."," While \citet{hibi06} and HHS07 claimed that the subcorrelation can be reproduced with dust emission with multiple temperature components, we see here that the upper part of the subcorrelation can be explained with a single temperature."73" FIR emission comes from dust at different optical depths, where the ISRF intensities are different because of dust extinction."," FIR emission comes from dust at different optical depths, where the ISRF intensities are different because of dust extinction."74" As modeled in Section 2.3,, the FIR intensity is the sum of all contributions from different optical depths."," As modeled in Section \ref{subsec:colour}, the FIR intensity is the sum of all contributions from different optical depths."75 Hibietal.(2006) expect that radiation transfer effects shift the FIR colours toward the subcorrelation on the colour-colour diagram., \citet{hibi06} expect that radiation transfer effects shift the FIR colours toward the subcorrelation on the colour–colour diagram.76" In reffig:clr;arAv, , weshowtheF Rcoloursforx =3, 30, and 300 with various values of Ay (AvI=0, 0.1, 0.2, 0.5, 1, and2)*."," In \\ref{fig:clr_varAv}, we show the FIR colours for $\chi =3$, 30, and 300 with various values of $A_V$ $A_V=0$, 0.1, 0.2, 0.5, 1, and."77". The FIR colours change little for Αν= 2, since the emission is negligible from such large optical depths in the wavelength range of interest because of low dust temperatures."," The FIR colours change little for $A_V\ga 2$ , since the emission is negligible from such large optical depths in the wavelength range of interest because of low dust temperatures."78" As expected by etal. (2006), there is a slight trend that the colours move toward the subcorrelation for x<30."," As expected by \citet{hibi06}, there is a slight trend that the colours move toward the subcorrelation for $\chi\la 30$."79" However, we observe that the radiative transfer effects shift the FIR colours along the main correlation or the subcorrelation for x230."," However, we observe that the radiative transfer effects shift the FIR colours along the main correlation or the subcorrelation for $\chi\ga 30$."80 This indicates that the radiative transfer effects are hard to be distinguished from the change of x on the colour-colour diagram., This indicates that the radiative transfer effects are hard to be distinguished from the change of $\chi$ on the colour–colour diagram.81 How can we distinguish the variation of Ay from that of x?, How can we distinguish the variation of $A_V$ from that of $\chi$?82 We expect that if the change of Ay controls the colour variation there may be a correlation between dust content and FIR colours., We expect that if the change of $A_V$ controls the colour variation there may be a correlation between dust content and FIR colours.83 Below we further discuss the observed FIR colours in BCDs in terms of the dustcontent., Below we further discuss the observed FIR colours in BCDs in terms of the dustcontent.84As already shown in Fig. 1..,"As already shown in Fig. \ref{maps_stars},"85 our eight simulated galaxies have a variety of morphologies and. in particular. their disces show a great variety. of shapes and masses.," our eight simulated galaxies have a variety of morphologies and, in particular, their discs show a great variety of shapes and masses."86 Moreover. the distributions of disc stellar ages (Fig. 2))," Moreover, the distributions of disc stellar ages (Fig. \ref{hist_stellarage}) )"87 are in general characterized by a superposition of bursts of dilferent age., are in general characterized by a superposition of bursts of different age.88 In order to investigate in more detail the structure of disces at 2c. we show in Fig.," In order to investigate in more detail the structure of discs at $z=0$, we show in Fig."89 4 the distribution of dise particles. in an edge-on view (note that Ae-E-5 has no disc). up to twice the corresponding optical radius.," \ref{disk_structure} the distribution of disc particles, in an edge-on view (note that Aq-F-5 has no disc), up to twice the corresponding optical radius."90 We plot separately stars formed in three different agebins?: F/Gvr< 4.4«Gr9 and αντ9.," We plot separately stars formed in three different age: $t/{\rm Gyr}\le 4$, $4 <91t/{\rm Gyr} \le 9$ and $t/{\rm Gyr}>9$."92 Phe plots are color-coded: according to the surface mass density at cach point: covering 4 orders of magnitude (101LON M. kpe 7)., The plots are color-coded according to the surface mass density at each point; covering 4 orders of magnitude $10^4-10^8$ $_\odot$ $^{-2}$ ).93" The diversity of clises is evident: we find not only very thin clises (Aq-C-5. Aq-E-5). but also a variety of shapes: ""boxv or 7X-shaped clises (Aq-D-5. Aq-G-5. Xq-11-5). warps (Aq-B-5). and a case where two misalignecl disces of dillerent age are present. (Aq-A-5)."," The diversity of discs is evident: we find not only very thin discs (Aq-C-5, Aq-E-5), but also a variety of shapes: “boxy” or “X”-shaped discs (Aq-D-5, Aq-G-5, Aq-H-5), warps (Aq-B-5), and a case where two misaligned discs of different age are present (Aq-A-5)."94 This diversity arises naturally in the context of ACDAL due to the cülferent formation. merger and aceretion histories of galaxics.," This diversity arises naturally in the context of $\Lambda$ CDM due to the different formation, merger and accretion histories of galaxies."95 From Fig., From Fig.96 4 we can also observe that stars in the voungest age bin (left-hand. panels) tend to define thinner discs than. older populations., \ref{disk_structure} we can also observe that stars in the youngest age bin (left-hand panels) tend to define thinner discs than older populations.97 In Fig., In Fig.98 5 νο show the cumulative fraction of stellar mass formed. f; as a function of stellar age for stars located. in three different bins. of (absolute value of) height above the dise plane:0.25]. (0.250.5] and (0.5—0.75] times the corresponding optical radius.," \ref{mean_z} we show the cumulative fraction of stellar mass formed $f_*$ as a function of stellar age for stars located in three different bins of (absolute value of) height above the disc plane:, $(0.25-0.5]$ and $(0.5-0.75]$ times the corresponding optical radius."99 In. general. we find that stars in the lower [2] bins. i.e. closer to the disc plane. are vounger than stars ab larger vertical distances.," In general, we find that stars in the lower $|z|$ bins, i.e. closer to the disc plane, are younger than stars at larger vertical distances."100 This behaviour is more clear in those galaxies with significant disc components. (Aq-C-5. Aq-D-5. Ag-E-5).," This behaviour is more clear in those galaxies with significant disc components (Aq-C-5, Aq-D-5, Aq-E-5)."101 Aq-G-5 has also an important disc component. but we detect the opposite trend: further above the dise plane we find vounger stars.," Aq-G-5 has also an important disc component, but we detect the opposite trend: further above the disc plane we find younger stars."102 It is interesting to note that this galaxy has a strong bar and mixing might play an important role in the distribution of voung stars., It is interesting to note that this galaxy has a strong bar and mixing might play an important role in the distribution of young stars.103 Galaxies with less prominent clises also show a trend of vounger stars being closer to the disc. plane. however. the behaviour is more diverse.," Galaxies with less prominent discs also show a trend of younger stars being closer to the disc plane, however, the behaviour is more diverse."104 ln Aq-A-5 and. Xe-1-5. the dependence of vertical extent on stellar age is not monotonic.," In Aq-A-5 and Aq-H-5, the dependence of vertical extent on stellar age is not monotonic."105 On the contrary. in Aq-B-5 we detect a very. well defined relation between stellar age and thickness.," On the contrary, in Aq-B-5 we detect a very well defined relation between stellar age and thickness."106 We also note that in Aq-A-5 the results might be influencecl by the fact that he voung stars define a second stellar disc. misaligned with he older disc component.," We also note that in Aq-A-5 the results might be influenced by the fact that the young stars define a second stellar disc, misaligned with the older disc component."107 The projection we adopt is such hat the older disc is contained in the wry plane. while the vounger disc is not.," The projection we adopt is such that the older disc is contained in the $xy$ plane, while the younger disc is not."108 In fact. if projected with respect to the atter. the voung disc appears very thin.," In fact, if projected with respect to the latter, the young disc appears very thin."109 Furthermore. we find that the voungest stars define more extended. discs.," Furthermore, we find that the youngest stars define more extended discs."110 In. Fig., In Fig.111 G6 we show the cumulative raction of stellar mass f; as a function of stellar age.ge now or disc stars in three dilferent radial bins according to their present-day positions: p<0.5rua. 0ragamorrape and ronXrrdbrugas," \ref{cum_Mstar} we show the cumulative fraction of stellar mass $f_*$ as a function of stellar age, now for disc stars in three different radial bins according to their present-day positions: $r\le1120.5\,r_{\rm opt}$, $0.5\,r_{\rm opt}<r\le r_{\rm opt}$ and $r_{\rm113 opt}<r\le 1.5\,r_{\rm opt}$."114 The behaviour of the cumulative stellar mass [fraction demonstrates an inside-out dise formation »utern for most simulated: discs., The behaviour of the cumulative stellar mass fraction demonstrates an inside-out disc formation pattern for most simulated discs.115 While the innermost regions are populated with stars older than S Cover. disc stars in the outermost regions are significantly. vounger.," While the innermost regions are populated with stars older than $8$ Gyr, disc stars in the outermost regions are significantly younger."116 There are two cases. Agq-D-5 and. Aq-E-5. for which we detect no significant dillerence between the three radial bins.," There are two cases, Aq-D-5 and Aq-E-5, for which we detect no significant difference between the three radial bins."117negative angular momentum.,negative angular momentum.118 In the development below. disks are assigned positive angular momentum with counter-clockwise rotation.," In the development below, disks are assigned positive angular momentum with counter-clockwise rotation."119 Our models may be transformed to the Milky Way system by reflection through the y z plane., Our models may be transformed to the Milky Way system by reflection through the $y$ $z$ plane.120" We will adopt a standard. galaxy. model with a hing model halo with tical radius £2,=28 (200 kpe). loge=0.67. and a mass of 10 times the clisk mass: this is “maximal” disk mocel."," We will adopt a standard galaxy model with a King model halo with tidal radius $R_t=28$ (200 kpc), $\log c=0.67$, and a mass of 10 times the disk mass; this is “maximal” disk model."121 “Phe bulge is Llernquist model with scale length 0.2 (1.4 kpc) and mass of of the disk (1.21027NL. 3., The bulge is Hernquist model with scale length 0.2 (1.4 kpc) and mass of of the disk $1.2\times10^{10}\msun$ ).122" Phe disk is the Llunter-Poomre 108 model with /2,,,;=4 (28 kpc).", The disk is the Hunter-Toomre 16X model with $R_{max}=4$ (28 kpc).123 In this system. one velocity unit is 350kms.I.," In this system, one velocity unit is $350\kms$."124 The rotation curve for this model rises from 0.6 at 2=0.5 to Moat R=LS. drops slowly to 0.6 at A?210 (70 kpe) and drops olf more rapidly bevond this point.," The rotation curve for this model rises from 0.6 at $R=0.5$ to 0.7 at $R=1.8$, drops slowly to 0.6 at $R=10$ (70 kpc) and drops off more rapidly beyond this point."125 Although better its to the observed Milky. Way rotation curve are available. our goal of understanding the underlving mechanism ancl he computational simplicity of these components supports our choice.," Although better fits to the observed Milky Way rotation curve are available, our goal of understanding the underlying mechanism and the computational simplicity of these components supports our choice."126 Finally. the standard moclel includes a satellite with an LAIC orbit.," Finally, the standard model includes a satellite with an LMC orbit."127 Phe magnitude of the response scales with satellite mass and need not be chosen a priori., The magnitude of the response scales with satellite mass and need not be chosen a priori.128 A full treatment requires the dynamical. coupling of the multiple time seales ancl multiple leneth scales of the external cisturbance and the galaxian components discussed above., A full treatment requires the dynamical coupling of the multiple time scales and multiple length scales of the external disturbance and the galaxian components discussed above.129 Relevant characteristic length and time scales may diller by an order of magnitude between satellite and ido or disk orbits., Relevant characteristic length and time scales may differ by an order of magnitude between satellite and halo or disk orbits.130 dn addition. we will see that the ialo disturbance may be relatively weak and a significant »erturbation of the outer disk at the same time.," In addition, we will see that the halo disturbance may be relatively weak and a significant perturbation of the outer disk at the same time."131 These multiple-scale weak regimes are a challenging task for an n-xod computation., These multiple-scale weak regimes are a challenging task for an n-body computation.132 However. this class of problems is ideally suited to linear techniques and the work here will use the expansion technique known as themethod.," However, this class of problems is ideally suited to linear techniques and the work here will use the expansion technique known as the."133 Although he matrix method is computationally intensive. it is no more so than n-bodsy methods and is practical on current workstations.," Although the matrix method is computationally intensive, it is no more so than n-body methods and is practical on current workstations."134 In this section. | will give a brief overview of he general method with details on posing ancl implementing he coupled response solutions in the references cited below and in the Xppendix.," In this section, I will give a brief overview of the general method with details on posing and implementing the coupled response solutions in the references cited below and in the Appendix."135 In short. the matrix method. represents the response of a galaxy to an external perturbation by a truncated series of orthogonal functions. similar to those one would use to solve an clectrostatics problem.," In short, the matrix method represents the response of a galaxy to an external perturbation by a truncated series of orthogonal functions, similar to those one would use to solve an electrostatics problem."136 The perturbation is also represented by this series and the temporal dependence of cach coefficient. is Fourier transformed. to a (complex) frequeney distribution., The perturbation is also represented by this series and the temporal dependence of each coefficient is Fourier transformed to a (complex) frequency distribution.137 The response of the galaxy to one of the orthogonal functions at a particular forcing frequency. is then computed in the continuum limit using the collisionless 3oltzmann (Vlasov) equation., The response of the galaxy to one of the orthogonal functions at a particular forcing frequency is then computed in the continuum limit using the collisionless Boltzmann (Vlasov) equation.138 Phe entire. procedure. is analogous to signal processing in Fourier space., The entire procedure is analogous to signal processing in Fourier space.139 Pursuing the analogy. we now do the inverse transform.," Pursuing the analogy, we now do the inverse transform."140 The response to any perturbation. the weighted superposition of the response to each basis function. is then a matrix equation.," The response to any perturbation, the weighted superposition of the response to each basis function, is then a matrix equation."141 Finally. to eet the Full time dependence of the response. one resums the solutions to the matrix equation at each frequency. weighted by the Fourier coefficients.," Finally, to get the full time dependence of the response, one resums the solutions to the matrix equation at each frequency weighted by the Fourier coefficients."142 This method assumes that the perturbation is small enough that the overall change to the structure of the galaxy is small., This method assumes that the perturbation is small enough that the overall change to the structure of the galaxy is small.143 In this limit. the method. has the advantage of accuracy and sensitivity to the large scale structures. of interest.," In this limit, the method has the advantage of accuracy and sensitivity to the large scale structures of interest."144 For contrast. the n-bodyw. simulation determines the response of a galaxy to a perturbation by solving the equations of motion for a representative set of orbits.," For contrast, the n-body simulation determines the response of a galaxy to a perturbation by solving the equations of motion for a representative set of orbits."145 The orbit is advanced in a fixed potential for a short time interval and the gravitational potential or force is then recomputed., The orbit is advanced in a fixed potential for a short time interval and the gravitational potential or force is then recomputed.146 The simulation works well for large perturbations but because the simulation uses a finite number of particles. Iuctuation noise limits the sensitivity to small amplitude distortions.," The simulation works well for large perturbations but because the simulation uses a finite number of particles, fluctuation noise limits the sensitivity to small amplitude distortions."147 Phe matrix method. nicely complements the n-body simulations. excelling in the regimes where the n-body simulation are suspect.," The matrix method nicely complements the n-body simulations, excelling in the regimes where the n-body simulation are suspect."148 Historically. the approach is related to the treatment of eeneral eigenvalue problems described in the mathematical physies literature (e.g. Courant Hilbert 1953. Chap V3).," Historically, the approach is related to the treatment of general eigenvalue problems described in the mathematical physics literature (e.g. Courant Hilbert 1953, Chap \nocite{CoHi:53}) )."149 The matrix method. in. stellar dynamics πας varied applications beginning with lIxalnajs (1977)) who investigated the unstable modes of stellar disks., The matrix method in stellar dynamics had varied applications beginning with Kalnajs \nocite{Kaln:77}) ) who investigated the unstable modes of stellar disks.150 Polvachenko Shukhman (1981)) adapted. the method. to study a spherical svstem (see also Fridman Polvachenko 1984. Appendix)) and it) was later emploved by both Palmer Papaloizou (1987)) in the study of the radial orbit. instability and by Bertin Pegoraro (1980)) to study the instability of a family of moclels proposed by Bertin Stiavelli (1984)).," Polyachenko Shukhman \nocite{PoSh:81}) ) adapted the method to study a spherical system (see also Fridman Polyachenko 1984, \nocite{FrPo:84b}) ) and it was later employed by both Palmer Papaloizou \nocite{PaPa:87}) ) in the study of the radial orbit instability and by Bertin Pegoraro \nocite{BePe:89}) ) to study the instability of a family of models proposed by Bertin Stiavelli \nocite{BeSt:84}) )."151 In addition to Paper ]. Weinberg (1989.. Paper LE) used the matrix formulation to study the response ofa spherical galaxy to an encounter with adwarl companion and Saha (1991)) ancl Weinberg (1991)) investigated the stability of anisotropic galaxian mocels.," In addition to Paper I, Weinberg \nocite{Wein:89}, , Paper II) used the matrix formulation to study the response of a spherical galaxy to an encounter with a dwarf companion and Saha \nocite{Saha:91}) ) and Weinberg \nocite{Wein:91a}) ) investigated the stability of anisotropic galaxian models."152 The response of a galaxy initially in equilibrium. to a eravitational interaction with à companion is describe w the simullancous solution of the Boltzmann anc Poisson equations., The response of a galaxy initially in equilibrium to a gravitational interaction with a companion is described by the simultaneous solution of the Boltzmann and Poisson equations.153 The simultaneous system is a set. of coupled partial integro-dillerential equations., The simultaneous system is a set of coupled partial integro-differential equations.154 However if he orbits in cach component are regular. any phase-space quantity.such as density and gravitational potentialmay he expanced in a Fourier series in the orbita requencies.," However if the orbits in each component are regular, any phase-space quantity—such as density and gravitational potential---may be expanded in a Fourier series in the orbital frequencies."155 Truncating this expansion. the quantity may » represented as a vector of Fourier. coellicients: this is standard practice in filtering and approximation theory ancl canonical perturbation theory (e.g. Lichtenberg. Lieberman: 1983)).," Truncating this expansion, the quantity may be represented as a vector of Fourier coefficients; this is standard practice in filtering and approximation theory and canonical perturbation theory (e.g. Lichtenberg Lieberman \nocite{LiLi:83}) )."156 In. Fourier space. the Boltzmann PDE becomes an algebraic integral equation.," In Fourier space, the Boltzmann PDE becomes an algebraic integral equation."157 The system is further simplified if the basis functions are chosen to satisfy the Poisson equation explicitly., The system is further simplified if the basis functions are chosen to satisfy the Poisson equation explicitly.158 After a Laplace transform in time. the remaining solution of the Boltzmannequation becomes the solution of a matrix equation. cach column," After a Laplace transform in time, the remaining solution of the Boltzmannequation becomes the solution of a matrix equation, each column"159number density of neutral hvdrogen is about 10—10? em7.,number density of neutral hydrogen is about $10^{4}-10^{5}$ $cm^{-3}$.160" Due to the n,/njDi~10. the critical mass loss rate is al the order of magnitude of 10?e /s. As mentioned in Section 3.1. the ratios of two velocity components behave as parabolic curves."," Due to the $n_{p}/n_{h}\sim 10$, the critical mass loss rate is at the order of magnitude of $10^{9}$ g/s. As mentioned in Section 3.1, the ratios of two velocity components behave as parabolic curves."161 To maintain the common flow. a sufficient amount of momentum must be transferred between two components.," To maintain the common flow, a sufficient amount of momentum must be transferred between two components."162 The most important process of translerring momentum is charge exchauge., The most important process of transferring momentum is charge exchange.163 Near the bottom of the wind. the wind is relatively dense so that the process X momentum exchange is effective.," Near the bottom of the wind, the wind is relatively dense so that the process of momentum exchange is effective."164 However. with the increase of radius the rate of harge exchange decreases (The solid line al the bottom of Figure 5.).," However, with the increase of radius the rate of charge exchange decreases (The solid line at the bottom of Figure 5.)."165" Thus. the transfer "" monientun is also decrease will radius."," Thus, the transfer of momentum is also decrease with radius."166 We note that the process of photoionization xl recombination can also redistribute momentum from one component to the other component. and the variations of photoionization and recombination rates (dashed and dotted lines) are contrary to that of charge exchange rate.," We note that the process of photoionization and recombination can also redistribute momentum from one component to the other component, and the variations of photoionization and recombination rates (dashed and dotted lines) are contrary to that of charge exchange rate."167 Therefore. at the outer of the wind the momentum transfered by photoionization and recombination also plavs a role.," Therefore, at the outer of the wind the momentum transfered by photoionization and recombination also plays a role."168" Finally. there is minimum value of u;/u, in the middle of wind."," Finally, there is minimum value of $u_{h}/u_{p}$ in the middle of wind."169 Loanmuner οἱ al. (, Lammer et al. (1702003) presented that the energy deposition of X-ray and UV radiation from parent star can lead (to a high temperature. aud (that a hyedroclvuamic process can occur in planetary. atmosphere.,"2003) presented that the energy deposition of X-ray and UV radiation from parent star can lead to a high temperature, and that a hydrodynamic process can occur in planetary atmosphere."171 The mass loss rates of energy deposition Gehily depend on the fluxes of NUV radiation., The mass loss rates of energy deposition tightly depend on the fluxes of XUV radiation.172 In general voung stars can radiate more energv than old ones in XUV band., In general young stars can radiate more energy than old ones in XUV band.173" The enerev-limit mass loss rate can be written as where 3j is the ratio of the expansion radius R1 to the planetary radius i. R1 is altitude where the NUV radiation is absorbed. 2, represents the distance Lorm the center"," The energy-limit mass loss rate can be written as where $\beta$ is the ratio of the expansion radius R1 to the planetary radius $R_{p}$, R1 is altitude where the XUV radiation is absorbed, $R_{p}$ represents the distance form the center"174"cd and itis found at Ni;20.3. in contradiction with our assumption that yen,71 that S; is of order .A;.","$\epsilon^{th}\beta$ and it is found at $\chi_{crit}\approx 0.3$, in contradiction with our assumption that $\chi_{crit}\approx 1$ that ${\cal S}_{i} $ is of order ${\cal A}_{i} $."175 Since the corrections to the location of the maximum would only be of order L/S. we conclude that it is very. ασ to support a whistler dominated plasma that does not generate olf-axis waves without imposing strict fine tuning.," Since the corrections to the location of the maximum would only be of order $1/\aleph $, we conclude that it is very difficult to support a whistler dominated plasma that does not generate off-axis waves without imposing strict fine tuning."176 The heat lux vector is. after integration hy parts. When eq.," The heat flux vector is, after integration by parts, When eq."177 59. is used in eq., \ref{eqqq:tcur_free} is used in eq.178 61. one gets: Carrying the integration over the angles vields Carrying the integral over the velocities we find: where is the Meijer G function ( Ciradshteyn Itvzhik. 1980: p. 597. f 4). and © denotes an empty set.," \ref{eq:heat_fon} one gets: Carrying the integration over the angles yields Carrying the integral over the velocities we find: where is the Meijer G function ( Gradshteyn Ryzhik 1980; p. 897, f. 4), and $\phi$ denotes an empty set."179 The numerical evaluation of C was carried out bv the use of Mathematica., The numerical evaluation of $G$ was carried out by the use of Mathematica.180 The last equation shows the heat {lux stronely suppressed compared to the Spitzer value when the scattering rate by oll-axis waves exceeds the electron-ion collision frequency. (Levinson Eichler 1992)., The last equation shows the heat flux strongly suppressed compared to the Spitzer value when the scattering rate by off-axis waves exceeds the electron-ion collision frequency (Levinson Eichler 1992).181 Previous literature for heat (ux inhibiting astrophysical environments used a term. οος the so called. suppression factor. that multiplied the collision dominated. plasma heat [lux i.e. where we used eq.," Previous literature for heat flux inhibiting astrophysical environments used a term $f^{supp}$, the so called suppression factor, that multiplied the collision dominated plasma heat flux i.e. where we used eq."182 17. in eq., \ref{eq:knud} in eq.183 61. to obtain eq., \ref{eq:heat_fon} to obtain eq.184" 66 and the factor f"""""" was introucec by hand.", \ref{eqq:knud} and the factor $f^{supp}$ was introduced by hand.185" Vhe value of "" obtained from eq.", The value of $f^{supp}$ obtained from eq.186" 64. and 66. is I"" the distribution. function were not to. relax to quasilinear marginal sability then there would. be less suppression."," \ref{eq:final} and \ref{eqq:knud}187 is If the distribution function were not to relax to quasilinear marginal stability then there would be less suppression."188 Llowever. the non-linear damping terms have been shown to be much smaller than the quasilinear damping term (which in marginal stability is balanced. by a growth term) andthus it can safely. be argued that the suppression factor computed aboveis of general applicability (provided. that ;2 satisfies the required. constraints).," However, the non-linear damping terms have been shown to be much smaller than the quasilinear damping term (which in marginal stability is balanced by a growth term) andthus it can safely be argued that the suppression factor computed aboveis of general applicability (provided that $\beta$ satisfies the required constraints)."189 Since [UU has been caleulatecl under the assumption eq., Since $f^{supp}$ has been calculated under the assumption eq.190 32. we sugeest the following extrapolation: Note that the suppression factor has been caleulated relative to a Lorentzian plasma.," \ref{eq:symmm}191 we suggest the following extrapolation: Note that the suppression factor has been calculated relative to a Lorentzian plasma."192 Taking into account that the ρίζο-νεα heat. [lux is about a factor of five higher relative to à Lorentzian plasma. the suppression factor reads: Hleat-Dlux inhibition along field. lines obtains when oll- waves are present in the plasma.," Taking into account that the Spizer-Härrm heat flux is about a factor of five higher relative to a Lorentzian plasma, the suppression factor reads: Heat-flux inhibition along field lines obtains when off-axis waves are present in the plasma."193 We have found within quasilincar theory that whistler instability indeed generates oll-axis whistlers., We have found within quasilinear theory that whistler instability indeed generates off-axis whistlers.194 ‘Thus. heat Uus inhibition along Ποιά lines by whistlers should be a common ;»henomenon in à weakly magnetized plasma.," Thus, heat flux inhibition along field lines by whistlers should be a common phenomenon in a weakly magnetized plasma."195 The basic argument for oll-axis whistlers is. in qualitative terms. that if the waves were excited. only in a narrow cone along the axis. then the distribution function would evolve to a state in which the erowth rate of oll-axis waves would generally exceed that of he on-axis ones.," The basic argument for off-axis whistlers is, in qualitative terms, that if the waves were excited only in a narrow cone along the axis, then the distribution function would evolve to a state in which the growth rate of off-axis waves would generally exceed that of the on-axis ones."196 One of our assumptions is that the energy. density in he magnetic field of the whistler will not exceed the energy density of the background magnetic field., One of our assumptions is that the energy density in the magnetic field of the whistler will not exceed the energy density of the background magnetic field.197 We find that this is generally the case by a large margin in tenuous astrophysical Plasmas., We find that this is generally the case by a large margin in tenuous astrophysical plasmas.198 While Gary Feldman (1977) find whistlers inellicient or inhibition of heat [lux in the solar wind. purr l. Levinson lIZchler (1992) find a suppression factor of I027«[UUx10 i in the interstellar medium," While Gary Feldman (1977) find whistlers inefficient for inhibition of heat flux in the solar wind, $f^{supp}\sim 1$ , Levinson Eichler (1992) find a suppression factor of $10^{-2}199\le f^{supp}\le10^{-1}$ , in the interstellar medium"200Geneva Observatory. University of Geneva. Maillettes 51. CH-1290 Sauverny.,"Geneva Observatory, University of Geneva, 	 Maillettes 51, CH-1290 Sauverny,"201"Stellar masses are taken from the ? catalog, also taken from ? estimates.","Stellar masses are taken from the \cite{Nair10} catalog, also taken from \cite{Kauffmann03} estimates."202 In figure[TT] we show the observed distribution of stellar masses for the whole sample for different morphological types using the probability estimator., In figure \ref{fig:mass_counts_proba} we show the observed distribution of stellar masses for the whole sample for different morphological types using the probability estimator.203" In this case, stellar masses are computed with the ? formula, adapted from ? to account for evolution: We observe the expected trend; i.e, the mass function peaks at lower values for later morphological types."," In this case, stellar masses are computed with the \cite{Bell03} formula, adapted from \cite{Bernardi10} to account for evolution: We observe the expected trend; i.e, the mass function peaks at lower values for later morphological types."204" In the same figure, we compare the distribution of masses obtained from the Galaxy Zoo classification."," In the same figure, we compare the distribution of masses obtained from the Galaxy Zoo classification."205" We compare the one obtained with galaxies flagged as ellipticals (FLAG ELLIPTICAL - 1) with the one obtained using the two estimators described above, i.e. galaxies having P(E)>0.5 and probability weighting."," We compare the one obtained with galaxies flagged as ellipticals (FLAG ELLIPTICAL = 1) with the one obtained using the two estimators described above, i.e. galaxies having $p(E)>0.5$ and probability weighting."206 The same is computed for spirals., The same is computed for spirals.207" There is almost a perfect match with the distributions computed using galSVM, which again confirms the accuracy of the automated classification presented in this paper."," There is almost a perfect match with the distributions computed using galSVM, which again confirms the accuracy of the automated classification presented in this paper."208" Another common application is to study the color-stellar mass diagrams for different ""robust"" morphological types."," Another common application is to study the color-stellar mass diagrams for different ""robust"" morphological types."209" Again, the probability estimator can be used by computing the 2D histogram of galaxies in the color-mass plane weighted with the probabilities."," Again, the probability estimator can be used by computing the 2D histogram of galaxies in the color-mass plane weighted with the probabilities."210 Figure [[3] shows the probability contours in the color-stellar mass plane for the 4 morphological types., Figure \ref{fig:CMR_morpho} shows the probability contours in the color-stellar mass plane for the 4 morphological types.211" We observe the expected trend: elliptical and SO galaxies are redder with less scatter, while Sab and Scd are bluer."," We observe the expected trend: elliptical and S0 galaxies are redder with less scatter, while Sab and Scd are bluer."212 An interesting feature of Sab galaxies (and for some Scd) is that there seems to be 2 distinct populations: one red population and another one lying in the so-called green valley between the blue cloud and the red sequence., An interesting feature of Sab galaxies (and for some Scd) is that there seems to be 2 distinct populations: one red population and another one lying in the so-called green valley between the blue cloud and the red sequence.213" After careful visual inspection of an important fraction of these red galaxies, we can confirm that for most of them they are in fact edge-on spirals probably reddened by dust."," After careful visual inspection of an important fraction of these red galaxies, we can confirm that for most of them they are in fact edge-on spirals probably reddened by dust."214" A small fraction are, however, passive spirals as shown and carefully studied by ??.."," A small fraction are, however, passive spirals as shown and carefully studied by \cite{Masters10a, Masters10b}."215 Most of them are classified as Sab galaxies with high probability (see figure B)., Most of them are classified as Sab galaxies with high probability (see figure \ref{fig:gal_examples}) ).216 This result confirms that a pure color selection is not enough to select ellipticals or SO galaxies since it is highly polluted by edge-on spirals as already shown in previous works (e.g. ???)).," This result confirms that a pure color selection is not enough to select ellipticals or S0 galaxies since it is highly polluted by edge-on spirals as already shown in previous works (e.g. \citealp{Schawinski07, Lintott08, Bernardi10}) )."217 These plots are just shown here to validate the morphological classification., These plots are just shown here to validate the morphological classification.218 A more detailed analysis of the fundamental parameters of galaxies is expected to come in future dedicated papers., A more detailed analysis of the fundamental parameters of galaxies is expected to come in future dedicated papers.219 We have presented an automated morphological classification of the SDSS DR7 spectroscopic sample., We have presented an automated morphological classification of the SDSS DR7 spectroscopic sample.220" The algorithm used is based on SVM, and the most interesting and new property is that it associates a probability value to each galaxy instead of a single class."," The algorithm used is based on SVM, and the most interesting and new property is that it associates a probability value to each galaxy instead of a single class."221" This way, the transition between one class and another is continuous, which should be a better approximation to nature and to visual classifications."," This way, the transition between one class and another is continuous, which should be a better approximation to nature and to visual classifications."222" As a matter of fact, when the brain decides which morphological class is closer to a given object we are looking at, it probably also implicitly some parameters and computes distances in this virtual parameter space to decide which one is the closest canonical class to the object it is classifying."," As a matter of fact, when the brain decides which morphological class is closer to a given object we are looking at, it probably also implicitly some parameters and computes distances in this virtual parameter space to decide which one is the closest canonical class to the object it is classifying."223" In that sense, even if the list of parameters we measure is reduced and much more simplistic than what our brain can do (e.g we are not including spiral arms nor tidal features that certainly play an important role in a visual classification), the spirit of our approach is closer to a classical visual classification than other existing automated methods."," In that sense, even if the list of parameters we measure is reduced and much more simplistic than what our brain can do (e.g we are not including spiral arms nor tidal features that certainly play an important role in a visual classification), the spirit of our approach is closer to a classical visual classification than other existing automated methods."224 The results obtained are in good agreement with existing visual classifications and are robust even at the faint end of the, The results obtained are in good agreement with existing visual classifications and are robust even at the faint end of the225made more ellicient by the development of a method Chat could identify the best and worst candidates from. the collection of blends. binaries and exoplanets that comprise a tvpical candidate set. [rom transit searches.,"made more efficient by the development of a method that could identify the best and worst candidates from the collection of blends, binaries and exoplanets that comprise a typical candidate set from transit searches."226 Seager&Alallén-Ornelas(2003) touched on (his possibility while exploring the leasibilitv of estimating stellar parameters from the photometric properties of an observed (transit., \citet{seager} touched on this possibility while exploring the feasibility of estimating stellar parameters from the photometric properties of an observed transit.227 Using a fully analytical derivation. thev showed that four parameters (depth. period. fall transit duration. ancl duration minus ineress and eeress limes) could be used to caleulate physical parameters such as mean stellar density and radius ratio for the svstem. assuming that the (ransiting body is an exoplanet and that the orbit is circular.," Using a fully analytical derivation, they showed that four parameters (depth, period, full transit duration, and duration minus ingress and egress times) could be used to calculate physical parameters such as mean stellar density and radius ratio for the system, assuming that the transiting body is an exoplanet and that the orbit is circular."228 Non-planetary transiting bodies will produce somewhat aplvsical parameters. particularly in the radius of the transiting body.," Non-planetary transiting bodies will produce somewhat aphysical parameters, particularly in the radius of the transiting body."229 A typical blend. for example. would produce a radius lor the transiting body that would be larger than that expected for a close-in giant. planet.," A typical blend, for example, would produce a radius for the transiting body that would be larger than that expected for a close-in giant planet."230 Unfortunately. this techiique requires extremely precise photometry.," Unfortunately, this technique requires extremely precise photometry."231 Seager Mallénu-Ornelas quote a need for 5 millimag precision with 5 minute sampling for two iransits (provided (hese (vo transits define the true period) for short-period giant planets., Seager Mallénn-Ornelas quote a need for 5 millimag precision with 5 minute sampling for two transits (provided these two transits define the true period) for short-period giant planets.232 Current (ransi( search campaigns do not produce data of (his qualitv. which limits the applicability of this technique.," Current transit search campaigns do not produce data of this quality, which limits the applicability of this technique."233 llowever. as we show. it is still possible to use the photometric properties of (ransils derived [rom less precise data to identily the best exoplanet candidates from a laree sample.," However, as we show, it is still possible to use the photometric properties of transits derived from less precise data to identify the best exoplanet candidates from a large sample."234" By using a set of reasonable approximations. we derive a numerical tool (called the exoplanet diagnostic) that indicates how ""planet-like"" a particular event is using only the transit period. duration and depth."," By using a set of reasonable approximations, we derive a numerical tool (called the exoplanet diagnostic) that indicates how “planet-like” a particular event is using only the transit period, duration and depth."235 This diagnostic makes it possible to exclude many of the candidates from (rausil searches without the need for follow-up observations. including many of those caused by blends.," This diagnostic makes it possible to exclude many of the candidates from transit searches without the need for follow-up observations, including many of those caused by blends."236 In Section 2. we derive the exoplanet diagnostic and discuss the impact of orbital eccentricitv.," In Section 2, we derive the exoplanet diagnostic and discuss the impact of orbital eccentricity."237 In Section 3. the results of our analvsis of existing (ransit searches and of the elfectiveness of the diagnostic in distinguishing modeled blends is presented The duration. D. of a transit depends on many parameters: the radii and masses of the {wo transiting objects. semi-major axis. orbital inclination. eccentricity. viewing orientation and period.," In Section 3, the results of our analysis of existing transit searches and of the effectiveness of the diagnostic in distinguishing modeled blends is presented The duration, $D$, of a transit depends on many parameters: the radii and masses of the two transiting objects, semi-major axis, orbital inclination, eccentricity, viewing orientation and period."238 A completely general equation describing the duration of the transit can be derived [rom these variables., A completely general equation describing the duration of the transit can be derived from these variables.239 We begin with the derivation of transit durationgiven by Sackett (1999)..," We begin with the derivation of transit durationgiven by \citet{sackett}, ,"240"Vea about the IIubble line in Fig 1 for a rauge of IL,-values.",$_{\rm CMB}$ about the Hubble line in Fig 1 for a range of $_{\rm o}$ -values.241 It is now possible to make a siniülar plot of the RAIS deviation in Vesp between the sources and their nearest eril line in Fie 5. for a range of IL;-values.," It is now possible to make a similar plot of the RMS deviation in $_{\rm CMB}$ between the sources and their nearest grid line in Fig 5, for a range of $_{\rm o}$ -values."242 The result is shown in Fig., The result is shown in Fig.243 G for the niue N= 1 sources. for a erid spacing defined by σε = 0.62. the value found iu carlicr work (BurbidgeaudHewitt1990:Bell2002c.d).," 6 for the nine $N$ = 1 sources, for a grid spacing defined by $_{f}$ = 0.62, the value found in earlier work \citep{bur90,bel02c,bel02d}."244. Clearly there are two places ou this curve where the RAIS is low. indicating a good fit to the exid lines.," Clearly there are two places on this curve where the RMS is low, indicating a good fit to the grid lines."245" A broad one is located near IL, = sl and the other. a much lower and narrower one. occurs near IL, = 71 dans ! ."," A broad one is located near $_{\rm o}$ = 84 and the other, a much lower and narrower one, occurs near $_{\rm o}$ = 71 km $^{-1}$ $^{-1}$."246 The broad feature is similar to that found for the raw data in Fig., The broad feature is similar to that found for the raw data in Fig.247 2 aud is expected., 2 and is expected.248 This is discussed ii more detail iu section 2.5 below describing randomly generated test data., This is discussed in more detail in section 2.5 below describing randomly generated test data.249" The second one. near IL, = Tl. corresponds to the case preseuted in Fig."," The second one, near $_{\rm o}$ = 71, corresponds to the case presented in Fig."250 5 where the sources lock ou to the eid lines., 5 where the sources lock on to the grid lines.251 Tn order to ect a fecling for what kiud of results would be obtained if the velocity dispersion iu Fig., In order to get a feeling for what kind of results would be obtained if the velocity dispersion in Fig.252 l was due to peculiar velocities of raucous aüuplitude. instead of discrete intrinsic components. we attempted to simulate the raw FP data by eoncrating several sets of 1l peculiar velocities.," 1 was due to peculiar velocities of random amplitude, instead of discrete intrinsic components, we attempted to simulate the raw FP data by generating several sets of 11 peculiar velocities."253 We used three different approaches to do this., We used three different approaches to do this.254 First. we generated several sets of peculiar velocities between 0 aud 3500 kin +.," First, we generated several sets of peculiar velocities between 0 and 3500 km $^{-1}$."255 We used uniform weighting aud only positive values were used to resemble the real data as closcly as possible. (, We used uniform weighting and only positive values were used to resemble the real data as closely as possible. (256"Note that for IL, = 82. the value reported by Freediuanetal.(20013... all peculiar velocity components except one are positive.","Note that for $_{\rm o}$ = 82, the value reported by \citet{fre01}, all peculiar velocity components except one are positive."257 It is not inunediatelv obvious what weighting was used in the IIubble Ney Project to obtain this value)., It is not immediately obvious what weighting was used in the Hubble Key Project to obtain this value).258 The cutoff value of 3500 was chosen here because it falls midway between the highest intrinsic value present iu the data (2311 kin 1j and the next highest intrinsic value (1628 lau ly, The cutoff value of 3500 was chosen here because it falls midway between the highest intrinsic value present in the data (2314 km $^{-1}$ ) and the next highest intrinsic value (4628 km $^{-1}$ ).259 A value higher than 3500 would have been fitted to the 1628 lau + level and the FP data contained no sources at this discrete velocity level or above., A value higher than 3500 would have been fitted to the 4628 km $^{-1}$ level and the FP data contained no sources at this discrete velocity level or above.260" Iu each case the rancdom-amplitude peculiar velocities we generated were added to the IIubble velocities calculated for cach source usus its known distance aud IL, = 71 lans | il", In each case the random-amplitude peculiar velocities we generated were added to the Hubble velocities calculated for each source using its known distance and $_{\rm o}$ = 71 km $^{-1}$ $^{-1}$.261" We then calculated the RAIS deviation in Voor between the eleven sources aud their nearest erid line. as was done above for the FP data. for a range of IL,-values and zp = 0.62."," We then calculated the RMS deviation in $_{\rm CMB}$ between the eleven sources and their nearest grid line, as was done above for the FP data, for a range of $_{\rm o}$ -values and $_{f}$ = 0.62."262 Allrandomly ecuerated sets gave similar results and a typical example is presented iu Fig., All randomly generated sets gave similar results and a typical example is presented in Fig.263 7., 7.264 In every case the curve showed a single. broad dip in the RAIS deviation. with widths covering 18-20 IL-values at a point on the curve where the RAIS value was equal to twice the minima RAIS value (horizontal line in Fig.," In every case the curve showed a single, broad dip in the RMS deviation, with widths covering 18-20 $_{\rm o}$ -values at a point on the curve where the RMS value was equal to twice the minimum RMS value (horizontal line in Fig."265 7)., 7).266 The broad width aud low RAIS of the curve was a characteristic common to all test data sets., The broad width and low RMS of the curve was a characteristic common to all test data sets.267" Note that a lower RAIS is expected when several exid lines are fitted to random velocities than when one IL, line alone is fitted. as can be seen by comparing figures 2 aud 6."," Note that a lower RMS is expected when several grid lines are fitted to random velocities than when one $_{\rm o}$ line alone is fitted, as can be seen by comparing figures 2 and 6."268" In no case. in these test data. was there a narrow RAIS dip (width ~5 IL,-values) seen that had a depth below 0.5 of the RAIS value of the adjacent bascline."," In no case, in these test data, was there a narrow RMS dip (width $\sim5$ $_{\rm o}$ -values) seen that had a depth below 0.8 of the RMS value of the adjacent baseline."269" The broad RAIS dip centered ucar IL, = 76 in Fig 7. is also visible in the FP data in Fig."," The broad RMS dip centered near $_{\rm o}$ = 76 in Fig 7, is also visible in the FP data in Fig."270" 6 if the narrow dip near IL, = 71 is ignored as indicated by the dashed line.", 6 if the narrow dip near $_{\rm o}$ = 71 is ignored as indicated by the dashed line.271 In the real data in Fig 6. however. the curve does not have the same sviuuetrvy visible for the uniformly distributed test curve in Fie.," In the real data in Fig 6, however, the curve does not have the same symmetry visible for the uniformly distributed test curve in Fig."272" 7. and rises mere steeply ou the hieh-IL, side."," 7, and rises more steeply on the $_{\rm o}$ side."273 This is cliscussed further below., This is discussed further below.274 Iu the second test we generated 10 random data sets contains Ll values (both positive and negative). cach with a Caussian distribution having the same dispersion as the real data aud centered about a IIubble slope of 58.," In the second test we generated 10 random data sets containing 11 values (both positive and negative), each with a Gaussian distribution having the same dispersion as the real data and centered about a Hubble slope of 88."275" We again calculated RAIS vs IL, curves for these data sets.", We again calculated RMS vs $_{\rm o}$ curves for these data sets.276 These 10 curves were then averaged aud the result is shown in Fie 8., These 10 curves were then averaged and the result is shown in Fig 8.277 This shows clearly that there was nothing iu our data analysis that in auv wav favored the production of the quantized redshifts found previously by us aud by others., This shows clearly that there was nothing in our data analysis that in any way favored the production of the quantized redshifts found previously by us and by others.278" Note that the resulting curve is again svaunetrically spaced about an IL,-value of 76.", Note that the resulting curve is again symmetrically spaced about an $_{\rm o}$ -value of 76.279 Tn our third test we used the real data aud simply changed the polarity of the peculiar velocities, In our third test we used the real data and simply changed the polarity of the peculiar velocities280instrumental (E785LD) magnitudes. returned by the modelling code.,instrumental (F785LP) magnitudes returned by the modelling code.281 These instrumental magnitudes are then converted to apparent £ Cousins magnitudes. using the filler. transformations and colour equations detailed: in Holtzman et al. (, These instrumental magnitudes are then converted to apparent $I-$ Cousins magnitudes using the filter transformations and colour equations detailed in Holtzman et al. (2821995).,1995).283 The apparent colours requirecl for this transformation were caleulated from the 1995 version of Muzual Charlot single-burst elliptical galaxy stellar-population models (Bruzual Charlot 1993). under the assumption of az=5.0 formation redshift.," The apparent colours required for this transformation were calculated from the 1995 version of Bruzual Charlot single-burst elliptical galaxy stellar-population models (Bruzual Charlot 1993), under the assumption of a $z=5.0$ formation redshift."284 Following correction for cosmological dimmüng within our chosen cosmology. evolution and Ix corrections were then applied using the same Muzual Charlot moclels.," Following correction for cosmological dimming within our chosen cosmology, evolution and $K-$ corrections were then applied using the same Bruzual Charlot models."285 Galactic. extinction corrections were then applied. to each object (Schlegel et, Galactic extinction corrections were then applied to each object (Schlegel et286he ovientation of the secondary spin axis docs not affect the ϱ estimates.,the orientation of the secondary spin axis does not affect the $q$ estimates.287 Tu this investigation. we make a hird inprovemienut sed on astrophysical considerations.," In this investigation, we make a third improvement based on astrophysical considerations."288 In Valtoucn al. (, In Valtonen et al. (2892010a). the black hole spin of the primary lack hole was parallel to the accreion disk spin at 1¢ Initial epoch. which was the year 1856.,"2010a), the black hole spin of the primary black hole was parallel to the accretion disk spin at the initial epoch, which was the year 1856."290 Due to PN effects. the black hole spin wanders about 9° off from this direction duriug its uecession evcle iat lasts around 1300 vears.," Due to PN effects, the black hole spin wanders about $9^{ \circ }$ off from this direction during its precession cycle that lasts around 1300 years."291 In the preseut moel. le precession cone axis coincides with t10 Llenli accretion disk axis.," In the present model, the precession cone axis coincides with the mean accretion disk axis."292" After performing aiuber of Munerical experiments. we found that it is possile o choose a suitable initial direction for $41 ""lch hat the augle between the spin aud the «isk axes relmaius constant ( ~ 87) duriug the precessioial notion of 84."," After performing a number of numerical experiments, we found that it is possible to choose a suitable initial direction for $\vek s_1$ such that the angle between the spin and the disk axes remains constant ( $ \sim 8^{\circ}$ ) during the precessional motion of $\vek s_1$."293 It is reasonable to expect such a situalon ¢πο o the Bardecu-Petersou effect., It is reasonable to expect such a situation due to the Bardeen-Peterson effect.294 Because he tiLie scale of the Barcdecnu-Petersou effect is much longer han the black hole spin precession time scale (Lodato and Pringle 2006). tlre| two directions do not coincide.," Because the time scale of the Bardeen-Peterson effect is much longer than the black hole spin precession time scale (Lodato and Pringle 2006), the two directions do not coincide."295 The time scale of the Bardecu-Peterson effect is of the order of one million vears (Natara]an and Pringle 1998. Eq.," The time scale of the Bardeen-Peterson effect is of the order of one million years (Natarajan and Pringle 1998, Eq."296 2.16) which 15 internelatebetween the spin precession time scale of l0 lüvr audsux the| binary mereerveer evolutionevolutio tine SCe of about LOS vr (Isvasawa et al., 2.16) which is intermediatebetween the spin precession time scale of $10^3$ yr and the binary merger evolution time scale of about $10^8$ yr (Iwasawa et al.297 20]1)., 2011).298 Thus we| expect that in 105 xy the Bardecu-Peterson effect is inportaut up to the distance of abou 10? Schwarzschild radi in the «disk (Natarajan aud Pringle 1998. Eq. 2.8). but the disk can follow only the mean direction of the spin.," Thus we expect that in $10^8$ yr the Bardeen-Peterson effect is important up to the distance of about $10^2$ Schwarzschild radii in the disk (Natarajan and Pringle 1998, Eq, 2.8), but the disk can follow only the mean direction of the spin."299 It cannot keep τι »with the 10 xy evohtion of the actual spin., It cannot keep up with the $10^3$ yr evolution of the actual spin.300 With the above meifioned additional features. we have searched for orbit soluious.," With the above mentioned additional features, we have searched for orbit solutions."301 As before. au automatic search :deorithui is used.," As before, an automatic search algorithm is used."302" It takes atrial orbit. then improves it until all nine outbursts happen within their allotted time intervals,"," It takes a trial orbit, then improves it until all nine outbursts happen within their allotted time intervals."303 Typically oue solution is found iu 3 muntes of computing time with a modern PC., Typically one solution is found in 3 minutes of computing time with a modern PC.304 We have used sets of LOSO orbits with given standard paraueters., We have used sets of 1080 orbits with given standard parameters.305 Towever. the couveregcnce was not always foun Ih a reasonabo amount of time.," However, the convergence was not always found in a reasonable amount of time."306 Then the attempt to find a soutkn was ciscarded aud he next trial was started., Then the attempt to find a solution was discarded and the next trial was started.307 For this reason the mmmor of ordts in a set is always less than 1050., For this reason the number of orbits in a set is always less than 1080.308 Iu Table 2 we give the se nuuber. the orbit 1111111vor and value of the dimeusiouless spin of he primary να αι the first three coluuus. respectively.," In Table 2 we give the set number, the orbit number and value of the dimensionless spin of the primary $\chi_1$ in the first three columns, respectively."309 The spin value was generally taken as X4=0.275. except in two sets (3: 11) where a range of γα values were used.," The spin value was generally taken as $\chi_1=0.275$, except in two sets (3 11) where a range of $\chi_1$ values were used."310 The next comun iu Table 2 vives tre value of he secondary spin., The next column in Table 2 gives the value of the secondary spin.311" The spin X2 Collponents are either -0.5.-4.5.-0,5. (standard case}. 000 (set 6) oy |0.5.5.10.5. (set. 5)."," The spin $\chi_2$ components are either -0.5,-0.5,-0.5 (standard case), 0,0,0 (set 6) or +0.5,+0.5,+0.5 (set 5)."312 Siualler sets were caculated to ascertain that these three x» values arc represent:itive in statistical SCLISC ο ‘the different orientatiojs and magnitudes of so., Smaller sets were calculated to ascertain that these three $\chi_2$ values are representative in statistical sense of the different orientations and magnitudes of $\vek s_2$.313 The last colunn in Table (2 gives the rauge of the parameter qj» which is initially uuiforiilv distributed betweeji the Ims., The last column in Table 2 gives the range of the parameter $q_0$ which is initially uniformly distributed between the limits.314 The solutions converge toa distrinition of q which is narrower than this range., The solutions converge toa distribution of $q$ which is narrower than this range.315 Oilv du set Ja fixed value of qu= lowas used., Only in set 3 a fixed value of $q_0=1$ was used.316 Even though gy is not a physical xuiunueter but an iueredieut of the orbit finding algorithiu. its proper choice is still important.," Even though $q_0$ is not a physical parameter but an ingredient of the orbit finding algorithm, its proper choice is still important."317 We tried setting qy Mitially far from the value qu sug either (du= Oor w=2 but we forud that our code was not able to find enough solutions to justify these choices.," We tried setting $q_0$ initially far from the value $q_0=1$, using either $q_0=0$ or $q_0=2$, but we found that our code was not able to find enough solutions to justify these choices."318 For example. in the atter case oulv 23? solutiois were found which conceutrate around qeenter1.16 with a stand deviation of 0.15.," For example, in the latter case only 23 solutions were found which concentrate around $q_{center}=1.16$ with a standard deviation of 0.15."319 Taking the distribution unifonlv between these two limis produces more sohtions but mostly frou the range between qu0.6. aud qu= l.l.," Taking the distribution uniformly between these two limits produces more solutions, but mostly from the range between $q_0=0.6$ and $q_0=1.4$ ."320 Thereore we decided to carry out most expernmaents τς]ic this range of qo., Therefore we decided to carry out most experiments using this range of $q_0$ .321 ILoxwever. since it is possible to add some solutions also using the," However, since it is possible to add some solutions also using the"322Note that the amplitude at the ISCO is independent of AL. because fx[77M7 and [xAL3.,"Note that the amplitude at the ISCO is independent of $M$, because $h\propto f^{2/3}M^{2/3}$ and $f\propto M^{-1}$."323 The effective noise includes contributions [from the instrument aud from unresolved binaries (e.g.. see Larson. LHiscock. IHellings 2000 and /www.srl.caltech.edu/--shane/sensitivitv/ Mal," The effective noise includes contributions from the instrument and from unresolved binaries (e.g., see Larson, Hiscock, Hellings 2000 and $\sim$ shane/sensitivity/MakeCurve.html)."324 From ~2x10!—2x% Iz. unresolved Galactic double white dwarf binaries exceed the instrumental noise (e.g.. Farmer Phinney 2003): from ~2xLO*—10? Lz. in contrast. there will tvpically be one or zero double white dwarf binaries in a 10. Iz bin. hence alter several vears of operation. it will be possible to model individual binaries and subtract them from the data stream.," From $\sim 2\times 10^{-4}-2\times 10^{-3}$ Hz, unresolved Galactic double white dwarf binaries exceed the instrumental noise (e.g., Farmer Phinney 2003); from $\sim 2\times 10^{-3}-10^{-2}$ Hz, in contrast, there will typically be one or zero double white dwarf binaries in a $10^{-8}$ Hz bin, hence after several years of operation, it will be possible to model individual binaries and subtract them from the data stream."325 Unresolved extragalactic double white dwarf binaries will. however. continue to make a contribution.," Unresolved extragalactic double white dwarf binaries will, however, continue to make a contribution."326" The minimum total noise is in the few mllz range. where the total one-sided spectral noise density al a signal to noise S/N=10 is The time necessary to detect an SMDII-IMDII binaryat S/N—10 is Ti,=[5,(100)[ny"," The minimum total noise is in the few mHz range, where the total one-sided spectral noise density at a signal to noise $S/N=10$ is The time necessary to detect an SMBH-IMBH binaryat S/N=10 is $T_{\rm obs}=\left[S_n(10\sigma)/h\right]^2$."327" I[3x107?Hz<fy.7Iz. then Mhulliplving fü, bv Zon, gives the number of eveles in (he time 55 The minimum observational time and munber of eveles are obtained when the source is near the ISCO. which occurs in the most favorable frequency band 3x10/7Iz<fon.Hz when the redshifted mass M(1+2) is between 1.5xLOSM. and 4.4x10?M..."," If $3\times 10^{-3}~{\rm Hz}<f_{\rm obs}<10^{-2}~{\rm Hz}$, then Multiplying $f_{\rm obs}$ by $T_{\rm obs}$ gives the number of cycles in the time $T_{\rm obs}$: The minimum observational time and number of cycles are obtained when the source is near the ISCO, which occurs in the most favorable frequency band $3\times 10^{-3}~{\rm Hz}<f_{\rm obs}<10^{-2}~{\rm Hz}$ when the redshifted mass $M(1+z)$ is between $1.5\times 10^6\,M_\odot$ and $4.4\times 10^5\,M_\odot$."328 At (his point. More generally. as in Figure 1. one can compute the minimum observation (me and number of eveles for S/N=10. ji=10*M... and any MM. based on the frequency at the ISCO and the projected total noise curve.," At this point, More generally, as in Figure 1, one can compute the minimum observation time and number of cycles for S/N=10, $\mu=10^3\,M_\odot$, and any $M$, based on the frequency at the ISCO and the projected total noise curve."329 A prograde encounter with a rapidly rotating SMDII will eo to higher frequencies during its inspiral than will an encounter wilh a nonrotating SMDILII., A prograde encounter with a rapidly rotating SMBH will go to higher frequencies during its inspiral than will an encounter with a nonrotating SMBH.330 This increases the energy released in gravitational radiation ancl. importantly. increases the mass threshold at which the observed signal is in the most sensitive [frequency range of the band.," This increases the energy released in gravitational radiation and, importantly, increases the mass threshold at which the observed signal is in the most sensitive frequency range of the band."331 The numbers in Figure | are (therefore conservative., The numbers in Figure 1 are therefore conservative.332Despite many exciting progresses in observations. the nature of Ganuna-Ray Bursts (CRBs) remains to be a big puzzle sce vanParadijsetal.(2000) and Piran(2004). for recent reviews].,"Despite many exciting progresses in observations, the nature of Gamma-Ray Bursts (GRBs) remains to be a big puzzle [see \citet{par00} and \citet{pir04} for recent reviews]."333 ln such a situation. ib is extremely iniportant o identify some good correlations between the apparent (casv to measure or calculate) and intrinsic. properties. of CRBs.," In such a situation, it is extremely important to identify some good correlations between the apparent (easy to measure or calculate) and intrinsic properties of GRBs."334 Several such correlations have indeed. been found., Several such correlations have indeed been found.335 For example. an anti-correlation between the the peak uminosity and spectral lag of GRBs has beenfound. by ortisetal.(2000).. and a correlation between the peak uminosity and the variability of GRB lighteurves has been found by Fenimore Iamirez-Ituiz (2000. hereafter E1400) and Reiehart ct al. (," For example, an anti-correlation between the the peak luminosity and spectral lag of GRBs has beenfound by \citet{nor00}, and a correlation between the peak luminosity and the variability of GRB lightcurves has been found by Fenimore Ramirez-Ruiz (2000, hereafter FR00) and Reichart et al. ("3362001. hereafter. ROI).,"2001, hereafter R01)."337 A correlation »etween the total isotropic energy and the peak energy of the spectrum. (Amatietal.2002)... or the collimation-correctec otal energy and the peak energy of the spectrum al. 2004).. has also been discovered.," A correlation between the total isotropic energy and the peak energy of the spectrum \citep{ama02}, or the collimation-corrected total energy and the peak energy of the spectrum \citep{ghi04}, has also been discovered."338 Recently. Cuidorzi et al. (," Recently, Guidorzi et al. ("3392005. hereafter C05) teste 10 correlation between the variability ancl peak Iuminosity of GRBs. using an expanded sample of 32 CRBs with measured redshifts.,"2005, hereafter G05) tested the correlation between the variability and peak luminosity of GRBs, using an expanded sample of 32 GRBs with measured redshifts."340 The definitions of the variability anc 10 peak luminosity are the same. but the size of the GRB sample of G05 is about three times bigger than that of LOL.," The definitions of the variability and the peak luminosity are the same, but the size of the GRB sample of G05 is about three times bigger than that of R01."341 The existence of a correlation was confirmed. but the scatter in the correlation is significantly. larger than tha ound by ROL (sec. however. Reichart Nysewancder 2005).," The existence of a correlation was confirmed, but the scatter in the correlation is significantly larger than that found by R01 (see, however, Reichart Nysewander 2005)."342 Although the issue is in debate (CGuicorzi2005:Reichar&Nyvsewander2005:Reichart 2005).. it is clear that with he definition of variability given by ROL. the correlation οποσα the variability and the peak luminosity is not tight.," Although the issue is in debate \citep{gui05b,rei05,rei05b}, it is clear that with the definition of variability given by R01, the correlation between the variability and the peak luminosity is not tight."343 In this paper. we present a new definition for the variability of GRB lighteurves.," In this paper, we present a new definition for the variability of GRB lightcurves."344 We then apply it to a sample of 25 lone duration GRBs with measured redshifts. whose data are publicly. available.," We then apply it to a sample of 25 long duration GRBs with measured redshifts, whose data are publicly available."345 We show that. with the new definition of the variabilitv. the correlation between the variability and the peak luminosity of GRBs is significantly improved: the data scatter is considerably. reduced.," We show that, with the new definition of the variability, the correlation between the variability and the peak luminosity of GRBs is significantly improved: the data scatter is considerably reduced."346 ‘To measure the variability of a Lehteurve. first we must define alighteurce. Phe reference lightcurve should be sullieienthy smoother than the original raw lightcurve.," To measure the variability of a lightcurve, first we must define a. The reference lightcurve should be sufficiently smoother than the original raw lightcurve."347 Since an ultimate model for GRBs does not exist. vet. there is no first principle euiding us in choosing a reference lighteurve.," Since an ultimate model for GRBs does not exist yet, there is no first principle guiding us in choosing a reference lightcurve."348 What people usually do is to smooth the raw lighteurve with a linear box car” filter (or moving window). which smoothes the lighteurve with linear average (1100: 1101).," What people usually do is to smooth the raw lightcurve with a linear “box car” filter (or moving window), which smoothes the lightcurve with linear average (FR00; R01)."349 llere we use afiller (Pressetal.2002) to smooth a lighteurve., Here we use a \citep{pre02} to smooth a lightcurve.350 The Savitzkv-Golav. filter is a more general and more powerful approach for smoothing noisy data than the linear box-car filter., The Savitzky-Golay filter is a more general and more powerful approach for smoothing noisy data than the linear box-car filter.351 Phe basic idea of Savitzky-Golav filtering is to approximate the underlying function (i.c.. the reference lishteurve) within the moving window bv a polvnomial of higher order.," The basic idea of Savitzky-Golay filtering is to approximate the underlying function (i.e., the reference lightcurve) within the moving window by a polynomial of higher order."352 An advantage of the Savitzkv-CGolay filter to the linear filter is that the former preserves high moments while the latter does not., An advantage of the Savitzky-Golay filter to the linear filter is that the former preserves high moments while the latter does not.353 A Savitzky-Golay filter is specified hy three numbers: the order of the polynomial (m). the number of points used to the left of a data point (0). and the number of points used to the right ofa data point (ng).," A Savitzky-Golay filter is specified by three numbers: the order of the polynomial $m$ ), the number of points used to the left of a data point $n_{\rm L}$ ), and the number of points used to the right of a data point $n_{\rm R}$ )."354 To apply the Savitzky- filter. the data must be binned with constant spacing.," To apply the Savitzky-Golay filter, the data must be binned with constant spacing."355 For more details see Pressetal. (2002)., For more details see \citet{pre02}. .356 We use a third order Savitzky-Golay filter., We use a third order Savitzky-Golay filter.357 Phat is. we," That is, we"358spectral range coverage with this instrument. using the 79.0 lines/mun erating. is from 0.43 to 1.0 yan with some gaps between orders.,"spectral range coverage with this instrument, using the 79.0 lines/mm grating, is from 0.43 to 1.0 $\mu$ m with some gaps between orders."359 The projected size of the slit in the 2048x 2048 CCD was around two pixels (24 jmi) which gave a resolving power of ~50000., The projected size of the slit in the $\times$ 2048 CCD was around two pixels (24 $\mu$ m) which gave a resolving power of $\sim 50000$.360 We observed a loltal of 43 galactic carbon stars selected [rom the Qvo-micron skv survey by (1987)., We observed a total of 43 galactic carbon stars selected from the two-micron sky survey by \citet{cla87}.361.. Twelve J-tvpe carbon stars of this sample are analyzed here (see Table 1)., Twelve J-type carbon stars of this sample are analyzed here (see Table 1).362 The analvsis of the additional 31 normal (N-twpe) carbon stars will be presented in a future work., The analysis of the additional 31 normal (N-type) carbon stars will be presented in a future work.363 We used standard IRAF packages ancl procedures to perform bias level. dark current and scattered light subtraction and (o prepare a normalized flat-fielcl image to remove pixel-to-pixel sensitivity [Iuctuations.," We used standard IRAF packages and procedures to perform bias level, dark current and scattered light subtraction and to prepare a normalized flat-field image to remove pixel-to-pixel sensitivity fluctuations."364 A Th-Ar comparison lamp gave enough lines in all the echelle orders to perform an accurate wavelength. calibration., A Th-Ar comparison lamp gave enough lines in all the echelle orders to perform an accurate wavelength calibration.365 We carefullv. identified non-satirated Th-Ar emission lines and adjusted third-fourth order polynomials to obtain a calibration fit better than 10 in the residuals., We carefully identified non-saturated Th-Ar emission lines and adjusted third-fourth order polynomials to obtain a calibration fit better than 10 in the residuals.366 The calibrated spectra were then divided bv the spectrum of a hot. rapidly rotating star located in the skv as close as possible to the target star to eliminate telluric absorptions.," The calibrated spectra were then divided by the spectrum of a hot, rapidly rotating star located in the sky as close as possible to the target star to eliminate telluric absorptions."367 We note however. that most of the lines used in the abundance analvsis are not affected by terrestrial features (see below).," We note however, that most of the lines used in the abundance analysis are not affected by terrestrial features (see below)."368 Finally. different images of the same object were co-added after extraction and calibration to obtain the final spectrum.," Finally, different images of the same object were co-added after extraction and calibration to obtain the final spectrum."369 The 5/N ratio achieved in the final spectra varies from (he blue to the red orders., The S/N ratio achieved in the final spectra varies from the blue to the red orders.370 At ~4500 the S/N is 40-50 while at ~8000 the S/N frequently exceeded 400., At $\sim 4500$ the S/N is 40-50 while at $\sim 8000$ the S/N frequently exceeded 400.371 In contrast. below ~4400 the S/N ratios are poor because at these wavelengths carbon stars (J and N) are very difficult to observe.," In contrast, below $\sim 4400$ the S/N ratios are poor because at these wavelengths carbon stars (J and N) are very difficult to observe."372 The reason for this flux depression is still à matter of controversy., The reason for this flux depression is still a matter of controversy.373 In J-stars. particularly rich in oE PC. the absorption of triatomic carbon compounds can become nearly continuous at the shorter wavelengths.," In J-stars, particularly rich in $^{13}$ C, the absorption of triatomic carbon compounds can become nearly continuous at the shorter wavelengths."374 On the other hand. Johnsonetal.(1988) have pointed out that at the low temperatures of these stars. the resonance lines of some atoms become so wide that thev depress broad. areas of the continuum.," On the other hand, \citet{joh88} have pointed out that at the low temperatures of these stars, the resonance lines of some atoms become so wide that they depress broad areas of the continuum."375 This makes it almost impossible to observe theinteresting Tc I resonance lines, This makes it almost impossible to observe theinteresting Tc I resonance lines376computational cost. and they can retain information on he spatial distribution of the non-Caussian signal.,"computational cost, and they can retain information on the spatial distribution of the non-Gaussian signal."377 Also. hey provide useful analytic insights and. physical intuition.," Also, they provide useful analytic insights and physical intuition."378 For example. the derivation. ancl implementation of the analvtical formula for the CAIB Alinkowski funetionals in he limit of weak non-Gaussianity (Hikage. Komatsu Alatsubara 2006: Matsubara 2010) has allowed to obtain imits on various models. for which the optimal estimators are dillicult to implement: at the moment. a limit on the imordial non-Ciaussianity in the Iisocurvature perturbation is available from the Minkowski functionals (Llikage et al.," For example, the derivation and implementation of the analytical formula for the CMB Minkowski functionals in the limit of weak non-Gaussianity (Hikage, Komatsu Matsubara 2006; Matsubara 2010) has allowed to obtain limits on various models, for which the optimal estimators are difficult to implement; at the moment, a limit on the primordial non-Gaussianity in the isocurvature perturbation is available from the Minkowski functionals (Hikage et al."379 2009)., 2009).380" Note also that the concept of ""optimal is often misleacing. as it requires a posteriori knowledge of the ἵνρο of non-Gaussianity which is. at least in principle. unknown."," Note also that the concept of “optimal” is often misleading, as it requires a posteriori knowledge of the type of non-Gaussianity which is, at least in principle, unknown."381 The main question. instead. is whether or not it is possible to improve limits on κι using the CMD data only.," The main question, instead, is whether or not it is possible to improve limits on $f_{\rm NL}$ using the CMB data only."382 1ncluding realistic effects. in our simulations. such as inhomogeneous noise. point source contamination or foregrounds. so that we can compare our predictions with current observations. is subject of ongoing work (we provide some discussion in Appendices Bo and 12)).," Including realistic effects in our simulations, such as inhomogeneous noise, point source contamination or foregrounds, so that we can compare our predictions with current observations, is subject of ongoing work (we provide some discussion in Appendices \ref{noise_analytic} and \ref{spurious_ng}) )."383 We present results of these investigations in à companion paper. where we are also consider more terms in the expansion (1)).," We present results of these investigations in a companion paper, where we are also consider more terms in the expansion \ref{fnl_expansion_eq}) )."384 Application of the formalism. presented. in. Section 2.3 to peak rather than pixel statistics is a straightlorware exercise. and is also the subject. of another forthcoming publication.," Application of the formalism presented in Section \ref{excursion_set_formalism} to peak rather than pixel statistics is a straightforward exercise, and is also the subject of another forthcoming publication."385 Vhe Planck satellite with its increased. sensitivity and resolution is expected to. improve the measurements of most cosmological parameters by several factors compared to WALA. and in svnergies with future galaxy surveys (Colombo. Pierpaoli Pritchard 2009).," The Planck satellite with its increased sensitivity and resolution is expected to improve the measurements of most cosmological parameters by several factors compared to WMAP, and in synergies with future galaxy surveys (Colombo, Pierpaoli Pritchard 2009)."386 In fact. Planck gains a [actor of 2.5 in angular resolution and up to 10 in instantaneous sensitivity with respect to WALAP. and it is nearly photon noise limited in the CAIB channels (100-200 Cillz).," In fact, Planck gains a factor of 2.5 in angular resolution and up to 10 in instantaneous sensitivity with respect to WMAP, and it is nearly photon noise limited in the CMB channels (100-200 GHz)."387" Repeating this analysis at the Planck resolution may then provide more stringent limits on fx, from the excursion set statistics. and is also the subject of work in progress."," Repeating this analysis at the Planck resolution may then provide more stringent limits on $f_{\rm NL}$ from the excursion set statistics, and is also the subject of work in progress."388 We dedicate this paper to the memory of KLAS president Prof. Hyvo Chul Myung. who passed away on February 11. 2010.," We dedicate this paper to the memory of KIAS president Prof. Hyo Chul Myung, who passed away on February 11, 2010."389 We thank an anonymous referee for helpful comments and suggestions., We thank an anonymous referee for helpful comments and suggestions.390 We acknowledge the support of the Ixorea Science and Engineering Foundation (XOSEL) through the Astrophysical Research Center for the Structure and Evolution of the Cosmos (ARCSEC)., We acknowledge the support of the Korea Science and Engineering Foundation (KOSEF) through the Astrophysical Research Center for the Structure and Evolution of the Cosmos (ARCSEC).391 We acknowledge the use of the Leeeacy clrrcehive lor Adiicrowave Baackerouncl Daata Annalvsis (LAAIBDA)). support for whieh is provided bv the National Aeronautics ancl Space Administration (NASA) Ollice of Space Science.," We acknowledge the use of the egacy rchive for icrowave ackground ata nalysis ), support for which is provided by the National Aeronautics and Space Administration (NASA) Office of Space Science."392 Some of the results in this paper have been derived. using the package (Ciórrski ct al., Some of the results in this paper have been derived using the package (Górrski et al.393 1999)., 1999).394 The computation in the paper was done on the QUEST cluster at IKLAS., The computation in the paper was done on the QUEST cluster at KIAS.395the properties of theemitter in303.,the properties of the in.396". In this work, we present the results of the application of a leptonic one zone model to explain the measured light curves and spectra from these observations."," In this work, we present the results of the application of a leptonic one zone model to explain the measured light curves and spectra from these observations."397 Our goal is to obtain the physical parameters of the emitter robustly by making as few assumptions as possible., Our goal is to obtain the physical parameters of the emitter robustly by making as few assumptions as possible.398 wwas observed during ~60% of an orbital period simultaneously in the VHE and X-ray bands in September 2007(?)., was observed during $\sim$ of an orbital period simultaneously in the VHE and X-ray bands in September 2007.399". During a first part of the campaign (0.43«¢ 0.7), the MAGIC Cherenkov telescope observed the source for three hours every night and simultaneous observations were performed."," During a first part of the campaign $0.43<\phi<0.7$ ), the MAGIC Cherenkov telescope observed the source for three hours every night and simultaneous observations were performed."400 During a second part (0.71«$ 1.13) the X-ray observations were performed with Swift//XRT., During a second part $0.71<\phi<1.13$ ) the X-ray observations were performed with /XRT.401 The observation times were of about 15 ks for the observations and of about 3 ks for the Swift//XRT observations., The observation times were of about 15 ks for the observations and of about 3 ks for the /XRT observations.402 The longer observations and higher effective area of resulted in much higher statistics than the measurements from Swift//XRT., The longer observations and higher effective area of resulted in much higher statistics than the measurements from /XRT.403" To take into account the variability that the source shows on short time scales in the X-ray band when comparing these fluxes to the VHE measurements, the rms count rate variability of the X-ray light curve was considered in addition to the statistical uncertainty in the flux measurement to obtain realistic flux uncertaintiesdetails)."," To take into account the variability that the source shows on short time scales in the X-ray band when comparing these fluxes to the VHE measurements, the rms count rate variability of the X-ray light curve was considered in addition to the statistical uncertainty in the flux measurement to obtain realistic flux uncertainties."404". Using this method, the X-ray flux uncertainties take values between and of the flux."," Using this method, the X-ray flux uncertainties take values between and of the flux."405 The simultaneous campaign revealed very similar light curves in the X-ray and VHE bands: a first outburst at ¢=0.62 with a rise time below 20hh and a decay of about two days; and a second broader outburst spanning a few days between phases 0.8 and 1.1 with lower peak flux than the first., The simultaneous campaign revealed very similar light curves in the X-ray and VHE bands: a first outburst at $\phi=0.62$ with a rise time below h and a decay of about two days; and a second broader outburst spanning a few days between phases $0.8$ and $1.1$ with lower peak flux than the first.406" The correlation coefficient between the two bands for the first outburst was found to be r=0.97, whereas taking all simultaneous observations lowered the value to r=0.81."," The correlation coefficient between the two bands for the first outburst was found to be $r=0.97$, whereas taking all simultaneous observations lowered the value to $r=0.81$."407" Although all X-ray observations resulted in a clear detection, some of the VHE flux measurements have a significance below 2c."," Although all X-ray observations resulted in a clear detection, some of the VHE flux measurements have a significance below $\sigma$."408 For these cases we will consider the CL (confidence level) upper limits calculated by?., For these cases we will consider the CL (confidence level) upper limits calculated by.409. The detailed fluxes and uncertainties of the X-ray and VHE light curves may be found in Tables 1 and 2 of and the VHE upper limits in Table A.1 of?., The detailed fluxes and uncertainties of the X-ray and VHE light curves may be found in Tables 1 and 2 of and the VHE upper limits in Table A.1 of.410". The sensitivity of VHE observations precludes obtaining nightly spectra, and only a spectrum combining the observations with phases between 0.6 and 0.7 was published by?."," The sensitivity of VHE observations precludes obtaining nightly spectra, and only a spectrum combining the observations with phases between 0.6 and 0.7 was published by."411". In order to obtain a simultaneous SED, we extracted an spectrum of the source for the three X-ray observations that correspond to the MAGIC spectrum."," In order to obtain a simultaneous SED, we extracted an spectrum of the source for the three X-ray observations that correspond to the MAGIC spectrum."412 We filtered the data using SAS v10.0 and extracted three individual spectra from the pn instrument., We filtered the data using SAS v10.0 and extracted three individual spectra from the pn instrument.413" We used the SAS tool to convert the spectra from counts cchannel into physical units (flux density eenergy), averaged the three unbinned spectra and then grouped the bins to a signal-to-noise ratio of 20."," We used the SAS tool to convert the spectra from counts channel into physical units (flux density energy), averaged the three unbinned spectra and then grouped the bins to a signal-to-noise ratio of 20."414" In order to compare the measured spectrum to the computed intrinsic spectrum, we deabsorbed the former using the FORTRAN subroutine provided with Xspec v12.0(?)."," In order to compare the measured spectrum to the computed intrinsic spectrum, we deabsorbed the former using the FORTRAN subroutine provided with Xspec v12.0."415" We used a column density of Ny=5x10?!cm""? obtained from the average of the individual fits of an absorbed power law to the three observations."," We used a column density of $N_\mathrm{H}=5\times10^{21}\416\mathrm{cm}^{-2}$ obtained from the average of the individual fits of an absorbed power law to the three observations."417 This column density is consistent with that of the ISM alone(?)., This column density is consistent with that of the ISM alone.418. The discovery of a correlation between the X-ray and VHE bands points towards a common mechanism of emission modulation at both bands., The discovery of a correlation between the X-ray and VHE bands points towards a common mechanism of emission modulation at both bands.419" In a leptonic scenario, the fast and simultaneous changes in flux in both bands indicate that the modulation mechanism has to directly affect the emission level of the Inverse Compton (1C) and synchrotron processes."," In a leptonic scenario, the fast and simultaneous changes in flux in both bands indicate that the modulation mechanism has to directly affect the emission level of the Inverse Compton (IC) and synchrotron processes."420" Assuming constant injection, a way to obtain correlated X-ray and VHE emission is through a modulation of the number of emitting particles by dominant adiabatic losses, which would be ultimately related to the (magneto)hydrodynamical processes in the accelerator and emitter regions."," Assuming constant injection, a way to obtain correlated X-ray and VHE emission is through a modulation of the number of emitting particles by dominant adiabatic losses, which would be ultimately related to the (magneto)hydrodynamical processes in the accelerator and emitter regions."421" These processes may be related, for instance, to the interaction of the pulsar wind or the black hole jet with the stellar wind of"," These processes may be related, for instance, to the interaction of the pulsar wind or the black hole jet with the stellar wind of"422A recent measurement bv Fusco-Femiano et al. (,A recent measurement by Fusco-Femiano et al. (4231998. 1999) with the Deppo-SÀX satellite detected am excess clnission above 25 keV. consistent with the OSSE upper limits.,"1998, 1999) with the Beppo-SAX satellite detected an excess emission above 25 keV, consistent with the OSSE upper limits."424 Asstuuine that the excess is due to a secoud thermal conrponeut would require a temperature of 10 keV for it (Fusco-Fenuiano ot al., Assuming that the excess is due to a second thermal component would require a temperature of 40 keV for it (Fusco-Femiano et al.425 1998. 1999). which secius to be oeuplausible.," 1998, 1999), which seems to be implausible."426 The IIEX spectrum is plotted in Fig., The HEX spectrum is plotted in Fig.427 2 oe1 colmparison with a thermal. and a modified thermal Spectruni.," \ref{fig:HEX} in comparison with a thermal, and a modified thermal spectrum."428 If the WEN is due to IC scattering of CAIB photons. the necessary clectrous would be within the energy rauge of 2.8L9 GeV. aud therefore vossibly visible at radio frequencies.," If the HEX is due to IC scattering of CMB photons, the necessary electrons would be within the energy range of 2.8–4.9 GeV, and therefore possibly visible at radio frequencies."429 In order to scatter starlight photons iuto the observed enerev baud. electrous vetween 8E aud 150 MeV ire needed.," In order to scatter starlight photons into the observed energy band, electrons between 84 and 150 MeV are needed."430 Eusco-Feiniano ct al. (, Fusco-Femiano et al. (4311998) report that the TEN excess can be fitted satisfactorily with a power-law with photon nuniboer index of 0.973.15.,1998) report that the HEX excess can be fitted satisfactorily with a power-law with photon number index of 0.97–3.45.432 The ΠΕΝ excess flux is 04x2-103ου...2! between 20 aud 80 keV. aud within a radius of 1°.," The HEX excess flux is $2 \cdot 10^{-11}\, {\rm erg\, cm^{-2}\, s^{-1}}$ between 20 and 80 keV, and within a radius of $1^\circ$."433 For comparison: An extrapolation of the EUV spectra (Tab. 13) , For comparison: An extrapolation of the EUV spectra (Tab. \ref{tab:data}) )434to higher cucreies gives au excess flux between 2080 keV of 1-10Merecu7s+ within a radius of 18.," to higher energies gives an excess flux between 20–80 keV of $1\cdot 10^{-11}\, {\rm erg\,435cm^{-2}\, s^{-1}}$ within a radius of 18'."436 Since the difference by a factor of two night be due to the larger field of view in the second case. a variation or a systematic eror in the spectral iudices. or just a systematic effect m the estimate of the excess enudsson (e.g. Dowwer Derghóffer (1998) ect a higher EUV excess bv 50 )) the agreement suggests a possible plivsical connection.," Since the difference by a factor of two might be due to the larger field of view in the second case, a variation or a systematic error in the spectral indices, or just a systematic effect in the estimate of the excess emission (e.g. Bowyer Berghöffer (1998) get a higher EUV excess by 50 ) the agreement suggests a possible physical connection."437 Twang (1997) and Euflin Bierinanu (1998) discussed au inverse Compton model for the EUV excess in which the CAIB photous are scattered by a population of relativistic electrons. which are the low energy. tail of the population observed iu the radio halo of Coma.," Hwang (1997) and lin Biermann (1998) discussed an inverse Compton model for the EUV excess in which the CMB photons are scattered by a population of relativistic electrons, which are the low energy tail of the population observed in the radio halo of Coma."438 This inodel is problematic for three reasons:First. he spectral iudex of the radio oenmiüsson is 1.16 (excluding some high frequency data point. Bowver Berehotter 1998).," This model is problematic for three reasons:, the spectral index of the radio emission is 1.16 (excluding some high frequency data point, Bowyer Berghöffer 1998)."439 Thus. the syuchrotron cimitting electrons have a differcutia iuuber index of a.=3.32. steeper than a CAIB-IC scattering component with 2.5.," Thus, the synchrotron emitting electrons have a differential number index of $\ale = 3.32$, steeper than a CMB-IC scattering component with $\ale =2.5$ ."440 This means that a break has to be present in the electron specruni at lower than radio enütting cucreics if both componentsτσ belong to the sale population., This means that a break has to be present in the electron spectrum at lower than radio emitting energies if both components belong to the same population.441 Cüovinniul et al. (, Giovannini et al. (4421993) report a radial spectral index decrease of the radio halo.,1993) report a radial spectral index decrease of the radio halo.443 The ceutral spectral iudex is 0.5 a the outer L8., The central spectral index is 0.8 and the outer 1.8.444 The firs corresponds to an electron munber index of 2.6. which would be in good aerecmieut with the required uuuber index of the EUW proctucine electrons.," The first corresponds to an electron number index of 2.6, which would be in good agreement with the required number index of the EUV producing electrons."445 Although this solves the first problem. it Aoacreases the difficulties with the magnetic field estimate s explained below.S," Although this solves the first problem, it increases the difficulties with the magnetic field estimate as explained below.,"446econd. Bowyer and Derghóffer (1998) poiuted. out. that the radial profile of the EUV excess has a full width half masini (FWIIMD of 15/8 (19%ς12/6+ 1/5).," Bowyer and Berghöffer (1998) pointed out, that the radial profile of the EUV excess has a full width half maximum (FWHM) of $15'\!\!.8$ $19'\!\!.3\times 12'\!\!.6 \pm 1'\!\!.5$ )."447 If the EUV excess is due to scattered CMD. photous. the necessary electrous. which lave euergies of LLOQ350 MeV. have a profile with the same FWHAL as the excess chussion. whereas the low frequency radio profile has a immeh broader profile with a FWHM of z21.," If the EUV excess is due to scattered CMB photons, the necessary electrons, which have energies of $140 - 350$ MeV, have a profile with the same FWHM as the excess emission, whereas the low frequency radio profile has a much broader profile with a FWHM of $\approx 24'$."448 The streugth of the radio cussion. resulting from electrons with euereies of (1.2.3.6) GeV (B/(6pC))Ve. is a xoduct. of the spatial deusities of these electrons aud D? (approximately).," The strength of the radio emission, resulting from electrons with energies of $(1.2449- 3.6)$ ${\rm GeV}$ $(B/(6\,\mu{\rm G}))^{-1/2}$, is a product of the spatial densities of these electrons and $B^2$ (approximately)."450 Since any reasonable profile of the naenetic fields should decrease with radius ou the scale of acore radius. the spatial profile of these radio clectrous has ο be even broader than the radio emission itself. which is broader than he EUVX eunission.," Since any reasonable profile of the magnetic fields should decrease with radius on the scale of a core radius, the spatial profile of these radio electrons has to be even broader than the radio emission itself, which is broader than the EUV emission."451 Thus. the PWHAL of he electron population has to drop from a value which is cousiderably larger thau z21 at d GeV (the radio range) to 15/8 at 350 MeV (CAB-IC scattering electrons).," Thus, the FWHM of the electron population has to drop from a value which is considerably larger than $\approx 24'$ at 1 GeV (the radio range) to $15'\!\!.8$ at 350 MeV (CMB-IC scattering electrons)."452 Iu other words. a low cucrev electron population which is spatially very differently distributed compared to the population producing the radio halo is required (Bowver Derehóffer 1998).," In other words, a low energy electron population which is spatially very differently distributed compared to the population producing the radio halo is required (Bowyer Berghöffer 1998)."453 Aun extrapolating of the radial depeudoeu radio spectra of CHüovanuniui et al. (, An extrapolating of the radial dependent radio spectra of Giovannini et al. (4541993). would cive an olectrou population at lower euergies. which is less centrally concentrated as the radio population. due to the fat,"1993), would give an electron population at lower energies, which is less centrally concentrated as the radio population, due to the flat"455containing shifts of 6 observational data subsets with respect to the linear ephemeris. we conclude that our quadratic model of the phase function in is acceptable.,"containing shifts of 6 observational data subsets with respect to the linear ephemeris, we conclude that our quadratic model of the phase function in is acceptable."456 To be sure that non-zero P is not a mere conjunction of the non-Gaussian noise in ASAS data. we treated the observational set excluding all the ASAS data.," To be sure that non-zero $\dot P$ is not a mere conjunction of the non-Gaussian noise in ASAS data, we treated the observational set excluding all the ASAS data."457 Even in this case. we obtained P=2.81.6)x107. supporting the reality of the period lengthening.," Even in this case, we obtained $\dot458P=2.8(1.6)\times 10^{-9}$, supporting the reality of the period lengthening."459" The P,=0752144 rotational period of iis among the shortest known to date for CP stars: 1164429 (P=0l51899,Adelman 1999); VVir (P=0152070.Sokolov2000): 992385 (PESA 1997).."," The $P_1=0\fd52144$ rotational period of is among the shortest known to date for CP stars: 164429 \citep[$P=0\fd51899$,][]{adel}; ; Vir \citep[$P=0\fd 52070$,][]{sok}; 92385 \citep[$P=0\fd54909$,][]{ESA}."460 Among these fast rotating CP stars. is the hottest. most massive and. consequently. the largest thus. we conclude that hhas the largest equatorial rotational velocity (Vay=370480kms7! using the parallax-based My for a VV star and the period) and also the highest ratio of equatorial velocity to critical equatorial velocity (0.75+0.25) among all known CP stars.," Among these fast rotating CP stars, is the hottest, most massive and, consequently, the largest thus, we conclude that has the largest equatorial rotational velocity $V_{\mathrm{eq}}\approx 370 \pm 80 \ \mathrm461{km\,s}^{-1}$ using the parallax-based $M_V$ for a V star and the period) and also the highest ratio of equatorial velocity to critical equatorial velocity $(0.75\pm0.25)$ among all known CP stars."462 Therefore. we consider tto be the most rapid rotator of all known chemically peculiar stars.," Therefore, we consider to be the most rapid rotator of all known chemically peculiar stars."463 Because of its rapid rotation. it can serve as an important benchmark for theories describing the influence of rotational mixing on chemical peculiarity.," Because of its rapid rotation, it can serve as an important benchmark for theories describing the influence of rotational mixing on chemical peculiarity."464 Our analysis of the B.Hp.. and V light curves demonstrates that all three passbands have the same effective amplitude.," Our analysis of the $B$, and $V$ light curves demonstrates that all three passbands have the same effective amplitude."465 This suggests that the variability mechanism at optical wavelengths could be unique (Mikuláseketal., This suggests that the variability mechanism at optical wavelengths could be unique \citep{miksim}.4662008a).. We suggest that these light variations are caused by the uneven distribution of optically active. overabundant elements on the surface of the star.," We suggest that these light variations are caused by the uneven distribution of optically active, overabundant elements on the surface of the star."467 Unfortunately. we do not have maps of the abundance distribution or spectrograms suitable for their creation.," Unfortunately, we do not have maps of the abundance distribution or spectrograms suitable for their creation."468 We consider the possibility that the broad-band optical light variability in aarises from variations in the spectral lines of Hel. οἱΠΠ. and CI1. as depicted for im Fig.," We consider the possibility that the broad-band optical light variability in arises from variations in the spectral lines of $\ion{He}{i}$, $\ion{Si}{iii}$, and $\ion{C}{ii}$, as depicted for in Fig."469 | of Riviniusetal.(20068)., 1 of \citet{riv}.470.. They compare the line profiles of two spectra obtained at quadrature (HJD Ξ2451385.507.9=-1882.445(20) and HJD 2453191.879.f)= 1581.731(15). as defined for eqrefinverse)): their first spectrum was thus taken shortly after secondary light maximum. while the second was acquired at the secondary light minimum.," They compare the line profiles of two spectra obtained at quadrature (HJD $=2\,451\,385.507,\ \vartheta=-1882.445(20)$ and HJD $=2\,453\,191.879,\ \vartheta=1581.731(15)$ , as defined for ); their first spectrum was thus taken shortly after secondary light maximum, while the second was acquired at the secondary light minimum."471 The only overabundant element whose line intensity reaches maximum in the optical is helium (seetherelevantanalysisofHe-strongHD37776inKrti¢ka 2007).," The only overabundant element whose line intensity reaches maximum in the optical is helium \citep[see the472relevant analysis of He-strong HD\,37776 in][]{krt}."473. Lines of the other ions mentioned above are relatively weak and nearly constant., Lines of the other ions mentioned above are relatively weak and nearly constant.474 The photometric effect of the weak emission in Ha is also negligible., The photometric effect of the weak emission in $\alpha$ is also negligible.475 We modelled the light curves of wwith the code described by Krti¢kaetal.(2007) assuming the inclination angle of ¢=S54°418° (vsiné=300415kms!.. and found that two circular. helium-rich spots with |[He/H]=1.4 and radii 60° on opposite hemispheres of rreproduce the observed light variations in all three passbands.," We modelled the light curves of with the code described by \citet{krt} assuming the inclination angle of $\mathit{i}=54^\circ\!\pm18^\circ$ \citep[$v\,\sin\,i=300\pm\!15$476km\,s$^{-1}$ and found that two circular, helium-rich spots with [He/H]=1.4 and radii $60^\circ$ on opposite hemispheres of reproduce the observed light variations in all three passbands."477" We therefore conclude that light variations in mmavy be the result of the uneven distribution of helium,", We therefore conclude that light variations in may be the result of the uneven distribution of helium.478 This hypothesis should be tested with Doppler tomography. which we plan to do in the near future.," This hypothesis should be tested with Doppler tomography, which we plan to do in the near future."479" An increase in the rotational period with P/P,=2.48)x107?yr7! is observed at the 3.1o level of certainty."," An increase in the rotational period with $\dot{P}/P_1=2.4(8)\times48010^{-6}\,\mathrm {yr}^{-1}$ is observed at the $3.1\,\sigma$ level of certainty."481 During the past 20 years. the period has increased by 2.1 s!," During the past 20 years, the period has increased by 2.1 s!"482 Unfortunately. no observations were taken in the interval 1994-2000.," Unfortunately, no observations were taken in the interval 1994-2000."483" This adds some uncertainty to our quadratic fit of the O-C residuals,", This adds some uncertainty to our quadratic fit of the O-C residuals.484 If the period change were real. then wwould be the fourth known CP star displaying an increase in its rotational period.," If the period change were real, then would be the fourth known CP star displaying an increase in its rotational period."485 The star is similar in several aspects to the nost rapidly braking He-strong CP star 337776 with a well-determined P/P=4.0117)x1075 yyear! (Mikuláseketal.2008b).., The star is similar in several aspects to the most rapidly braking He-strong CP star 37776 with a well-determined $\overline{\dot{P}/P}=4.01(17)\times10^{-6}$ $^{-1}$ \citep{mikbra}.486 The period increase in ccould also be interpreted as a deceleration of the rotation of its due to momentum loss by a magnetically confined stellar wind (seealsoud-Doulaetal.2009)., The period increase in could also be interpreted as a deceleration of the rotation of its due to momentum loss by a magnetically confined stellar wind \citep[see also][]{ud}.487. However. à possible change in the rate of period change for 337776 (P=-29(13)x107 dd!) suggests that the process of the rotational braking need not be fully monotonic!," However, a possible change in the rate of period change for 37776 $\ddot{P}=-29(13)\times10^{-13}$ $^{-1}$ ) suggests that the process of the rotational braking need not be fully monotonic!"488 Both stars have strong magnetic fields: that of lis approximately dipolar ranging in strength from kkG to +2.5kkG (Oksalaetal.2010).. while the field of 337776 is dominated by a quadruple component (Thompson&Land-street 1985).," Both stars have strong magnetic fields; that of is approximately dipolar ranging in strength from kG to kG \citep{oks}, while the field of 37776 is dominated by a quadruple component \citep{thola}."489. However. the main difference between the stars discussed here is their age.," However, the main difference between the stars discussed here is their age."490 While 337776 1s à very young CP star with an age of around 1 Myr. lis about twenty times older (see Sect.," While 37776 is a very young CP star with an age of around 1 Myr, is about twenty times older (see Sect."491 2.1)., 2.1).492 Because the characteristic braking time of (P/Px4x10° yyr) is about fifty times shorter than its stellar age. It seems probable that variations in rotational period are confined to the outer layers of the star.," Because the characteristic braking time of $P/\dot{P}\approx 4 \times 10^{5}$ yr) is about fifty times shorter than its stellar age, it seems probable that variations in rotational period are confined to the outer layers of the star."493 The period variations could be eyelie with a long interval of period increase followed by a rapid period decrease., The period variations could be cyclic with a long interval of period increase followed by a rapid period decrease.494 The period decrease may be caused by greater friction between the surface and inner layers of the star caused by. e.g.. reconnection events.," The period decrease may be caused by greater friction between the surface and inner layers of the star caused by, e.g., reconnection events."495 The length of this cycle can be roughly estimated as the time when the surface layers lag behind the inner part of the star by one revolution Qe. Ta~P V2/P).," The length of this cycle can be roughly estimated as the time when the surface layers lag behind the inner part of the star by one revolution (i.e., $T_{\mathrm{cycle}}\sim496P\,\sqrt{\,2/\dot{P}}$ )."497 This produces estimates of 35 yr and 45 yr for aand 337776. respectively.," This produces estimates of 35 yr and 45 yr for and 37776, respectively."498 The hypothesis should be testeda few decades hence with additional observations., The hypothesis should be testeda few decades hence with additional observations.499Maenetolvdrodvuaimic (MIID) turbulence is prescut iu many astronondcal settings. such as the solar wiud. the iuterstellar imedimim. molecular clouds. accretion disks. and clusters of galaxies (Diskuup2003:EKulsud2005:Schekochilin&Cowley 2005).,"Magnetohydrodynamic (MHD) turbulence is present in many astronomical settings, such as the solar wind, the interstellar medium, molecular clouds, accretion disks, and clusters of galaxies \citep{bis03,kul05,sch05}."500. Its theory has attracted a sizable literature Croshuikov1963:Kraichnuan1965:She-2005:Deresuvak&Lazarian 20053...," Its theory has attracted a sizable literature \citep{iro63,kra65,she83,gol95,gol97,ng96,cho00,bis00,501mar01,cho02,gal00,gal02,mul03,gal05,bol05,mul05,ber05}."502 The simplest of cases concerns the smiallscale dvuamics of the excitations of an incompressible fiuid with a mean maeuetic field., The simplest of cases concerns the small–scale dynamics of the excitations of an incompressible fluid with a mean magnetic field.503 The turbulent cascade of cherey to small scales is the result of non linear interactions between Alfvén waves traveling in opposite directions along the local. mean maguetic field (LoshuikovL963:Iraichnan1965).," The turbulent cascade of energy to small scales is the result of non linear interactions between Alfvénn waves traveling in opposite directions along the local, mean magnetic field \citep{iro63,kra65}."504. Whereas this broad picture of LIroshuikov and παπα still eudures. our appreciation of MIID turbulence has uudergoue siguificaut revisions due. mainly. to the recognition of the importance of anisotropy and the consequent strengthening of nou linear interactions.," Whereas this broad picture of Iroshnikov and Kraichnan still endures, our appreciation of MHD turbulence has undergone significant revisions due, mainly, to the recognition of the importance of anisotropy and the consequent strengthening of non linear interactions."505 The inertialrange. which iucludes leugth scales between the stirring aud dissipation scales. is best understood iu those cases in which the oppositely directed waves are excited with equal power: these badanced cascades can beweak (Ng&Bhattacharjeeich&Sridhar 1997).. as well asstrony (Goldreich&Srid-har 1995).," The inertial–range, which includes length scales between the stirring and dissipation scales, is best understood in those cases in which the oppositely directed waves are excited with equal power: these cascades can be \citep{ng96,gol97}, as well as \citep{gol95}."506fadedenced cascades are uuderstood oulv iu he case when the turbulence isweek (Galtieretal.2000:Lithwick&Coldveich 2003).," cascades are understood only in the case when the turbulence is \citep{gal00,lit03}."507. In tlis Letter we consider he general case of iibalauced cascades., In this Letter we consider the general case of imbalanced cascades.508 The solu wind is the best laboratory that we have o investicate ΑΠΟ turbulence., The solar wind is the best laboratory that we have to investigate MHD turbulence.509 In-situ imueasurenments we spacecraft vield spectra for velocity auc magnetic ποια fluctuations over many decades of lenetlscale (6.8. Horburv 1999).," In-situ measurements by spacecraft yield spectra for velocity and magnetic field fluctuations over many decades of lengthscale (e.g., Horbury 1999)."510 On the largest scales. the spectrum is flat. prestunably reflecting the spectrum with which Huctuations are injected into the solar wind by shocks or dynamical iustabilities.," On the largest scales, the spectrum is flat, presumably reflecting the spectrum with which fluctuations are injected into the solar wind by shocks or dynamical instabilities."511 On smaller scales. the spectrum is Wolnoevorov. and fluctuations are thought to be undergoing an active turbulent cascade.," On smaller scales, the spectrum is Kolmogorov, and fluctuations are thought to be undergoing an active turbulent cascade."512 On these scales. the amplitudes of the two Elsasser fields are not equal: waves travelling away from the Sun have higher amplitudes Ενα those travelling towards Because of this imbalance. the theory of ATID turbulence has been inadequate for application to the solar wind.," On these scales, the amplitudes of the two Elsasser fields are not equal: waves travelling away from the Sun have higher amplitudes than those travelling towards Because of this imbalance, the theory of MHD turbulence has been inadequate for application to the solar wind."513 Our solution for the strong imbalanced cascade removes this inadequacy., Our solution for the strong imbalanced cascade removes this inadequacy.514 Tn §2.. we stmuarize the properties of MIID cascades that were previously understood.," In \ref{sec:balanced}, we summarize the properties of MHD cascades that were previously understood."515 Our solution for the strong mibalauced cascade is eiven iu 83.., Our solution for the strong imbalanced cascade is given in \ref{sec:imbalanced}.516 The system πο consider1 an incompressible iuagnetofluid of mass density p and mean magnetic field Bor., The system we consideris an incompressible magnetofluid of mass density $\rho$ and mean magnetic field $B_0\hat{z}$ .517 Let wí(r.f) be the fluid velocity. and b(ir.£) theimaenetic field fluctuation.," Let ${\bf v}({\bf r}, t)$ be the fluid velocity, and ${\bf b}({\bf r}, t)$ themagnetic field fluctuation."518 The ANID, The MHD519fact that the second redshift detected was also the largest so far (GRB 97121I. ;Do— 3.1). has now vanished.,"fact that the second redshift detected was also the largest so far (GRB 971214, $z=3.4$ ), has now vanished."520 Secoud. iu order to place the energy release of CRB 990123 in coutext. oue should notice that Lx10°!ergs is the eucrev obtained by converting the restmass of two solar masses. or. alternatively. the energy emitted by the whole Universe out to 2%1 within the burst duration.," Second, in order to place the energy release of GRB 990123 in context, one should notice that $4\times 10^{54}\; ergs$ is the energy obtained by converting the rest–mass of two solar masses, or, alternatively, the energy emitted by the whole Universe out to $z\approx 1$ within the burst duration."521 So. a single (perhaps double) star outshines the whole Universe.," So, a single (perhaps double) star outshines the whole Universe."522 Besides the distance and cnerev scales. the major nupact of the discovery of afterelows has ρου the establishment of some key features of the fireball model (Rees aud Mésszauvos 1992): Twill illustrate these poiuts in the following. but. lest we become too proud. we should also remember that the fireball model has met some fülures.," Besides the distance and energy scales, the major impact of the discovery of afterglows has been the establishment of some key features of the fireball model (Rees and Mèsszàrros 1992): I will illustrate these points in the following, but, lest we become too proud, we should also remember that the fireball model has met some failures."523 The original version of the model (Alésszarros aud Rees 1993) advocated the dissipation of the explosion energy at external shocks(7.6... those with the interstellar medium).," The original version of the model (Mèsszàrros and Rees 1993) advocated the dissipation of the explosion energy at external shocks, those with the interstellar medium)."524" Savi and Piran (1997). following a point originally made by Ruderman (1975) showed hat these shocks smooth out millisecoucl timescale variability, which can only be naintained bv the internal shocks proposed by Paczvüsski and Nu (1991)."," Sari and Piran (1997), following a point originally made by Ruderman (1975) showed that these shocks smooth out millisecond timescale variability, which can only be maintained by the internal shocks proposed by Paczyǹsski and Xu (1994)."525 Also. he fireball model originally. ascribed even the emission. from the burst proper (as opposed to the afterelow) to optically thin svuchrotron processes: Twill discuss iu he section why tlis is exceedingly unlikely.," Also, the fireball model originally ascribed even the emission from the burst proper (as opposed to the afterglow) to optically thin synchrotron processes; I will discuss in the section why this is exceedingly unlikely."526 Furthermore. even the ast teuct of mid908 Common wiscdounZ6... that bursts are due to ucutron binary uerecrs. does uot look too promising at the moment (since some bursts ποσα to o located inside star formüug regious. compatible with the loug spiralin time). hough of course it is bv no means ruled out vet.," Furthermore, even the last tenet of mid–90s common wisdom, that bursts are due to neutron binary mergers, does not look too promising at the moment (since some bursts seem to be located inside star forming regions, incompatible with the long spiral–in time), though of course it is by no means ruled out yet."527 Ire. one may asse that an unknown agent deposits 100110°!ergs inside a stall volume of linear dimension z10°—10*en.," Here, one may assume that an unknown agent deposits $10^{51}-10^{54}\; ergs$ inside a small volume of linear dimension $\approx 10^6-10^7\;cm$."528 The resulting typical cucrey deusity corresponds to a temperature of a few AfeWs. so that electrons and positrous cannot," The resulting typical energy density corresponds to a temperature of a few $MeV$ s, so that electrons and positrons cannot"529"in the Sgr body show a clear increasing trend as a funcion of distance to the Sgr center (Figure [6], top panel).","in the Sgr body show a clear increasing trend as a funcion of distance to the Sgr center (Figure \ref{fig:dist_trends}, top panel)."530 A similar relation has also been noticed in our Galactic globular cluster system (e.g.?) and in many others (e.g.????)..," A similar relation has also been noticed in our Galactic globular cluster system \citep[e.g.][]{vandenbergh00} and in many others \citep[e.g.][]{vandenbergh00,barmby02,cantiello07,hwang11}."531" A similar relation between central density and galactocentric distance has been shown by ?,, although based on the observational data from ?,, which may not be appropriate for the more extended clusters (see below)."," A similar relation between central density and galactocentric distance has been shown by \citet{penarrubia09}, although based on the observational data from \citet{mackey03c}, which may not be appropriate for the more extended clusters (see below)."532 Core radii and concentrations also show clear trends with respect to Sgr distance (Figure [6]. middle and low panels).," Core radii and concentrations also show clear trends with respect to Sgr distance (Figure \ref{fig:dist_trends}, middle and low panels)."533" The inclusion of former Sgr clusters (like NGC 5634 and Palomar 12) into these plots would increase the scatter in the relations, although their original positions within Sgr are unknown."," The inclusion of former Sgr clusters (like NGC 5634 and Palomar 12) into these plots would increase the scatter in the relations, although their original positions within Sgr are unknown."534The majority are early type objects: ouly three have spectral type F or later.,The majority are early type objects; only three have spectral type F or later.535 Roughly half of these stars lie above the ZAMS on the HRD. suggestingMOD that these are probably cluster stars with extra (circumstellar) reddeuius.," Roughly half of these stars lie above the ZAMS on the HRD, suggesting that these are probably cluster stars with extra (circumstellar) reddening."536 Seven of the stars (id3. id6. id23252. id215. 12200. 11062. id1238) have B spectral types.," Seven of the stars (id3, id6, id2352, id215, id2209, id1062, id1238) have B spectral types."537 All ave defiuite enulssion lines except id3., All have definite emission lines except id3.538 Two (id1062 and 12209) lie above the main sequence aud are included in our PMS caudidate sample., Two (id1062 and id2209) lie above the main sequence and are included in our PMS candidate sample.539 In the case of id6 and id1062. the whole Baliner series is iu emission: id2322. id215. 02209 and id1238 show detectable emission ouly in the Aa liue.," In the case of id6 and id1062, the whole Balmer series is in emission; id2352, id215, id2209 and id1238 show detectable emission only in the $H\alpha$ line."540 There are six A type stars in this group (102320. id2192. id1651.101093. 1026237. 1421506).," There are six A type stars in this group (id2320, id2492, id1651,id1093, id2637, id2156)."541 Only wo (id2320 aud 12192) show definite Aa emission: four liave a weak Ha absorptiou line., Only two (id2320 and id2492) show definite $H\alpha$ emission; four have a weak $H\alpha$ absorption line.542 We identify four (1102320.)2 id2192. id16251. id2156) as candidate PMS stars according to their position on the HRD.," We identify four (id2320, id2492, id1651, id2156) as candidate PMS stars according to their position on the HRD."543 One of these stars (id2320) shows emission in [NH] aud [SI] Because they lie above the main sequence. all of the three late type objects (Gd1379. idis15. id2215) are among our PMS cauclicates.," One of these stars (id2320) shows emission in [NII] and [SII] Because they lie above the main sequence, all of the three late type objects (id1379, id1845, id2245) are among our PMS candidates."544 Ouly oue (id2215) shows Li E A6708 absorption line., Only one (id2245) shows Li I $\lambda$ 6708 absorption line.545 Walter(1987). aud Walteretal.(1988). divide the low mass PMS stars into two groups according to their spectroscopic aud photometric properties., \citet{walt87} and \citet{walt88} divide the low mass PMS stars into two groups according to their spectroscopic and photometric properties.546 Classical T Tauri stars (¢TTs) have strong Ha emission. with EM(Ha)>10À: wTTs have EM(Hà)<10À..," Classical T Tauri stars (cTTs) have strong $H\alpha$ emission, with $EW(H\alpha) > 10$; wTTs have $EW(H\alpha) < 10$."547 Most cTTs have other strong emission lines from HE. Call aud sometimes Hel. Many have [NIJ]. [SII] aud [OI] emission [rom winds or collimated jets.," Most cTTs have other strong emission lines from HI, CaII and sometimes HeI. Many have [NII], [SII] and [OI] emission from winds or collimated jets."548 eTTs also display large infrared excesses [from a circumstellar disk., cTTs also display large infrared excesses from a circumstellar disk.549 Optical veiling is observable in the spectra of ¢TTs which iudicates the presence of extra emission from a boundary layer or accretion hot spot (Bertout1980)., Optical veiling is observable in the spectra of cTTs which indicates the presence of extra emission from a boundary layer or accretion hot spot \citep{bert89}.550. wTTs often have Call and other Chromospheric eiuissiou lines., wTTs often have CaII and other chromospheric emission lines.551 They usually have uearly blackbody spectra aud rarely display jet or wind emission features (Bertout1989)., They usually have nearly blackbody spectra and rarely display jet or wind emission features \citep{bert89}.552. To place our emission line stars in context with other PMS stars. we compare our sample witli stars in the well studied Taurus-Auriga cloud (e.g..Ixeuvon&Hartmann1995).," To place our emission line stars in context with other PMS stars, we compare our sample with stars in the well studied Taurus-Auriga cloud \citep[e.g.,][]{keny95}."553. Fie Ll., Fig 4.554 compares the distribution of the Ha indices of T Tauri stars in Taurus-Auriga (Ivenvouetal.1998) with late type PMS stars in the field of NGC 6871., compares the distribution of the $H\alpha$ indices of T Tauri stars in Taurus-Auriga \citep{keny98} with late type PMS stars in the field of NGC 6871.555 The two histograms peak at the same iudex. value., The two histograms peak at the same index value.556 Compared to Taurus-Auriga. NGC 6371 has few stroug emission stars and an overabundance of weak emission liue stars.," Compared to Taurus-Auriga, NGC 6871 has few strong emission stars and an overabundance of weak emission line stars."557 With age of 105 vr. the PMS stars in Taurus-Auriga are much younger than the apparent age (~10* vr) of PMS stars in NGC 6871.," With age of $\simeq 10^6$ yr, the PMS stars in Taurus-Auriga are much younger than the apparent age $\simeq 10^7$ yr) of PMS stars in NGC 6871."558 Observations of other voung clusters suggest that the disk accretion which powers ¢TTs emission declines on timescales of ~10* vr etal. 2001).," Observations of other young clusters suggest that the disk accretion which powers cTTs emission declines on timescales of $\simeq 10^7$ yr \citep{hart98, hais01}."559. Our apparent discovery of wTTs in NGC 6871 is consistent with these observations., Our apparent discovery of wTTs in NGC 6871 is consistent with these observations.560 We plan to return to tliis issue in future papers where we analyze the uou emission, We plan to return to this issue in future papers where we analyze the non emission561This rate is still subject to large uncertainties at low teiiperatures (Pzi2000 KJ.,This rate is still subject to large uncertainties at low temperatures $T\la 2000$ K).562 Our fit in Fig., Our fit in Fig.563 1 (solid line) is based ou the cross sectious of Peterson et al. (, 1 (solid line) is based on the cross sections of Peterson et al. (5641971) and Moscelev et al. (,1971) and Moseley et al. (5651970) aud the experimental poiut at T=300 Is of Moseley et al. (,1970) and the experimental point at $T=300$ K of Moseley et al. (5661970).,1970).567 At temperatures below ~ 10? IW. we have extrapolated as a power-law ονE. 1) the cross section of Moseley. et al. (," At temperatures below $\sim$ $^3$ K, we have extrapolated as a power-law $\propto E^{-1}$ ) the cross section of Moseley et al. ("5681970).,1970).569 The rate used by Abel et al. (, The rate used by Abel et al. (5701997) is the same as Dalgarno Lepp (1957) and it is shown by the lone-dashed line.,1997) is the same as Dalgarno Lepp (1987) and it is shown by the long-dashed line.571 Finally. the rate adopted by Shapiro Nang (1987). taken from Duley Williams (1981). is shown by the dashed noe.," Finally, the rate adopted by Shapiro Kang (1987), taken from Duley Williams (1984), is shown by the dashed line."572 This reaction rate has been computed cchanmiccallly by Biuuaker Peek (1976) aud more recently by Stancil et al. (, This reaction rate has been computed ly by Ramaker Peek (1976) and more recently by Stancil et al. (5731993).,1993).574 The two calculations agree to within frou T= 10K up to T=109 K. Iu Fig., The two calculations agree to within from $T=10$ K up to $T=10^6$ K. In Fig.575 1e show the values tabulated by Ramaker Peck (1976) (triangles). our polynomial fit (solid line). aud the fit bv Abel et al. (," 1 we show the values tabulated by Ramaker Peek (1976) (triangles), our polynomial fit (solid line), and the fit by Abel et al. ("5761997) (dashed line),1997) (dashed line)577Alost astroplivsical Structures result of eravitational instabilities. from large scae cosmolocical structures down to planets.,"Most astrophysical structures result of gravitational instabilities, from large scale cosmological structures down to planets."578" Yet. among f1ο least uuderstood fpies dn astroplivsies we find. ealass formation aud star fornation. which both involve fragnentation and the LOWlnear erowthn of structures occ""urine durus the nolinear phases of eravitational iusability."," Yet, among the least understood topics in astrophysics we find galaxy formation and star formation, which both involve fragmentation and the nonlinear growth of structures occurring during the non-linear phases of gravitational instability."579 Perhaps. one «ft the fuudaiuenutal renson why racsnientation and structire formation via graviational iustability appears x» diffiatIt is that we lack of coisistout heoretical tools allewine ο. combile gravitv with eas ohyvsies.," Perhaps, one of the fundamental reason why fragmentation and structure formation via gravitational instability appears so difficult is that we lack of consistent theoretical tools allowing to combine gravity with gas physics."580" Tudeed. οQ often ignored. ix ti classical hermoclyranucs doc"" nof hold for eyavitalug svstenis. )ocause these ire noin-extesive in fje thernodvuamical seuse (Laudsberg 1972..198E: Tsallis 1999: » Plastino Platino 1999))."," Indeed, too often ignored is that classical thermodynamics does not hold for gravitating systems, because these are non-extensive in the thermodynamical sense (Landsberg \cite{Landsberg72}, \cite{Landsberg84}; ; Tsallis \cite{Tsallis99}; ; Plastino Plastino \cite{Plastino99}) )."581 Acnally. ΜΑΙ oficr natural svstcus do not respect the requisies of thermodyαλλος.," Actually, many other natural systems do not respect the requisites of thermodynamics."582 Such systems often featre iuterestius phenomCla such as erowing long range COLTCations or phase transitions., Such systems often feature interesting phenomena such as growing long range correlations or phase transitions.583 Amoug the svimptous of a fundamental «cep probleii i eravitatiug svsenis is the appearance of negative specificheat (LanderDell LyucdeBell 1977: Bell 199s . which was seen for a loug time as a paradox in statisical mechanics. since negaive specific heat was jought to be mipossible.," Among the symptoms of a fundamental deep problem in gravitating systems is the appearance of negative specificheat (Lynden-Bell Lynden-Bell \cite{Lynden77}; Lynden-Bell \cite{Lynden98}) ), which was seen for a long time as a paradox in statistical mechanics, since negative specific heat was thought to be impossible."584" DPreseuth. the «mlvo available approach to follow 10 nonlinear plases of eravitatioval distabilitics 1s to carry out numerical αλλαος,"," Presently, the only available approach to follow the nonlinear phases of gravitational instabilities is to carry out numerical simulations."585 Auong all the existi18o nuethods. AN-μον echuiques are thouelt to be the most effective to siniulae selberavitating svsCll sas well the continuous case as fje eranular phases.," Among all the existing methods, $N$ -body techniques are thought to be the most effective to simulate self-gravitating systems as well the continuous case as the granular phases."586 Yot. despite the considerable success of these methods im reproducing many observed features. way fundamental problems remain.," Yet, despite the considerable success of these methods in reproducing many observed features, many fundamental problems remain."587 As mentioned above. the fracinentation aud structure formation is not clearly understood.," As mentioned above, the fragmentation and structure formation is not clearly understood."588 Related to this. CDM simulations couflict with observations at ealactic scales (Moore 1999... Joannes et al. 2001..," Related to this, CDM simulations conflict with observations at galactic scales (Moore \cite{Moore99}, James et al. \cite{Bullock01},"589 Dolatto et al. 2002)).," Bolatto et al. \cite{Bolatto02}) ),"590 aud no theorv of the ISAL is preseulv able to the couditious of star formation., and no theory of the ISM is presently able to the conditions of star formation.591 Most of the time the star formation process relics on recipes with little physical coustraiut., Most of the time the star formation process relies on recipes with little physical constraint.592 Iu situatiois were N-body smaulatious have success (c.g. hot stelw systems) geravitatioual dwnandes is sufficient to a↸⊳⋯∏∐↑↕⋟∪↥⋅↑∐↸∖∐⋅⋯⋜∏∐∶↴⋁↕∪↴⋝⋜↧↻↥⋅∪↻↸∖↥⋅↕↸∖↴∖↴⋅ aclditional nici⋅∪↴∖↴↸⊳≺∏≻↕↸⊳↻∐⋅↖↽↴∖↴↕↸∷∖↴⋯∐↴⋝↸∖∐," In situations were $N$ -body simulations have success (e.g. hot stellar systems) gravitational dynamics is sufficient to account for their main global properties, additional microscopic physics can be neglected."593↸∖∶↴↜⊾↕↸∖↸⊳↑↸∖≼↧∙↕≧∏↑↖↖↽∐↸∖∐ eravitational istability via fragmentation involves sinall scale plivsics. the outcome max be stronely depeudenut on the propertics of the small scale plivsies.," But when gravitational instability via fragmentation involves small scale physics, the outcome may be strongly dependent on the properties of the small scale physics."594 In other words. in situations where the erowth on siue!laritics triggered by gravitv ds :dlowed. the chaotic nature of eyavitating systeus make them seusitive to the portirhations induced by uou-eravitational plivsics.," In other words, in situations where the growth on singularities triggered by gravity is allowed, the chaotic nature of gravitating systems make them sensitive to the perturbations induced by non-gravitational physics."595 Tierefore it is Προστ! to uuderstaxd t16 properties of N-body systems subjected to variots perturbations., Therefore it is important to understand the properties of $N$ -body systems subjected to various perturbations.596" For tjose purpOses, a numerical study of perturbed. evavitating N-boc vouvstenas ds carried out."," For these purposes, a numerical study of perturbed, self-gravitating $N$ -body systems is carried out."597 Anem tlic| relevant perturbations we expect that boundary coulitims at small and laree scales. as well as dissipative facors can play a kev role.," Among the relevant perturbations we expect that boundary conditions at small and large scales, as well as dissipative factors can play a key role."598 In order to characterize tlie dudividual effects of perturbations. in the tradition of analytical models. one is advised to deliberately us euuplified models.," In order to characterize the individual effects of perturbations, in the tradition of analytical models, one is advised to deliberately use simplified models."599 A study of dissipative systems is duportant because such svstenus may develop long-range correlations., A study of dissipative systems is important because such systems may develop long-range correlations.600 m the typical ISAL radiative cooling is very effective and induces ai temporary cucrev-flow leading the system far from eqiibri (DysonWilliams 1997)).," In the typical ISM, radiative cooling is very effective and induces a temporary energy-flow leading the system far from equilibrium (DysonWilliams \cite{Dyson97}) )."601 From laboratory ex]o)runents it is well mown that systems outside of equiliMMU iav spontaueouslv develop spatio-temporal stictures (Clausdorff Prigogiue 1971: Nicolis Prigoeine 1977: PrigogineOD 1980: Melo 1991 ))., From laboratory experiments it is well known that systems outside of equilibrium may spontaneously develop spatio-temporal structures (Glansdorff Prigogine \cite{Glansdorff71}; Nicolis Prigogine \cite{Nicolis77}; Prigogine \cite{Prigogine80}; Melo \cite{Melo94}) ).602 A pormanenu cherey-flow is induced when cucrev loss due 0 dissipatin is replenished. that is. when the svstem Is continuous vodriven. e by time-dependent boundary COLKitions.," A permanent energy-flow is induced when energy loss due to dissipation is replenished, that is, when the system is continuously driven, e.g., by time-dependent boundary conditions."603 Sucji wvstenis nav develop persistent loue-range correlatious., Such systems may develop persistent long-range correlations.604 Astroplivsical examples for this are. the erowtl of structures im cosmological simulations. or the longteqinpersistence of filamentary structures in shearme fkwv (Toomre IWalnajs 1991: IHuber Pfeunieer 2001 an Wisdom Tremaine 1988: Salo 1995:," Astrophysical examples for this are, the growth of structures in cosmological simulations, or the longtermpersistence of filamentary structures in shearing flows (Toomre Kalnajs \cite{Toomre91}; ; Huber Pfenniger \cite{Huber01a}; ; Wisdom Tremaine \cite{Wisdom88}; ; Salo \cite{Salo95}; ;"605convergence. for the dillerent source redshifts.,"convergence, for the different source redshifts."606 For a given angular scale. this product was found. to be almost independent of redshift for an Einstein-cle Sitter universe by Dernardeau ct al. (," For a given angular scale, this product was found to be almost independent of redshift for an Einstein-de Sitter universe by Bernardeau et al. ("607L997) and. we find a similar behaviour in the LCDAM cosmology here. particularly at high redshift.,"1997) and we find a similar behaviour in the LCDM cosmology here, particularly at high redshift."608 Because of the independence from redshif rere is no need o adjust this statistic when making comparisons amongst cilferent surveys. ACvided the median redshifts are not too small.," Because of the independence from redshift, there is no need to adjust this statistic when making comparisons amongst different surveys, provided the median redshifts are not too small."609 This act makes this salistic paricuarly useful for he discrimination o| cosmologies., This fact makes this statistic particularly useful for the discrimination of cosmologies.610" Our results for S30; al ow redshift are supported. by combining tje shear variance. oZE—ἐς(8.2.5zmoF. with he expressicn Lor:(0,τς) given by equation (23))."," Our results for $S_3 \sigma^2_\kappa$ at low redshift are supported by combining the shear variance, $\sigma^2_\gamma \equiv611\langle \gamma^2(\theta, z_s)\rangle \approx \sigma^2_\kappa$, with the expression for $S_3(\theta, z_s)$ given by equation \ref{S3approx}) )."612 Barber (2002) has sdown thial for⋅ source redshifts- ονPED1.6 and angular scales ofy 32y 0. so that the combination+. predicts the very slowly rising function of redshift for nLo« loand 250<8S10. which are the ranges of applicability common to both results.," Barber (2002) has shown that for source redshifts $z_s \leq 1.6$ and angular scales of $2'.0 \leq613\theta \leq 32'.0$ , so that the combination predicts the very slowly rising function of redshift for $z_s < 1$ and $2'.0 \leq \theta \leq 8'.0$, which are the ranges of applicability common to both results."614 We have shown that the convergence power spectrum values computed directly from the weak lensing simulations show remarkably σους agreement with the non-linear predictions [or the convergence power based on the Smith et al., We have shown that the convergence power spectrum values computed directly from the weak lensing simulations show remarkably good agreement with the non-linear predictions for the convergence power based on the Smith et al.615their light curves (Ligeza Sehwarzenbere-Czerny 2000).,their light curves (Ligeza Schwarzenberg-Czerny 2000).616 In our opinion the presence of such an cllect might indicate that some hidden factor (dilferent. from. the period. and shape of the light curve) significantly inlluences the average magnitudes of RRab stars (see point iv in Sect. 2?)), In our opinion the presence of such an effect might indicate that some hidden factor (different from the period and shape of the light curve) significantly influences the average magnitudes of RRab stars (see point iv in Sect. \ref{s311}) ).617 Yo verify the usefulness of the formula FG we decided ο determine the distance moculus of the LAIC., To verify the usefulness of the formula F6 we decided to determine the distance modulus of the LMC.618 To clo this we required high quality photometrv of RRO Lye variables rom the LMC., To do this we required high quality photometry of RR Lyr variables from the LMC.619 The first SOULCO We verified was the Whotometrv of RR. Lyre variabes in seven globular clusters Xaced in the LMC (Walker 19t2)., The first source we verified was the photometry of RR Lyr variables in seven globular clusters placed in the LMC (Walker 1992).620 Unfortunately. these light curves contained only about 3) points. which is insullicient o obtain valuable information about high. order Fourier coclicicnts.," Unfortunately, these light curves contained only about 30 points, which is insufficient to obtain valuable information about high order Fourier coefficients."621rely completely on asteroseismic models to choose between these two possibilities.,rely completely on asteroseismic models to choose between these two possibilities.622" We performed an analysis based on a modified form of the Petersen diagram (Petersen Jérgensen 1972)); i.e., we plotted the predicted radial period ratios against the shorter period and compared the resulting tracks with the observations."," We performed an analysis based on a modified form of the Petersen diagram (Petersen rgensen \cite{pet1972}) ); i.e., we plotted the predicted radial period ratios against the shorter period and compared the resulting tracks with the observations."623 The observational position in this diagram is different for the two hypotheses mentioned above., The observational position in this diagram is different for the two hypotheses mentioned above.624" In the case of Hypothesis 1, we presume that F1O (ie., the frequency with the highest amplitude) is a radial mode and compute its period ratios with the modes in group A. In the case of Hypothesis 2, the same is done for F12 (the dominant mode in group D) and the frequencies in group B. The theoretical period ratios for four models of different masses (1.5, 1.8, 2.2, and MM,) are given in Figure 6.."," In the case of Hypothesis 1, we presume that F10 (i.e., the frequency with the highest amplitude) is a radial mode and compute its period ratios with the modes in group A. In the case of Hypothesis 2, the same is done for F12 (the dominant mode in group D) and the frequencies in group B. The theoretical period ratios for four models of different masses (1.5, 1.8, 2.2, and $_\odot$ ) are given in Figure \ref{fig:petersenmass}."625 The empty circles denote the observational position following Hypothesis 1 and the filled circles correspond to Hypothesis 2., The empty circles denote the observational position following Hypothesis 1 and the filled circles correspond to Hypothesis 2.626 The results in Figure 6 confirm the very young evolutionary stage of HD 144277 near the ZAMS., The results in Figure \ref{fig:petersenmass} confirm the very young evolutionary stage of HD 144277 near the ZAMS.627 Within the given mass range the points derived with Hypothesis 2 are in better agreement with the models and indicate that we observe the sixth and seventh radial overtones., Within the given mass range the points derived with Hypothesis 2 are in better agreement with the models and indicate that we observe the sixth and seventh radial overtones.628" Hypothesis 1 leads to a period ratio that is in-between the predicted values, which means that the period ratio is not fitted simultaneously with the observed frequencies."," Hypothesis 1 leads to a period ratio that is in-between the predicted values, which means that the period ratio is not fitted simultaneously with the observed frequencies."629" Naturally the significance of this result needs to be checked, so, we examined the effect of changing various model parameters to study their influence on period ratios at high radial orders."," Naturally the significance of this result needs to be checked, so, we examined the effect of changing various model parameters to study their influence on period ratios at high radial orders."630" In particular we varied the mass fraction of metal from the solar value 00.0134 to 0.010 and 0.020 respectively, changed the hydrogen mass fraction, X, from the solar value 0.74 to 0.70 and 0.78, varied the equatorial rotation velocity from 0 to kkms! (based on a second-order perturbation approach and neglecting near-degeneracy effects), and also examined the effect of OPAL vs. OP opacities (Seaton 2005))."," In particular we varied the mass fraction of metal from the solar value 0.0134 to 0.010 and 0.020 respectively, changed the hydrogen mass fraction, X, from the solar value 0.74 to 0.70 and 0.78, varied the equatorial rotation velocity from 0 to $^{-1}$ (based on a second-order perturbation approach and neglecting near-degeneracy effects), and also examined the effect of OPAL vs. OP opacities (Seaton \cite{seaton05}) )."631 The corresponding models are shown in Figure 7 in comparison with a standard 1.8 Mo model., The corresponding models are shown in Figure \ref{fig:petersen} in comparison with a standard 1.8 $_{\odot}$ model.632" At high radial orders, the effect of these parameter changes on the period ratio is very small close to the ZAMS, and Hypothesis 2 is"," At high radial orders, the effect of these parameter changes on the period ratio is very small close to the ZAMS, and Hypothesis 2 is"633attempt. the wind speed must be less thau |2 ifs. When Bolt ran in Beijing. there was no measurable wiud speed at all. aud one cau therefore safely assume that the world record could have been further decreased. perhaps by as much as 0.1 seconds. under more favorable wiud conditions.,"attempt, the wind speed must be less than +2 m/s. When Bolt ran in Beijing, there was no measurable wind speed at all, and one can therefore safely assume that the world record could have been further decreased, perhaps by as much as 0.1 seconds, under more favorable wind conditions."634 A corollary of this study is that a new world record of less than 9.5 seconds is within reach for Usain Bolt in the near future., A corollary of this study is that a new world record of less than 9.5 seconds is within reach for Usain Bolt in the near future.635The amplitude of cach Fourier componcut is given by where p and 0 are polar coordinates. {εαν0) is the intensity at position (Inik.0). a represents the uuuber of arnis or nodes. aud pis the variable associated with the pitch angle P. defined by tanPτρ).,"The amplitude of each Fourier component is given by where $r$ and $\theta$ are polar coordinates, $I(\ln{r},\theta)$ is the intensity at position $(\ln{r},\theta)$, $m$ represents the number of arms or modes, and $p$ is the variable associated with the pitch angle $P$, defined by $\tan{P}=-(m/p)$."636 Throughout this work we measure the pitch anele P of the m=2 component., Throughout this work we measure the pitch angle $P$ of the $m=2$ component.637 The resulting pitch angle measured usine equation 2 is in radians. and this is later converted to degrees for case of perception.," The resulting pitch angle measured using equation \ref{fft} is in radians, and this is later converted to degrees for ease of perception."638 The range of radi over which the Fourier fits were applied were selected to exclude the bulge or bar (where there is no information about the arius) aud to exteud out to the outer lanits of the arms iu our nuages. m such a way that the LO kpe radius fell approximately in the middle of this range.," The range of radii over which the Fourier fits were applied were selected to exclude the bulge or bar (where there is no information about the arms) and to extend out to the outer limits of the arms in our images, in such a way that the 10 kpc radius fell approximately in the middle of this range."639 The radial exteut of the bar was incasured manually (see GGrosbol. Patsis Pompei 2001). and the inner radial limit applied to the FFT was chosen to be outside this radius.," The radial extent of the bar was measured manually (see Grosbol, Patsis Pompei 2004), and the inner radial limit applied to the FFT was chosen to be outside this radius."640 Physical distances are calculated using a IIubble coustaut 77)=75 hans + + aud recessional velocities from the NASA Extragalactic Database (NED)., Physical distances are calculated using a Hubble constant $H_{0}=75$ km $^{-1}$ $^{-1}$ and recessional velocities from the NASA Extragalactic Database (NED).641 Pitch augles are then deteriuued from peaks in the Fourier spectra. as this is the most powerful method to find periodicity in a distribution (Cousiderre Athanassoula 1988: Carcia-Gomez Athanassoula 1993).," Pitch angles are then determined from peaks in the Fourier spectra, as this is the most powerful method to find periodicity in a distribution (Considèrre Athanassoula 1988; Garcia-Gomez Athanassoula 1993)."642 The radial ranee over which the Fourier analysis was performed was chosen by eve aud is probably the dominant source of error in the calculation of pitch angles. as spiral arms are ouly approximately logarithiuic and sometimes abrupst changes can be seen in spiral aria pitch angles SSeiear James 10050) As a result. three radial ranges were chosen for each galaxy. aud a iiean pitch angle aud standard error calculated for every object.," The radial range over which the Fourier analysis was performed was chosen by eye and is probably the dominant source of error in the calculation of pitch angles, as spiral arms are only approximately logarithmic and sometimes abrupst changes can be seen in spiral arm pitch angles Seigar James 1998b) As a result, three radial ranges were chosen for each galaxy, and a mean pitch angle and standard error calculated for every object."643 The tages were first projected το face-on., The images were first projected to face-on.644 Alcan uucertaimtics of position angle aud inclination as a function of inclination were discussed by Cousiderre Athanassoula (1988)., Mean uncertainties of position angle and inclination as a function of inclination were discussed by Considèrre Athanassoula (1988).645 For a galaxy with low inclination. there are clearly ercater uncertainties in assigniug both a position angle aud aaccurate inclination.," For a galaxy with low inclination, there are clearly greater uncertainties in assigning both a position angle and accurate inclination."646 These uucertainties are discussed by Block et ((1999cD and Seigar ct 2005). who take a ealaxy wi low inclination (<<30°) and one with high iuclinatk (2607) and varied the inclination augle used in the correction to face-on.," These uncertainties are discussed by Block et (1999) and Seigar et (2005), who take a galaxy with low inclination $<30^{\circ}$ ) and one with high inclination $>60^{\circ}$ ) and varied the inclination angle used in the correction to face-on."647 They fouud that for the galaxy witli low inclination. the measured pitch angle remained the sale.," They found that for the galaxy with low inclination, the measured pitch angle remained the same."648 Towever. the measured pitch angle for the ealaxy with lich inclination varied by 10%..," However, the measured pitch angle for the galaxy with high inclination varied by $\pm 10$ ."649. Since inclinati- corrections are likely to be largest for ealaxies with tme hniehest inclinations cases where inclination is 76 are taken as the worst case scenario., Since inclination corrections are likely to be largest for galaxies with the highest inclinations cases where inclination is $>60^{\circ}$ are taken as the worst case scenario.650 For galaxies witli Πιοποια /2607 we take uto account this uncertainty., For galaxies with inclination $i>60^{\circ}$ we take into account this uncertainty.651 Our ιαdeprojection method assumes that spiral ealaxy disks are dutrinsically cireular aud flat iu nature., Our deprojection method assumes that spiral galaxy disks are intrinsically circular and flat in nature.652 31 of the galaxies observed here have Ta rotation curve data measured by Alathewsou et ((1992) and Persic Salucci (1995)., 31 of the galaxies observed here have $\alpha$ rotation curve data measured by Mathewson et (1992) and Persic Salucci (1995).653 These rotation curves are of good quality with an ris error <LO kan +. and an error associated with folding the two sides of the galaxy also <10 kin 1.," These rotation curves are of good quality with an rms error $<10$ km $^{-1}$, and an error associated with folding the two sides of the galaxy also $<10$ km $^{-1}$."654 These rotation curves have been used to estimate the shear rates iu these galaxies. using the same method used by other authors (e.g. Block et 11999: Seigar ot 22005: Seigar 2005).," These rotation curves have been used to estimate the shear rates in these galaxies, using the same method used by other authors (e.g. Block et 1999; Seigar et 2005; Seigar 2005)."655 Using equation 1. we have calculated the shear rates or these galaxies. over the same radial rauges for which he Fourier analysis was performed and pitch angles calculated.," Using equation \ref{shearrate}, we have calculated the shear rates for these galaxies, over the same radial ranges for which the Fourier analysis was performed and pitch angles calculated."656 We lave selected several cdiffereut radial ranges. just as in the Fourier analysis. aud we preseut uean shear rates and standard errors.," We have selected several different radial ranges, just as in the Fourier analysis, and we present mean shear rates and standard errors."657 The cominant sources of error on the shear rate are the rius error in 1e rotation curve and the error associated with folding je two sides of the galaxy., The dominant sources of error on the shear rate are the rms error in the rotation curve and the error associated with folding the two sides of the galaxy.658 This is typically <LOW, This is typically $<10$.659 Iu order to calculate the shear rate. the mean value of =xV/dR ineasured in kins | tis calculated by chtting a line of coustant eracdicnt to the outer part of ie rotation curve (ie. past the radius of turnover aud any bar or bulec that may exist iu the galaxy).," In order to calculate the shear rate, the mean value of $dV/dR$ measured in km $^{-1}$ $^{-1}$ is calculated by fitting a line of constant gradient to the outer part of the rotation curve (i.e. past the radius of turnover and any bar or bulge that may exist in the galaxy)."660 Mean shear rates are then calculated from shear rates 1ieasured over three racial ranges. corresponding to the same radial ranges over whichthe Fourier analysis was performed.," Mean shear rates are then calculated from shear rates measured over three radial ranges, corresponding to the same radial ranges over whichthe Fourier analysis was performed."661 The resulting shear rates are listed in Table 3., The resulting shear rates are listed in Table 3.662"for each resonance: coverage, small-scale noise, and large- noise (Weinberg&Katz2007a).","for each resonance: coverage, small-scale noise, and large-scale noise \citep{WK07a}."663". According to this estimate, we require more than 10? satellite particles, which translates to more than 3x10? within the initial virial radius, to correctly reproduce the -1:2:2 resonance."," According to this estimate, we require more than $10^{5}$ satellite particles, which translates to more than $3\times 10^5$ within the initial virial radius, to correctly reproduce the -1:2:2 resonance."664 This resonance requires the largest number of particles and is also the most important resonance as we show below., This resonance requires the largest number of particles and is also the most important resonance as we show below.665" Hence, our 10° equal-mass particle halo simulation easily satisfies the necessary criteria (see Fig. 5))"," Hence, our $10^{6}$ equal-mass particle halo simulation easily satisfies the necessary criteria (see Fig. \ref{fig:Nreq_XT}) )"666 for all the important resonances., for all the important resonances.667 The small-scale noise criterion is not relevant for our expansion-code simulations., The small-scale noise criterion is not relevant for our expansion-code simulations.668" However, if the N-body simulations were to suffer from small-scale noise, such as the case in N-body simulations using direct-summation, trees, or meshes, an order of magnitude larger particle number would be required for these resonances to be modelled correctly."," However, if the N-body simulations were to suffer from small-scale noise, such as the case in N-body simulations using direct-summation, trees, or meshes, an order of magnitude larger particle number would be required for these resonances to be modelled correctly."669 Fig., Fig.670 6 shows the amount of angular momentum deposited by an orbiting perturber calculated using numerical perturbation theory for different resonances., \ref{fig:ResPot_XT} shows the amount of angular momentum deposited by an orbiting perturber calculated using numerical perturbation theory for different resonances.671 The most significant angular momentum change is mediated by the -1:2:2 resonance., The most significant angular momentum change is mediated by the -1:2:2 resonance.672" The -1:3:3 and 0:1:3 resonances are the strongest among the /3=3 resonances, and the 1:0:4 resonance is the strongest resonance among the |3=4 resonances."," The -1:3:3 and 0:1:3 resonances are the strongest among the $l_{3}=3$ resonances, and the 1:0:4 resonance is the strongest resonance among the $l_{3}=4$ resonances."673 The amount of angular momentum deposited by the -1:2:2 resonance is more than an order of magnitude larger than the amount of angular momentum deposited by any of the [3—3 resonances and three orders of magnitude larger than the amount of angular momentum deposited by any of the [3=4 resonances., The amount of angular momentum deposited by the -1:2:2 resonance is more than an order of magnitude larger than the amount of angular momentum deposited by any of the $l_{3}=3$ resonances and three orders of magnitude larger than the amount of angular momentum deposited by any of the $l_{3}=4$ resonances.674" Hence, the -1:2:2 resonance dominates the resonant satellite torque."," Hence, the -1:2:2 resonance dominates the resonant satellite torque."675 Fig., Fig.676" 7 shows the location of the angular momentum transferred through resonant interactions in phase space by plotting the distribution of the change in L, in phase space, AL,, at different times from both the N-body simulation and the numerical perturbation theory calculation."," \ref{fig:plotdk} shows the location of the angular momentum transferred through resonant interactions in phase space by plotting the distribution of the change in $L_{z}$ in phase space, $\Delta L_{z}$, at different times from both the N-body simulation and the numerical perturbation theory calculation."677" We normalise this change by the total angular momentum at each energy E since L(E) at fixed κ. increases with energy, which biases the absolute AL, distribution toward higher energies."," We normalise this change by the total angular momentum at each energy $E$ since $L(E)$ at fixed $\kappa$ increases with energy, which biases the absolute $\Delta L_{z}$ distribution toward higher energies."678" By normalising to the total angular momentum at a given energy bin, the AL, distribution enhances AL, features at low energy."," By normalising to the total angular momentum at a given energy bin, the $\Delta679L_{z}$ distribution enhances $\Delta L_{z}$ features at low energy."680" Each panel shows the relative AL, over a fixed time span.", Each panel shows the relative $\Delta L_{z}$ over a fixed time span.681 Both the phase space location and magnitude of the angular momentum change from the simulation agrees well with the numerical perturbation calculation., Both the phase space location and magnitude of the angular momentum change from the simulation agrees well with the numerical perturbation calculation.682 The perturbation theory only includes the resonant torque and therefore this agreement is strong evidence that torque by resonant interactions is the major mechanism responsible for circular orbit satellite evolution., The perturbation theory only includes the resonant torque and therefore this agreement is strong evidence that torque by resonant interactions is the major mechanism responsible for circular orbit satellite evolution.683" Nonetheless, some minor discrepancies remain."," Nonetheless, some minor discrepancies remain."684" First, the amplitude of the relative AL, from the perturbation calculation is larger than that from the simulation at T —0.0-1.0."," First, the amplitude of the relative $\Delta L_{z}$ from the perturbation calculation is larger than that from the simulation at $T=$ 0.0–1.0."685 This results from the abrupt introduction of the perturbation., This results from the abrupt introduction of the perturbation.686" In our calculations, we abruptly introduce the external potential (for the simulation) and perturbations by resonances (for the perturbation calculation) to the initial satellite."," In our calculations, we abruptly introduce the external potential (for the simulation) and perturbations by resonances (for the perturbation calculation) to the initial satellite."687" This abrupt introduction may induce a readjustment of satellite halo equilibrium and/or cause non-linear features, which could cause the discrepancy."," This abrupt introduction may induce a readjustment of satellite halo equilibrium and/or cause non-linear features, which could cause the discrepancy."688" Second, the shape of the region of angular momentum change is mildly different in the simulation compared to the perturbation calculation."," Second, the shape of the region of angular momentum change is mildly different in the simulation compared to the perturbation calculation."689" In particular, the simulation shows a relative AL, distribution in the lower right region of phase space, while the perturbation calculation does not."," In particular, the simulation shows a relative $\Delta L_{z}$ distribution in the lower right region of phase space, while the perturbation calculation does not."690" The phase space responsible for this difference in the AL, distribution has low binding energy and is easily stripped.", The phase space responsible for this difference in the $\Delta L_z$ distribution has low binding energy and is easily stripped.691 The simulation results in Fig., The simulation results in Fig.692" 7 shows the distribution of the relative AL, for only the unstripped particles.", \ref{fig:plotdk} shows the distribution of the relative $\Delta L_{z}$ for only the unstripped particles.693" Unlike in the simulations, the satellite in the perturbation calculation does not lose mass."," Unlike in the simulations, the satellite in the perturbation calculation does not lose mass."694" Hence, the few minor disagreements between the simulation and the perturbation theory are a natural consequence of the idealisation required to compute the perturbation theory and does not invalidate our primary conclusion: resonant torque is the major mechanism responsible for satellite disruption for a satellite on a circular orbit."," Hence, the few minor disagreements between the simulation and the perturbation theory are a natural consequence of the idealisation required to compute the perturbation theory and does not invalidate our primary conclusion: resonant torque is the major mechanism responsible for satellite disruption for a satellite on a circular orbit."695 The absence of a |=1 resonance contribution is, The absence of a $l=1$ resonance contribution is696"approximated bv a à-function. Ίος, κ=ουδey). where ey—65 Do:is the svuchrotron criticaleye energy.","approximated by a $\delta$ -function, i.e., $j_s(x)=j_0 \delta(x-\epsilon_0)$ , where $\epsilon_0=b\gamma^2$ is the synchrotron critical energy."697 In all cases we will assume a monoenergeetie τας injection at enerev e.., In all cases we will assume a monoenergetic $\gamma-$ ray injection at energy $\egamma$.698 First we will exeiuine the stability of the svstenài using the simplest form for the photou-photon anmililation cross section (2): ld ). where wee. are the energies of the soft and οταν photons. respectively.," First we will examine the stability of the system using the simplest form for the photon-photon annihilation cross section \citep{zdziarski85}: x ), where $x,\eg$ are the energies of the soft and $\gamma$ -ray photons, respectively."699" The particle injection aud loss operators tale the following forms: — = eA (Lesh.FV = X11) and Qio., =LAs... because cach photou-photon aunibhilatiou results in a pair of leptous. cach oue with approximately half of the initial οταν energx."," The particle injection and loss operators take the following forms: = = ) = = ^2 ) and = -4, because each photon-photon annihilation results in a pair of leptons, each one with approximately half of the initial $\gamma$ -ray energy."700 In the above equatious the magnuetic conrpactuess was mtroduced loth: The system of eq. (7))-(9)), In the above equations the `magnetic compactness' was introduced R The system of eq. \ref{gammaray}) \ref{elec}) )701" can now be written as 250] role) |OX 1344, (E , lu this section we will examine the stabilitv of the trivial stationary solution of the svstem (17)): which corresponds to the free propagation of οταν photons through the source.", can now be written as = ) + = -n_0(x) + n_e = )+ + ^2 ) In this section we will examine the stability of the trivial stationary solution of the system \ref{systemfull}) ): which corresponds to the free propagation of $\gamma$ -ray photons through the source.702 To investigate the stability of the svsteni. we assuue that initially arbitrarily siall perturbations of the soft photon aj and electron 5] densities are present. which lead to the perturbation of the ~-rav photon density »/.," To investigate the stability of the system, we assume that initially arbitrarily small perturbations of the soft photon $n_0'$ and electron $n_e'$ densities are present, which lead to the perturbation of the $\gamma$ -ray photon density $n'$ ."703" After lmearization. the svsteii (173) becomes The stability aualvsis of the svsteii above can be sinplified when one works with the Laplace transformed uuuber deusities: Πρωτ) ραs)= πο, with s being the solution to the eigenvalue problem: (s]I1) nte...s)— ο...) (cn For large r both the softphoton aud electron distributions beliave as €."," After linearization, the system \ref{systemfull}) ) becomes = ) = -n_0'+ n_e' = ^2 ) The stability analysis of the system above can be simplified when one works with the Laplace transformed number densities: ) n_0'(x,s)= , with $s$ being the solution to the eigenvalue problem: (s+1) ,s) = (s+1)n_0'(x,s) = ,s) s ,s) = + ^2 For large $\tau$ both the softphoton and electron distributions behave as $e^{s\tau}$."704 Ths=1. then i=n—0 and the x-ray photous freely escape from the source.," If $s=-1$, then $n_0'=n_e'=0$ and the $\gamma$ -ray photons freely escape from the source."705 If s>0. one finds solutions that erow with clapsing time.," If $s>0$, one finds solutions that grow with elapsing time."706" The imiaregimallv stable solution. which is obtaiue whe- one sets s= O0, will be examined below."," The marginally stable solution, which is obtained when one sets $s=0$ , will be examined below."707 Combining equatious (21))-(26)) leads to an ordinarydifferential equation for the perturbed clectrou distribution with the following solution: 2t (53) = , Combining equations \ref{hard}) \ref{electrons}) ) leads to an ordinarydifferential equation for the perturbed electron distribution with the following solution: ^2 ) = where $\gcr=\sqrt{\frac{2}{b\eg}}$ .708Setting, Setting $\gamma=\gcr$ in the above equation one finds )=C )^2709"this is G287.3716+00.6444, which is discussed in more detail in Section 4.3..","this is G287.3716+00.6444, which is discussed in more detail in Section \ref{g287}."710 We compare the predicted bandhead fluxes with the un-reddened observed fluxes as a consistency check., We compare the predicted bandhead fluxes with the un-reddened observed fluxes as a consistency check.711" As mentioned in Section 2.3,, these un-reddened fluxes are inevitably subject to considerable uncertainties, yet still serve as an important validity test."," As mentioned in Section \ref{ext_det}, these un-reddened fluxes are inevitably subject to considerable uncertainties, yet still serve as an important validity test."712 We list both model and source fluxes in Table 2.., We list both model and source fluxes in Table \ref{ext}.713" These are similar to within a factor of 23, and generally consistent within the uncertainty from the extinction estimate (neglecting the addition error due to uncertainties in the kinematic distances)."," These are similar to within a factor of 2–3, and generally consistent within the uncertainty from the extinction estimate (neglecting the addition error due to uncertainties in the kinematic distances)."714" Therefore, the observed and model fluxes are essentially consistent."," Therefore, the observed and model fluxes are essentially consistent."715 This provides a further confirmation that disc models provide a good fit to the data., This provides a further confirmation that disc models provide a good fit to the data.716 The spectroastrometric ⋅⋅signatures associated⋅ with⋅ the spectra presented in Fig., The spectroastrometric signatures associated with the spectra presented in Fig.717 2 are displayed in Fig. 3.., \ref{co_spec} are displayed in Fig. \ref{spec_ast_obs}.718 The spectroastrometric data have been re-binned by a factor of ~11 times the resolution element., The spectroastrometric data have been re-binned by a factor of $\mathrm{\sim}$ 11 times the resolution element.719 This rebinning factor was chosen as it was the maximum bin size that could still resolve the expected spectroastrometric signatures across the bandhead., This rebinning factor was chosen as it was the maximum bin size that could still resolve the expected spectroastrometric signatures across the bandhead.720 The resulting average positional precision is approximately 0.4 mas., The resulting average positional precision is approximately 0.4 mas.721" In principle, this means we are probing au size scales at the kpc distances of the sample."," In principle, this means we are probing au size scales at the kpc distances of the sample."722" Here, we compare the spectroastrometric data to the best-fitting models to determine whether these data can be used to further probe the circumstellar environments of the sample."," Here, we compare the spectroastrometric data to the best-fitting models to determine whether these data can be used to further probe the circumstellar environments of the sample."723 The spectroastrometric signatures associated with the, The spectroastrometric signatures associated with the724total line fix is repressed if the flare is located above the receding side of the disk.,total line flux is repressed if the flare is located above the receding side of the disk.725 This asviuimetric effect introduces a large scatter in the line flux and EW. especially for observers with laree inclination angles auc flares with large bulk velocities.," This asymmetric effect introduces a large scatter in the line flux and EW, especially for observers with large inclination angles and flares with large bulk velocities."726 For out-flowine flares. the direct flux is significantly affected by the angle between the flare bulk velocity vector aud the line of sight.," For out-flowing flares, the direct flux is significantly affected by the angle between the flare bulk velocity vector and the line of sight."727 The direct flux is significantly chhanced for a flare moving towards the observer. ic. located above the part of the disk facing the observer.," The direct flux is significantly enhanced for a flare moving towards the observer, i.e. located above the part of the disk facing the observer."728 The most intriguing cases have flares with invard/outwird bulls iotious (e.g. Fig. 8)), The most intriguing cases have flares with inward/outward bulk motions (e.g. Fig. \ref{fig:offaxisrew70}) )729 in whichME., in which.730 Tt can be clearly seen in Figures 5 8 that a coustaut line flux can arise only for fares with low height above the disk aud outward/mward (along the radius) bulk velocity., It can be clearly seen in Figures \ref{fig:offaxiszew} — \ref{fig:offaxisrew70} that a constant line flux can arise only for flares with low height above the disk and outward/inward (along the radius) bulk velocity.731 This requirement is possibly satisfied in realistic cases since it has been argued that the height of huuinous maenetic flares caunot be much mere than a few times the pressure height above a thin accretion disk (Navakshin&INazanas2001)., This requirement is possibly satisfied in realistic cases since it has been argued that the height of luminous magnetic flares cannot be much more than a few times the pressure height above a thin accretion disk \citep[]{nk01}.732. If oulv the effects of the bulk motion of flares on the profile aud EW of the line are considered. a lusor EW is found to be correlated with a more exteuded red wing of the line (see Figs.," If only the effects of the bulk motion of flares on the profile and EW of the line are considered, a larger EW is found to be correlated with a more extended red wing of the line (see Figs."733 1. and 2))., \ref{fig:onaxisprof} and \ref{fig:onaxisew}) ).734 This teudeucy is roughly consistent with observations: the larger the line EW. the more extended the red wine (e.g.Lubinski&Zdziarski2001.intheparametersobtainedfromLuemodeling.alargerIsacconrpaniedbyasmallerimmer radius).," This tendency is roughly consistent with observations: the larger the line EW, the more extended the red wing \citep[e.g.][in the735parameters obtained from the line modeling, a larger EW is 736accompanied by a smaller inner radius]{lz01}."737 Therefore. bulk motion iu the corona can be introduced as a xossible mechanism for producing the “narrowness” of the lie seen in some Sevfert 1 galaxies (see low): this is in additiouüLc to the ecuecrally introduced paramcter of the truucation radius of the cold disk the cold disk is truucated at a larger radius rather than the radius at the marginal stable orbit due to he transition of the oeimmer disk to a hot ecometrically thick aud. optically thin accretion flow or the high ionization of the disk material within this radius (Lubiünski&Zdziarski2001.audrefereuces thercin)||.," Therefore, bulk motion in the corona can be introduced as a possible mechanism for producing the `narrowness' of the line seen in some Seyfert 1 galaxies (see below); this is in addition to the generally introduced parameter of the truncation radius of the cold disk [the cold disk is truncated at a larger radius rather than the radius at the marginal stable orbit due to the transition of the inner disk to a hot geometrically thick and optically thin accretion flow or the high ionization of the disk material within this radius \citep[and references therein]{lz01}] ]."738 It las been suggested that outflow/inflow m the corona provides a possible explanation for the RoD relation (Beloborodoy1909j., It has been suggested that outflow/inflow in the corona provides a possible explanation for the $R-\Gamma$ relation \citep[]{bel99b}.739 With the caleulatiou in 3.1.1.. this out-flowing magnetic flares model is expected ο consistently account for the narrowness’ of the line profile. the variation of the EW. and the RV τοαο in some Sevtert 1 galaxies (Beloborodoy1999h:Zdziarski.&Zdziarski 2001).," With the calculation in \ref{sec:reson_line}, this out-flowing magnetic flares model is expected to consistently account for the `narrowness' of the line profile, the variation of the EW, and the $R-\Gamma$ relation in some Seyfert 1 galaxies \citep[]{bel99b,zls99,lz01}."740 Note that the “narrowness” ofthe line also cepends on the location of the flare as secu in Fig. 1.., Note that the “narrowness” of the line also depends on the location of the flare as seen in Fig. \ref{fig:onaxisprof}.741 The model of a poiut source of X-ray cussion along the rotation axis of the accretion disk is ouly an approximation to an accretion disk corona., The model of a point source of X-ray emission along the rotation axis of the accretion disk is only an approximation to an accretion disk corona.742 Perhaps. a standard corona with upward/cdowmuward (or imward/outward) bulk motion is better approximated bv a ring as shown in top (bottom) Fie. L.," Perhaps, a standard corona with upward/downward (or inward/outward) bulk motion is better approximated by a ring as shown in top (bottom) Fig. \ref{fig:offaxisprof}."743 Even with bulk velocity of 0.5 the line appears relatively broad with a red-wine extending down below 5 keV if the ring ds located at a small radius. e.g.B. GAL (see Fig.," Even with bulk velocity of 0.5 the line appears relatively broad with a red-wing extending down below 5 keV if the ring is located at a small radius, e.g. $6M$ (see Fig."744 Lo left panels)., \ref{fig:offaxisprof} left panels).745 Were. one important question is: can au," Here, one important question is: can an"746(seo relsee:xir below).,(see \\ref{sec:xir} below).747 Table 2. shows the breakdown of our AGN sample into NED classification and redshift., Table \ref{tab:z} shows the breakdown of our AGN sample into NED classification and redshift.748 AGN classification and our exclusion of AGN with prominent jets is discussed in more detail in re[sec:xir below., AGN classification and our exclusion of AGN with prominent jets is discussed in more detail in \\ref{sec:xir} below.749 As far as AGN redshift is concerned. most (~ SB) of the AGN in our sample are at low redshift 0.1). so the 12jum. Ht flux and. 2-10. keV band. X-ray flux does not include large amounts of Dux redshifted from higher energies.," As far as AGN redshift is concerned, most $\sim 85\%$ ) of the AGN in our sample are at low redshift $z<0.1$ ), so the $\micron$ IR flux and 2-10 keV band X-ray flux does not include large amounts of flux redshifted from higher energies."750 Llowever. for a small fraction ( 15%) of the higher luminosity AGN. the observed. 1240 and 2-10 keV. [luxes may correspond to fluxes in the ACN frame of ~ο12tun and ~2) 15keV respectively.," However, for a small fraction $\sim 15 \%$ ) of the higher luminosity AGN, the observed $\micron$ and 2-10 keV fluxes may correspond to fluxes in the AGN frame of $\sim 6-12751\micron$ and $\sim 2-15$ keV respectively."752" Generally in these AGN. high energy X-ray Ες falls olf faster than the near HX Dux. so in the small fraction of very distant luminous AGN we expect Rie, tobe slightly larger than the nearby group 1 AGN (see also Fig."," Generally in these AGN, high energy X-ray flux falls off faster than the near IR flux, so in the small fraction of very distant luminous AGN we expect $R_{ir/x}$ to be slightly larger than the nearby group 1 AGN (see also Fig."753 Ll and related discussion below)., \ref{fig:deep} and related discussion below).754 In this paper. we discuss luminosity ratios.," In this paper, we discuss luminosity ratios."755" Phe Ht flux is measured in Jv (=3.0..10H ere Cnbp“s+5 at LOOpun ancl 2.5.107"" erg em7s at 12j) and the X-ray [lux is measured in. units. of LO|il ere ems c. ⊐⊥⊳"," The IR flux is measured in Jy $3.0\times10^{-11}$ erg $\rm{cm}^{-2} \rm{s}^{-1}$ at $\micron$ and $2.5\times10^{-10}$ erg $\rm{cm}^{-2} \rm{s}^{-1}$ at $\micron$ ) and the X-ray flux is measured in units of $10^{-11}$ erg $\rm{cm}^{-2} 756\rm{s}^{-1}$ ."757∖The luminosity. (and (lux) ratios described hereafter are unitless., The luminosity (and flux) ratios described hereafter are unitless.758" In this section we will start. by presenting our entire AGN sample in 2;,., space using observed 2-LOkeW X-rav and LRAS-band LR measurements.", In this section we will start by presenting our entire AGN sample in $R_{ir/x}$ space using observed 2-10keV X-ray and IRAS-band IR measurements.759" We shall then use AGN classifications to begin. constraining the clispersions of dilferent AGN types in /25,;,.", We shall then use AGN classifications to begin constraining the dispersions of different AGN types in $R_{ir/x}$ .760 We shall also introduce well-known. ACN Ἱνρισα of their. classification {ο aid interpretation of the ΑΝ. distribution., We shall also introduce well-known AGN 'typical' of their classification to aid interpretation of the AGN distribution.761" We shall. then compare the distribution of AGN in £2;,;, using [ar-I]t (100pum) and. mid-LHt (1210) observed. Luminosity.", We shall then compare the distribution of AGN in $R_{ir/x}$ using far-IR $\micron$ ) and mid-IR $\micron$ ) observed luminosity.762 Figure 1. shows the observed 2-10ke X-ray flux plotted against the μα mic-LR flux. for 240/245V. AGN in our sample (5 AGN had. 12 tun upper limits only)., Figure \ref{fig:fir12fx} shows the observed 2-10keV X-ray flux plotted against the $\micron$ mid-IR flux for 240/245 AGN in our sample (5 AGN had 12 $\micron$ upper limits only).763 Lines of constant [lux ratio are plotted (Fir/Ex-1.10.100) to guide the eve.," Lines of constant flux ratio are plotted (Fir/Fx=1,10,100) to guide the eye."764 Lowe express the flux ratios from Figure 1. in erms of luminosity ratios. the remain constant. but he AGN separate by a factor proportional to the distance scuared.," If we express the flux ratios from Figure \ref{fig:fir12fx} in terms of luminosity ratios, the remain constant, but the AGN separate by a factor proportional to the distance squared."765 Since jets will complicate our interpretation of he central engine. we excluded. 20. AGN with NED classifications that include. prominent jets (c.g. BL Lac. Blazar. LPQ. BLRG).," Since jets will complicate our interpretation of the central engine, we excluded 20 AGN with NED classifications that include prominent jets (e.g. BL Lac, Blazar, LPQ, BLRG)."766 Figure 2 shows the mean harcl X-ray 2-10keV. luminosity plottec against the mean mic-LhR 121 uminosity for 215/245 of the AGN in our sample., Figure \ref{fig:nojets} shows the mean hard X-ray 2-10keV luminosity plotted against the mean mid-IR $\micron$ luminosity for 215/245 of the AGN in our sample.767 Lines of constant luminosity ratio (11 —1.10.100) are indicated o guide the eve.," Lines of constant luminosity ratio $R_{ir/x}$ =1,10,100) are indicated to guide the eye."768 From Fig. 2..," From Fig. \ref{fig:nojets},"769" the more luminous ACGN seem to emerge at by.Lir;~1tj13 cress1 and. mostly ic in à band around ;,;,~>1.30]."," the more luminous AGN seem to emerge at $L_{x}, L{ir} \sim 10^{42-43}$ ergs $\rm{s}^{-1}$ and mostly lie in a band around $R_{ir/x} \sim [1,30]$."770 Lower luminosity AGN appear to span a much wider range of observed Iuminosities. suggestive of both highly absorbed X-ray Luminosity and/or a noisy host galaxy background in HX or X-ravs.," Lower luminosity AGN appear to span a much wider range of observed luminosities, suggestive of both highly absorbed X-ray luminosity and/or a 'noisy' host galaxy background in IR or X-rays."771 The AGN in Fig., The AGN in Fig.772 2 span {ον space in a manner broadly similar to studies carried out using soft. N-ravs (Cireen.Anderson&Ward.1992:Bolleretal. 1992).," \ref{fig:nojets} span $R_{ir/x}$ space in a manner broadly similar to studies carried out using soft X-rays \citep{b62,b69}."773. Although we excluded AGN with prominent jets. the remaining ACN may well contain weak jets. but they are not prominent enough to ellect AGN classification.," Although we excluded AGN with prominent jets, the remaining AGN may well contain weak jets, but they are not prominent enough to effect AGN classification."774" ACGIN with prominent jets accounted for more than half the AGN with L,23.107 cress1C. so ifτρ present and. prominent.. jets account for a significant proportion of X-ray Iuminositv."," AGN with prominent jets accounted for more than half the AGN with $L_{x}>3 \times 10^{43}$ ergs $\rm{s}^{-1}$, so if present and prominent, jets account for a significant proportion of X-ray luminosity."775 From Fig. 2..," From Fig. \ref{fig:nojets},"776" there are only 3/225 AGN with fy,<1. sugeesting either that £2).« Lis atwpical for AGN or that there isa bias against AGNwith 5,5,«Lin our sample."," there are only 3/225 AGN with $R_{ir/x}<1$, suggesting either that $R_{ir/x}<1$ is atypical for AGN or that there is a bias against AGNwith $R_{ir/x}<1$in our sample."777 It is noteworthy that the 3/215 AGN with νο« lin Fig., It is noteworthy that the 3/215 AGN with $R_{ir/x}<1$ in Fig.778 2 have weak associated jets., \ref{fig:nojets} have weak associated jets.779 They are. in order of increasing X-ray [uminositv: Cen A. PO. 1416-129 and PC 0056|129 respectively," They are, in order of increasing X-ray luminosity: Cen A, PG 1416-129 and PG 0026+129 respectively"780we have a litlle more than one disk per unit area.,we have a little more than one disk per unit area.781 Because of overlap. αἱ (his point only of space is covered by disks. remain empty.," Because of overlap, at this point only of space is covered by disks, remain empty."782" We therefore emphasize that 7, is only the average overall densitv for (he onset of percolation.", We therefore emphasize that $n_p$ is only the average overall density for the onset of percolation.783" The density in the largest and hence percolating cluster at this point must evidently be larger than 1,,/0.6871.66/777: it is in fact Iound to be nhcL12/sr7. [46]..", The density in the largest and hence percolating cluster at this point must evidently be larger than $n_p/0.68 \simeq 1.66/\pi r^2$; it is in fact found to be $n_p^{\rm cl} \simeq 1.72/\pi r^2$ \cite{DFS}.784 In three dimensions. the corresponding problem is one of overlapping spheres in a large volume.," In three dimensions, the corresponding problem is one of overlapping spheres in a large volume."785" Here the critical density for the percolating spheres becomes n»,70.34/[(4/3)07]. wilh r denoting the radius of the little spheres now taking the place of (he small disks we had in (wo dimensions."," Here the critical density for the percolating spheres becomes $n_p \simeq 0.34/[(4\pi/3)r^3]$, with $r$ denoting the radius of the little spheres now taking the place of the small disks we had in two dimensions."786 At the critical point in three dimensions. however. only of space is covered by overlapping spheres. while remains empty. and here both spheres and empty space form infinite connected networks.," At the critical point in three dimensions, however, only of space is covered by overlapping spheres, while remains empty, and here both spheres and empty space form infinite connected networks."787" The density ni of the largest connected cluster al (his point in overall density is (hus much larger than 0.34/V5: in fact. it must exceed 1.τι, "," The density $n_p^{\rm cl}$ of the largest connected cluster at this point in overall density is thus much larger than $0.34/V_0$; in fact, it must exceed $1.17 /V_0$ ."788"Let us then consider hadrons of intrinsic size V,=(4x/3)r7. with rj20.8 fm."," Let us then consider hadrons of intrinsic size $V_h=(4\pi/3)r_h^3$, with $r_h \simeq 0.8$ fm."789 In space. the formation of a connected large-scale cluster [ist occurs at the overall average density ne= 0.16(," In three-dimensional space, the formation of a connected large-scale cluster first occurs at the overall average density n_c= 0.16."79023) This point cli the onset of large-scale connected strongly interacting matter. in contrast to a gas of hadrons.," This point specifies the onset of large-scale connected strongly interacting matter, in contrast to a gas of hadrons."791 However. as we saw. the densitv of the largest matter clusters is much hieher (han the average value given by ((3)). ancl assuming all non-empty space to form one cluster. we obtain ΠριIyvo-dimensionalc12/V50.55fm as (lower bound for the) critical density.," However, as we saw, the density of the largest matter clusters is much higher than the average value given by \ref{hadronmatter}) ), and assuming all non-empty space to form one cluster, we obtain $n_{\rm cl}\simeq 1.2/V_h \simeq 0.55~{\rm fm}^{-3}$ as (lower bound for the) critical density."792 pacedon results Lor case. we expect the threshold densitv 24 to be about (1.5- knowhidron:~(0.7ueud9)Bn.7.," Based on results for the two-dimensional case, we expect the threshold density $n_{\rm cl}$ to be about (1.5 - $V_h \simeq (0.7 - 0.9)~{\rm fm}^{-3}$."793 HE we assume (hat at (his point. the cluster is of an ideal gas ol all n hacronic resonances. then we can calculate the temperature of the eas al (he density nq: n(1=T.)n4 implies 7;110—190 MeV. which agrees quite well with the value of the ceconfinement temperature found in lattice QCD [for ji=0.," If we assume that at this point, the cluster is of an ideal gas of all known hadrons and hadronic resonances, then we can calculate the temperature of the gas at the density $n_{\rm cl}$: $n_{\rm res}(T=T_c) = n_{\rm cl}$ implies $T_c \simeq 170 - 190$ MeV, which agrees quite well with the value of the deconfinement temperature found in lattice QCD for $\mu=0$."794 Cluster formation and percolation theory. thus provide a possible tool to specify the deconfinement transition in strongly interacting matter., Cluster formation and percolation theory thus provide a possible tool to specify the deconfinement transition in strongly interacting matter.795 such considerations may in [act well be of a more general nature (han the problem of states and transitions in strong interaction physics., Such considerations may in fact well be of a more general nature than the problem of states and transitions in strong interaction physics.796 The question of whether svimnmietry or connectivity (cluster formation) determines the dillerent states of many-body systems has intrigued theorists in statistical physics for a long time [47].., The question of whether symmetry or connectivity (cluster formation) determines the different states of many-body systems has intrigued theorists in statistical physics for a long time \cite{F-K}.797 The lesson learned from spin svstenis appears to be that cluster formation and the associated critical behavior are the more general features. which under certain conditions can also lead to (thermal criticalitvy. ie. singular behavior of the partition function.," The lesson learned from spin systems appears to be that cluster formation and the associated critical behavior are the more general features, which under certain conditions can also lead to thermal criticality, i.e., singular behavior of the partition function."798 Next we tum to (he more general phase structure as function of 7' and µ. as illustrated! in relphase-d..," Next we turn to the more general phase structure as function of $T$ and $\mu$, as illustrated in \\ref{phase-d}."799 What conceptual aspects of hadronic interactions could lead to such behavior. and in particular. what features in hacdronie dynamics result in (he observed changes of the transition structure as function of barvon densitv?," What conceptual aspects of hadronic interactions could lead to such behavior, and in particular, what features in hadronic dynamics result in the observed changes of the transition structure as function of baryon density?"800 At low barvon densitv. the constituents of hadronic matter are mostly mesons. and the dominant interaction is resonance formation: will increasing temperature. different resonance species of increasing mass are formed. leading to a gas of ever increasing degrees ofIreedom.," At low baryon density, the constituents of hadronic matter are mostly mesons, and the dominant interaction is resonance formation; with increasing temperature, different resonance species of increasing mass are formed, leading to a gas of ever increasing degrees offreedom."801" Thev are all of a typical hadronic size (with a radius A,~1 fm) and can overlap or", They are all of a typical hadronic size (with a radius $R_h \simeq 1$ fm) and can overlap or802Variability iu radio sources can be due to either iutrimsic varatious in the source itself. or due to a propagation effect known as scintillation.,"Variability in radio sources can be due to either intrinsic variations in the source itself, or due to a propagation effect known as scintillation."803 Diseutaugling these two effects ds critical to our understaudiug of the central regions of quasars aud radio galaxies. as i both cases the variability eives dimensions of the cutting region. but the interpretation (and the implied size) are quite different.," Disentangling these two effects is critical to our understanding of the central regions of quasars and radio galaxies, as in both cases the variability gives dimensions of the emitting region, but the interpretation (and the implied size) are quite different."804 Tutrvinsically variable extragalactic radio sources include blazars. which exhibit chanecs in flux deusity of up to an order of magnitude or more occurrins over decades (Alleretal.1985). and sinaller outbursts o- shorter timescales (e.g.Polletal.1996:Stevensct 1995).," Intrinsically variable extragalactic radio sources include blazars, which exhibit changes in flux density of up to an order of magnitude or more occurring over decades \citep{all85}, and smaller outbursts on shorter timescales \cite[e.g.][]{poh96,ste95}."805. Dutradav variability is a phenomenon at CIIz frequencies with typically a few percent variations on day timescales (c.g.Ieeschenetal.1987:Quirrenbachct 20003.," Intraday variability is a phenomenon at GHz frequencies with typically a few percent variations on day timescales \cite[e.g.][]{hee87,qui00}."806. Au intrinsic explanation requires the sources to have brightness temperatures far in excess of 10111 up to lo107? K. Scintillation occurs due to changes in clectrou density in the intervening material., An intrinsic explanation requires the sources to have brightness temperatures far in excess of $^{12}$ K – up to $10^{17}-10^{19}$ K. Scintillation occurs due to changes in electron density in the intervening material.807 Iuterplauetary scintillation is caused by the solar wiud., Interplanetary scintillation is caused by the solar wind.808 The variations of the fiux density of quasars close to the Stu was used to deduce that some quasars had components of aresecoud size (IHewishlctal.1961:Cohenetal.1967:Readhead&Tewish1976) a clad since confirmed by radio interferometry.," The variations of the flux density of quasars close to the Sun was used to deduce that some quasars had components of arcsecond size \citep{hew64,coh67,rea76} – a claim since confirmed by radio interferometry."809 Iuterstellar scintillation 18 cause by the material throughout the Calaxy. and is responsible both for many effects seen iu pulsus (Rickett1990.andreferencestherein) aud low frequency variability (LEV) of some extragalactic radio sources (IIuustead1972).," Interstellar scintillation is caused by the material throughout the Galaxy, and is responsible both for many effects seen in pulsars \cite[ and references therein]{ric90} and low frequency variability (LFV) of some extragalactic radio sources \citep{hun72}."810. The compact structure in LFVs is expected to be of the order of a few inilliaresec. and ix indeed seen in VLBI observatiouns(e.g.Spangleretal. 1993).," The compact structure in LFVs is expected to be of the order of a few milliarcsec, and is indeed seen in VLBI \cite[e.g.][]{spa93}."811. The scintillation regimes ecucrally appropriate for extragalactic sources are the (broad-baud) weak and refractive regines. (, The scintillation regimes generally appropriate for extragalactic sources are the (broad-band) weak and refractive regimes. (812Pulsar observations are eenerallv concerned with narrow-band diffractive phenomena.,Pulsar observations are generally concerned with narrow-band diffractive phenomena.813 Sec Naravan. 1992 for a review of scintillation).," See Narayan, 1992 for a review of scintillation)."814 Although refractive ISS is now commonly believed o be a major coutributor to the variability at low requencies (Spangleretal.1989.1993:Dondi1996).. as first sugeested by Rickettctal.(198D)... its relevance o observed variations at GIIz frequencies has been the subject of some debate (Waener&Witzel1995). i- articular because it cannot account for the reported correlation between optical aud radio variability. which wave been observed iu a few sources (Wageneretal.1996:Peugetal. 2000).," Although refractive ISS is now commonly believed to be a major contributor to the variability at low frequencies \citep{spa89,spa93,bon96}, as first suggested by \citet{ric84}, its relevance to observed variations at GHz frequencies has been the subject of some debate \citep{wag95}, in particular because it cannot account for the reported correlation between optical and radio variability, which have been observed in a few sources \citep{wag96,pen00}."815.. The origin of the IDV in 00917|62 oue of the most variable classical IDV sources. with (variations. las been discussed by a variety of authorpA with different views (6.8Quirreubachetal.1989:Qiauetal.1995:Ianus 1999).," The origin of the IDV in 0917+624, one of the most variable classical IDV sources, with variations, has been discussed by a variety of authors with different views \cite[e.g][]{qui89b,qia91,sim91,sha91,ric95,kra99}."816. Au intrinsic explanation for the variability in this source gives au apparent brielitucss temperature of LOTS. which eui be brought under the Compton limit by a Doppler factor of ~ 17 (Quirrenbach 1989)..," An intrinsic explanation for the variability in this source gives an apparent brightness temperature of $^{18}$ K, which can be brought under the Compton limit by a Doppler factor of $\sim$ 17 \citep{qui89b}."817" 0005-385 was the first extragalactic radio source to show variations at Gz frequencies that were fairly ""uenbiguouslv interpreted as due to ISS (hNedziora- ).", 0405-385 was the first extragalactic radio source to show variations at GHz frequencies that were fairly unambiguously interpreted as due to ISS \citep{ked97}.818. Using the simplest assumptions about the location aud the velocity of the scaeror. Iedziori-Clhudzuer ot abl," Using the simplest assumptions about the location and the velocity of the scatterer, Kedziora-Chudzner et al."819 calculated the brightuess eiperatire of 00105-385 to be 5« 10111. or 1000 nues the iuverse Compton linüt.," calculated the brightness temperature of 0405-385 to be $5\times 10^{14}$ K, or 1000 times the inverse Compton limit."820 Towever. this fieure depends critically ou the assumptions about the scatterer.," However, this figure depends critically on the assumptions about the scatterer."821 Tn this paper we investigate the properties of the flux density variations of he quasar Ji819|3815., In this paper we investigate the properties of the flux density variations of the quasar J1819+3845.822 The variations in this source are the most extreme known iu he radio sky., The variations in this source are the most extreme known in the radio sky.823 We previously interpreted the variability as due to interstellar scintillation (ISS). based on the extreme ative of the variations and their frequeney dependeuce (Deunctt-Thorpe&deBruyn2000.hereafterPaperD..," We previously interpreted the variability as due to interstellar scintillation (ISS), based on the extreme nature of the variations and their frequency dependence \cite[ hereafter Paper I]{den00}."824 We lave suce xoved thei to be due to ISS by detecting a difference iu the arrival times (of up to sec) of the flux deusitv variatious at two widely spaced telescopes (Deunctt-Thorpe&deBrawn2001.hereafterPaper ID.., We have since proved them to be due to ISS by detecting a difference in the arrival times (of up to sec) of the flux density variations at two widely spaced telescopes \cite[ hereafter Paper II]{den01}. .825A short time ~30Myr after a burst of star formation. stars withmasses Af>SAL. complete most of their nuclear burning aud explode iun what are expected to be Type II aud Type Ib supernovae. although the evidence for this association is not irou-clad hereiu)..,"A short time $\sim30~\mathrm{Myr}$ after a burst of star formation, stars withmasses $M> 8\,M_\odot$ complete most of their nuclear burning and explode in what are expected to be Type II and Type Ib supernovae, although the evidence for this association is not iron-clad \citep[eg,][and references therein]{filippenko97a}."826 These supernovae and their remuants are bright at radio frequencies 1<<»«100GHz or /100Mvr (eg.?.andreferencestherein)..," These supernovae and their remnants are bright at radio frequencies $1<\nu<100~\mathrm{GHz}$ for $t\sim 100~\mathrm{Myr}$ \citep[eg,][and827references therein]{condon92a}."828 adio observations have the great advantage that they are insensitive to dust., Radio observations have the great advantage that they are insensitive to dust.829 Star formation ueasurement is not rocket science. but the radio indicator is the least well-calibrated. simply jecause the energetics of radio supernovae are less well-uucderstoocd than other aspects of stellar ;»opulations.," Star formation measurement is not rocket science, but the radio indicator is the least well-calibrated, simply because the energetics of radio supernovae are less well-understood than other aspects of stellar populations."830 Like the other indicators. radio measurements cau be contaminated by active nuclei. which. at faint levels. are not easily clistineuished [rom superuovae.," Like the other indicators, radio measurements can be contaminated by active nuclei, which, at faint levels, are not easily distinguished from supernovae."831 Many other methods have been suggested but wait for uew data., Many other methods have been suggested but wait for new data.832 It lias been suggested that the X-ray sources created by stellar evolution could be used as an iudicator (?).., It has been suggested that the X-ray sources created by stellar evolution could be used as an indicator \citep{ghosh01a}.833 Much work is golug into uuderstauding the winds from forming aud young stellar populatious relerences therein): oue can imagine measuriug star formation rates using mechanical. rather tliau electromaguetic. luminosity.," Much work is going into understanding the winds from forming and young stellar populations \citep[eg,][and references therein]{kudritzki00a}; one can imagine measuring star formation rates using mechanical, rather than electromagnetic, luminosity."834 When the SIRTF missiou is able to calibrate the relatiouships between stroug mid-infrared spectral features from interstellar molecules and the ultraviolet radiation field:4. that excite the transitionJd. (eg.?).. there will be a new industry of uuderstaucdiug star formatio[un activity vla the mid-infrarec.," When the SIRTF mission is able to calibrate the relationships between strong mid-infrared spectral features from interstellar molecules and the ultraviolet radiation fields that excite the transitions \citep[eg,][]{li02a}, there will be a new industry of understanding star formation activity via the mid-infrared."835 This meta-analysis is of star-lormation rate variation a single observational study. at redshifts 2<1.," This meta-analysis is of star-formation rate variation a single observational study, at redshifts $z<1$."836 For this reason. uo study was included iu this meta-analysis i it did not report uore than one iudependeut 2<1 star-formation rate measurement.," For this reason, no study was included in this meta-analysis if it did not report more than one independent $z\leq 1$ star-formation rate measurement."837 This excluced several otherwise ‘elevant studies (es.2222777).," This excluded several otherwise relevant studies \citep[eg,][]{connolly97,madau98a,treyer98,yan99,sullivan00,thompson01}."838 An exception was mace for a group of very similar surveys for line luminosity density. which were put together to make a “combined Πα study. described below.," An exception was made for a group of very similar surveys for line luminosity density, which were put together to make a “combined ' study, described below."839 Several relevant studies were dropped because the targets were selected or the results were sresentecd such that the results could uot be fairly used as cosmic star-lormatiou rate measurements (eg.2222?) or because estimates of nieasuremeut uncertainties were uot provided (eg. ?)..," Several relevant studies were dropped because the targets were selected or the results were presented such that the results could not be fairly used as cosmic star-formation rate measurements \citep[eg,][]{schade96,cowie97,guzman97a,lilly98a,blain99}, or because estimates of measurement uncertainties were not provided \citep[eg,][]{cram98}. ."840 Only publications appearingOm in the refereed literature prior to 2002 AugustOm 1 were considered., Only publications appearing in the refereed literature prior to 2002 August 1 were considered.841 ipparameter. as follows: We should note. however. that there are several factors whieh max introduce significant uncertainties in (he parameter.,"$\eta$ -parameter, as follows: We should note, however, that there are several factors which may introduce significant uncertainties in the $\eta$ -parameter."842 In particular. the wind porosity may lead to an overestimation of (he mass-loss rate of the star (Owocki&Cohen2006). and consequently (o a significant underestimate of (he + parameter value.," In particular, the wind porosity may lead to an overestimation of the mass-loss rate of the star \citep{owocki06} and consequently to a significant underestimate of the $\eta$ parameter value."843 The opposite situation may occur if the pulsar wind interacts with the stellar wind close to the star equatorial plane. where a dense Ixeplerian disk is lormed.," The opposite situation may occur if the pulsar wind interacts with the stellar wind close to the star equatorial plane, where a dense Keplerian disk is formed."844 Since (he disk is expected to have a significantly higher density Caan the polar wind. and its typical velocity al distance r (i.e. IXeplerian velocitv) may be as high as the disk effective ram pressure may significantlv exceed the polar wind one. ie. the ipparameter may be remarkably smaller Chan the estimate of Eq.(2)).," Since the disk is expected to have a significantly higher density than the polar wind, and its typical velocity at distance $r$ (i.e. Keplerian velocity) may be as high as the disk effective ram pressure may significantly exceed the polar wind one, i.e. the $\eta$ -parameter may be remarkably smaller than the estimate of \ref{eq:eta}) )."845 Moreover. because of the disk rotation ancl pulsar orbital velocity. the structure of the wind termination shock. in respect to (he observer direction. may be rather different for (wo pulsarclisk interaction points.," Moreover, because of the disk rotation and pulsar orbital velocity, the structure of the wind termination shock, in respect to the observer direction, may be rather different for two pulsar–disk interaction points."846 Because of these uncertainties related (o the value of the j-parameter. below we will consider a fairly broad range of the 7 parameter.," Because of these uncertainties related to the value of the $\eta$ -parameter, below we will consider a fairly broad range of the $\eta$ parameter."847 In Figure 1. the shapes of the termination shock for three different values of the 7 parameter are shown., In Figure \ref{fig:shock} the shapes of the termination shock for three different values of the $\eta$ parameter are shown.848 The points in the figure are from the results of numerical modeling performed by Bogovalovοἱal. (2003).. for a=1 (squares). jj;=0.05 (filled circles) and η=Llx10* (open circles).," The points in the figure are from the results of numerical modeling performed by \citet{bogovalov08}, , for $\eta=1$ (squares), $\eta=0.05$ (filled circles) and $\eta=1.1\times10^{-3}$ (open circles)."849 Here the value of jj=1 roughly corresponds to the case of the interaction with the clumpxv polar wind: 57=0.05 to the case of collision with the stellar wind: and 5=1.1x107 is a lower limit value. which can be realized if e.g. pulsar wind is significantly anisotropic al binary svsten scales: or if the stellar disk plavs an important role in (he interaction.," Here the value of $\eta=1$ roughly corresponds to the case of the interaction with the clumpy polar wind; $\eta=0.05$ to the case of collision with the stellar wind; and $\eta=1.1\times10^{-3}$ is a lower limit value, which can be realized if e.g. pulsar wind is significantly anisotropic at binary system scales; or if the stellar disk plays an important role in the interaction."850 To simplify the calculations we have approximated the termination shock bvthe following analvtical expressions: for 7=1 for 1j;=0.05 , To simplify the calculations we have approximated the termination shock bythe following analytical expressions: for $\eta=1$ for $\eta=0.05$ 851In this Section. we consider executing the galaxy surveys using a spectrograph dillering [rom the WIEMOS specifications presented. in. Table. 2...,In this Section we consider executing the galaxy surveys using a spectrograph differing from the WFMOS specifications presented in Table \ref{constraintparameters}.852 \We consider. three alternate possibilities: reducing the WIEMOS field-of-view from 1.5 deg to LO deg diameter. using the XOmega spectrograph on the Anglo-Australian Telescope (AAT). and using the Sloan Digital Sky Survey (SDSS) hardware.," We consider three alternate possibilities: reducing the WFMOS field-of-view from $1.5$ deg to $1.0$ deg diameter, using the AAOmega spectrograph on the Anglo-Australian Telescope (AAT), and using the Sloan Digital Sky Survey (SDSS) hardware."853 The reduction of the field-of-view is a simple alteration. as it does not alfect. the exposure time required to obtain the redshift of a galaxy (and thus the number density. for a given exposure). but only changes the total number of redshifts taken in a single pointing.," The reduction of the field-of-view is a simple alteration, as it does not affect the exposure time required to obtain the redshift of a galaxy (and thus the number density for a given exposure), but only changes the total number of redshifts taken in a single pointing."854 Altering the telescope aperture and fibre aperture is a more complex change as it will alfect the exposure times., Altering the telescope aperture and fibre aperture is a more complex change as it will affect the exposure times.855 This can be accommocated by changes in the parameters of the number counts calculator., This can be accommodated by changes in the parameters of the number counts calculator.856 The parameters for the different instruments considered are given in Table 9.., The parameters for the different instruments considered are given in Table \ref{instruments}.857 The smaller apertures and larger fibre diameters of the σος and AANOmega systems mean that their. exposure times to obtain the same angular source density as a WEALOS survey are longer. but this is partially. countered by. a Larger field-of-view which allows them to survey more of the sky per pointing.," The smaller apertures and larger fibre diameters of the SDSS and AAOmega systems mean that their exposure times to obtain the same angular source density as a WFMOS survey are longer, but this is partially countered by a larger field-of-view which allows them to survey more of the sky per pointing."858 We compared the different hardware possibilities hy finding the best Figure-of-Merit for a survey with a single bin at low redshift (where all other survey parameters are allowed to vary)., We compared the different hardware possibilities by finding the best Figure-of-Merit for a survey with a single bin at low redshift (where all other survey parameters are allowed to vary).859 The result of the previous section showed that the optimal targetted galaxy population changes with the number of fibres of the instrument. so we also compared targetting red. (continuum) ancl blue. (line emission) galaxies at low redshifts.," The result of the previous section showed that the optimal targetted galaxy population changes with the number of fibres of the instrument, so we also compared targetting red (continuum) and blue (line emission) galaxies at low redshifts."860 Ehe results are shown in Table 10.., The results are shown in Table \ref{instrumentfom}.861 We [nd that ldinc-emitting galaxies are strongly preferred as targets for WIEMOS (regardless of field-of-view). whereas red galaxies are marginally preferred for SDSS and AAOmeega. which only have a lew hundred fibres.," We find that line-emitting galaxies are strongly preferred as targets for WFMOS (regardless of field-of-view), whereas red galaxies are marginally preferred for SDSS and AAOmega, which only have a few hundred fibres."862 This is consistent with the result for WEALOS for a small number of ibres (see Fig. 6)).," This is consistent with the result for WFMOS for a small number of fibres (see Fig. \ref{fibres}) ),"863 where red galaxies are preferred., where red galaxies are preferred.864 We find hat the SDSS and AAT are almost equivalent in terms of l'igure-of-Merit. as the smaller aperture of the SDSS system (and so longer exposure times) is balanced by the larger ield-of-view and number of fibres.," We find that the SDSS and AAT are almost equivalent in terms of Figure-of-Merit, as the smaller aperture of the SDSS system (and so longer exposure times) is balanced by the larger field-of-view and number of fibres."865 Considering the de-scope option of reducing the WEMOS field-of-view to 1 degree cliameter. this reduces the survey area by a factor of 2. and hus the FoM drops by almost the same factor (in detail. since the number of fibres is held constant. the fibre density increases. which olfsets the loss of area to some extent).," Considering the de-scope option of reducing the WFMOS field-of-view to 1 degree diameter, this reduces the survey area by a factor of 2, and thus the FoM drops by almost the same factor (in detail, since the number of fibres is held constant, the fibre density increases, which offsets the loss of area to some extent)."866 In other words. equivalent results will be obtained by a 3-vear survey with a 1.5-deg-ciamoeter svstem and a 4.5-vear survey with a l-cleg-ciameter system.," In other words, equivalent results will be obtained by a 3-year survey with a 1.5-deg-diameter system and a 4.5-year survey with a 1-deg-diameter system."867 During the construction period of a WEMOS-like instrument. a number of other dark energy surveys will be xrformed.," During the construction period of a WFMOS-like instrument, a number of other dark energy surveys will be performed."868 These. measurements of the angular clameter istance ancl Llubble parameter in the case of BAO surveys. wv luminosity distance in the case of Tvpe la Supernovae (SN-la) surveys. will have alreacky constrained. some of the ark energy. parameter space.," These measurements of the angular diameter distance and Hubble parameter in the case of BAO surveys, or luminosity distance in the case of Type Ia Supernovae (SN-Ia) surveys, will have already constrained some of the dark energy parameter space."869 By including the predictions or these surveys in our analvsis. we can determine whether oir optimal survey design changes.," By including the predictions for these surveys in our analysis, we can determine whether our optimal survey design changes."870 We consider (wo surveys ja are currently underway: (1) WigeleZ. a barvon acoustic mcillation. survey being carried. out with the AAOmeesa spectrograph: ancl (2) the full five-vear SuperNovae Legacy Survey and the Sloan Digitized Sky Survey LE Supernova Survey (SNLS-SDSS).," We consider two surveys that are currently underway: (1) WiggleZ, a baryon acoustic oscillation survey being carried out with the AAOmega spectrograph; and (2) the full five-year SuperNovae Legacy Survey and the Sloan Digitized Sky Survey II Supernova Survey (SNLS-SDSS)."871 The WigeleZ survey has the following parameters: Area = 100ί) sq deg. 2=O75. d;=0.25. number density =8&5«10! A? 7. observing linc-emission ealaxies (Glazebrook et al.," The WiggleZ survey has the following parameters: Area = 1000 sq deg, $z = 0.75$, $dz = 0.25$, number density $= 8.5 \times 10^{-4}$ $h^3$ $^{-3}$, observing line-emission galaxies (Glazebrook et al."872 2007)., 2007).873 Using our fitting formula code (Blake et al.2006) we find that this corresponds to measurement accuracies of in d and in H(z)., Using our fitting formula code (Blake et al.2006) we find that this corresponds to measurement accuracies of in $d_A$ and in $H(z)$.874 This is casy to include in our optimization. as it counts as an extra measurement at a redshift of 0.75. without any time cost.," This is easy to include in our optimization, as it counts as an extra measurement at a redshift of 0.75, without any time cost."875 We find that the inclusion of the WigeleZ measurement has no effect. on any of the survey parameters. as shown in Ligure S.. as the curves with ancl without the WigeleZ survey are virtually identical.," We find that the inclusion of the WiggleZ measurement has no effect on any of the survey parameters, as shown in Figure \ref{WFMOS-WiggleZ}, as the curves with and without the WiggleZ survey are virtually identical."876 This is because the NEMOS. measurement: would. produce a much more accurate measurement of dark energy. properties., This is because the WFMOS measurement would produce a much more accurate measurement of dark energy properties.877" The SNLS-SDSS SN-la survey will find. around. 1000 Supernovae distributed approximately evenly in the range Ql«""EE1] (D. Xndrew Lowell and. the SNLS collaboration 2004: SDSS-LL Supernovae Survey Fall 2005).", The SNLS-SDSS SN-Ia survey will find around 1000 Supernovae distributed approximately evenly in the range $0.1 < z < 1$ (D. Andrew Howell and the SNLS collaboration 2004; SDSS-II Supernovae Survey Fall 2005).878 The measurement is the apparent magnitude (m) of the supernovae. defined as = |25].," The measurement is the apparent magnitude $m$ ) of the supernovae, defined as m(z) = +25]."879 The luminosity distance will give us information about the expansion. but we have the added: complication of mareinalizine over the absolute magnitude. AZ. The supernova surveys therefore do not. constrain the Llubhle," The luminosity distance will give us information about the expansion, but we have the added complication of marginalizing over the absolute magnitude $M$ The supernova surveys therefore do not constrain the Hubble"880We consider four possible OB associations containing 10. 50. 100. 500 SNe respectively.,"We consider four possible OB associations containing 10, 50, 100, 500 SNe respectively."881 Assuming an explosion energy of 10?! erg. the luminosities Lo of these OB associations are 107. 5x107. 109 αιd 5x10? eres”! respectively.," Assuming an explosion energy of $10^{51}$ erg, the luminosities $L_0$ of these OB associations are $10^{37}$ , $5 \times 10^{37}$, $10^{38}$ and $5 \times 10^{38}$ $^{-1}$ respectively."882 These numbers of massive stai rin OB associations are consistent with the observations (de Zeeuw et al., These numbers of massive star in OB associations are consistent with the observations (de Zeeuw et al.883" 1999),", 1999).884 We simulate galactic fountains with 3 different throwing radial coordinates Ro: 4. 8. 12 kpe.," We simulate galactic fountains with 3 different throwing radial coordinates $R_{0}$: 4, 8, 12 kpc."885 Given the assumed Galaxy model. Ro defines the disk density po. whereas the scale height is constant (see Sect 2.3)).," Given the assumed Galaxy model, $R_0$ defines the disk density $\rho_0$, whereas the scale height is constant (see Sect \ref{galaxy}) )."886 In Tabs. 2.. 3..," In Tabs. \ref{ta4}, \ref{ta8},"887 4. we summarize the results for fragmentation times and the velocities of the superbubbles in the direction perpendicular to the galactic plane at those times for 4 kpe. 8 kpe.12 kpe. respectively.," \ref{ta12} we summarize the results for fragmentation times and the velocities of the superbubbles in the direction perpendicular to the galactic plane at those times for 4 kpc, 8 kpc,12 kpc, respectively."888 For all the values of SNe and Ro considered at the time πω: at Which clouds are thrown out of the disk. the supershell presents: zj=448 pe. zjj=165 pe and 6=259 pe.," For all the values of $SNe$ and $R_0$ considered at the time $t_{final}$, at which clouds are thrown out of the disk, the supershell presents: $z_{L}=448$ pc, $z_{H}=165$ pc and $b=259$ pc."889 Our results are in agreement with the work of Mac Low MeCray (1988): instabilities. for roughly the same luminosity range. become important at 3H height scale.," Our results are in agreement with the work of Mac Low McCray (1988): instabilities, for roughly the same luminosity range, become important at $3H$ height scale."890 The total mass of gas swept up by the SN shock wave for positive z-coordinates is given by the eq. (20)., The total mass of gas swept up by the SN shock wave for positive z-coordinates is given by the eq. \ref{MzP}) ).891 In conclusion. we obtain that the masses of the ISM swept up into the thin shell for Ro= 4. 8. 12 kpe. respectively are: All the results about the O and Fe abundances in the clouds ejected by sequential SN explosions as functions of $Ne and Ro are reported in the Online material.," In conclusion, we obtain that the masses of the ISM swept up into the thin shell for $R_0$ = 4, 8, 12 kpc, respectively are: All the results about the $O$ and $Fe$ abundances in the clouds ejected by sequential SN explosions as functions of $SNe$ and $R_0$ are reported in the Online material."892" Mj, and M.o,, are the total amounts of Fes; and Oye in unit of Mo... whereas M,,j is the total mass ejected by the OB association: where i,01) 1s the total mass ejected by a SN as a function of its initial mass and metallicity. Mj. νο Xeo,,"," $M_{*Fe_{56}} $ and $M_{*O_{16}} $ are the total amounts of $Fe_{56}$ and $ O_{16}$ in unit of $M_{\odot}$ , whereas $ M_{\star ej}$ is the total mass ejected by the OB association: where $m_{tot}(m)$ is the total mass ejected by a SN as a function of its initial mass and metallicity. $M_{tot}$, $ X_{*Fe_{56}}$,"893 and [O/Fe] are: In Fig + we show the predicted [O/Fe] ratio as a function of the number of SNe and of the initial metallicity in. the solar vicinity., $X_{*O_{16}}$ and $[O/Fe]$ are: In Fig \ref{result} we show the predicted $[O/Fe]$ ratio as a function of the number of SNe and of the initial metallicity in the solar vicinity.894 In the meridional plane of the Galaxy the initial conditions are (R. z)2( 8 kpe. 448 pe).," In the meridional plane of the Galaxy the initial conditions are $(R,z)$ =( 8 kpc, 448 pc)."895 We note that significant over-abundances of O relative to Fe are found only 1n the case of a large number of SNe and low initial metallicity., We note that significant over-abundances of $O$ relative to $Fe$ are found only in the case of a large number of SNe and low initial metallicity.896 In Fig., In Fig.897 5 we report the same quantities but using stellar yields given by Kobayashi et al. (, \ref{resultk} we report the same quantities but using stellar yields given by Kobayashi et al. (8982006).,2006).899 In Fig., In Fig.900" 6 we show [O/Fe] ratios as functions of the number of SNe assuming solar metallicity but varying the initial throwing coordinate R,.", \ref{zsol} we show $[O/Fe]$ ratios as functions of the number of SNe assuming solar metallicity but varying the initial throwing coordinate $R_o$.901 We note that larger radial coordinates yield a larger [O/Fe]. because the amount of the swept-up pristine gas is smaller (see eq. 41))," We note that larger radial coordinates yield a larger $[O/Fe]$, because the amount of the swept-up pristine gas is smaller (see eq. \ref{M12}) )"902 and therefore the new « elements ejected by SNe are less diluted., and therefore the new $\alpha$ elements ejected by SNe are less diluted.903 In Fig., In Fig.904 7 we report the [O/Fe] ratios varying the initial throwing coordinate Ry and taking for the initial ISM metallicities the average observed values givenby Andreievsky et al. (, \ref{zreal} we report the $[O/Fe]$ ratios varying the initial throwing coordinate $R_0$ and taking for the initial ISM metallicities the average observed values givenby Andreievsky et al. (9052002a-c. 2004) and Luck et al. (,"2002a-c, 2004) and Luck et al. ("9062003). as a function of galactocentric distance. by analyzing Galactic Cepheids (see Cescutti at al.,"2003), as a function of galactocentric distance, by analyzing Galactic Cepheids (see Cescutti at al."907 2006).Referring to the Tab., 2006).Referring to the Tab.908 4 of the work of Cescutti et al. (, 4 of the work of Cescutti et al. (909"2006). we find: Z=1.65xZ. for Ro=4 kpe andZ=0.74xZ, for Ro=12 kpe.","2006), we find: $Z= 1.65 \times Z_{\odot}$ for $R_0=4$ kpc and $Z= 0.74 \times Z_{\odot}$ for $R_0=12$ kpc."910LID 141943 is only the second (orthirdincludingthere- voung carly-CG star for which the large-scale magnetic topology has been determined. the other being. HD. 171488. (Marsdeneal.20062:Jellers&Donati2008:ct 2010).,"HD 141943 is only the second \citep[or third including the results for HD 106506 by][]{WaiteIA:2010} young early-G star for which the large-scale magnetic topology has been determined, the other being HD 171488 \citep{MarsdenSC:2006a, JeffersSV:2008, JeffersSV:2010}."911. However. there have been five voung earlv-€ stars for which rot maps and cdillerential rotation measures have been determined. (and. a number of others that have Just. spot maps. see Table 4 in Strassmeierctal. 2003)).," However, there have been five young early-G stars for which spot maps and differential rotation measures have been determined (and a number of others that have just spot maps, see Table 4 in \citealt{StrassmeierKG:2003}) )."912 Alone with LD 141943. LD 171488 and LD 106506. the other two stars are. R58 (Marsdenetal.2005a.b) and LQ Lup (Donatiοἱal. 2000).," Along with HD 141943, HD 171488 and HD 106506, the other two stars are, R58 \citep{MarsdenSC:2005a, MarsdenSC:2005b} and LQ Lup \citep{DonatiJF:2000}."913. For comparative purposes in this discussion the stellar parameters of all these five stars are given in Table 5.., For comparative purposes in this discussion the stellar parameters of all these five stars are given in Table \ref{Tab_gstars}.914 The surface spot topology of LED. 141948 at four epochs is shown in Fig. 2..," The surface spot topology of HD 141943 at four epochs is shown in Fig. \ref{Fig_map2006},"915 Fig., Fig.916 3. (top-left image). Fig.," \ref{Fig_allmap2007} (top-left image), Fig."917 4 (top-left image) and Fig., \ref{Fig_allmap2009} (top-left image) and Fig.918 5 (top-left image)., \ref{Fig_allmap2010} (top-left image).919 Phe 4 maps show that the spot topology of LID 141943 was remarkably consistent over the span of the observations (4. vears)., The 4 maps show that the spot topology of HD 141943 was remarkably consistent over the span of the observations $\sim$ 4 years).920 ALL maps show that LID 141943 has a smallish polar spot. with a number of Ilower-Iatitude features. situated: predominantly between the equator and. latitude.with only the 2010 epoch showing some significant spot features between ancl laitude at around. phase 70.90.," All maps show that HD 141943 has a smallish polar spot with a number of lower-latitude features situated predominantly between the equator and latitude,with only the 2010 epoch showing some significant spot features between and latitude at around phase $\sim$ 0.90."921 “Phe total spot coverage Lor al 4 epochs is also very similar ranging from 2.1 per cent ο 3.1 per cent., The total spot coverage for all 4 epochs is also very similar ranging from 2.1 per cent to 3.1 per cent.922 Comparing these maps to those of other voung carly- stars creaed using the same imagine code. such as 1558 (Marsden:ctal.2005b).. LO. Lup (Donatictal.2000).. LD 171488 (Marsdenctal.20062:Jeffers&Donati2008:Jellorsetal.POLO) and LID 106506 (Waiteetal.2010).. it is quite noticeable that while all stars appear to have some lower-latituce features. the polar spot on ID 141948 is significantly smaller than that shown by these other targets.," Comparing these maps to those of other young early-G stars created using the same imaging code, such as R58 \citep{MarsdenSC:2005b}, LQ Lup \citep{DonatiJF:2000}, HD 171488 \citep{MarsdenSC:2006a, JeffersSV:2008, JeffersSV:2010} and HD 106506 \citep{WaiteIA:2010}, it is quite noticeable that while all stars appear to have some lower-latitude features, the polar spot on HD 141943 is significantly smaller than that shown by these other targets."923 Marsdenetal.(2005b) has shown that. starspot mapping assuming hieh stellar inclination angles leads a dramatic increase in the amount of polar spot. features needed to match the observed deviations in the LSD profiles., \citet{MarsdenSC:2005b} has shown that starspot mapping assuming high stellar inclination angles leads to a dramatic increase in the amount of polar spot features needed to match the observed deviations in the LSD profiles.924 Given that Η 141943 has a higher stellar inclination than the other stars listed in Table 5 it is not an incorrectly determined stellar inclination that is responsible for the small polar spot on LID 1431943., Given that HD 141943 has a higher stellar inclination than the other stars listed in Table \ref{Tab_gstars} it is not an incorrectly determined stellar inclination that is responsible for the small polar spot on HD 141943.925 As can be seen in Table 5.. ID. 141948 is tje second voungest and second most massive (behind LID 06506) of the voung carly-G stars so lar imaged using this code.," As can be seen in Table \ref{Tab_gstars}, HD 141943 is the second youngest and second most massive (behind HD 106506) of the young early-G stars so far imaged using this code."926 Lt, It9275truciu BStrueiu Cnr Cnr Cnr Cnr σα1) clussilü ον CLUSSS ciusshbxlO 1102 ciutir clurd cutis clures ,"5truein 8truein cmr8 cmr8 cmr8 cmr8 cmr10 cmssi10 cmss10 cmss8 cmssbx10 2 cmti7 cmr6 cmti8 cmr8 \def\ref{\par\noindent\hangindent 15pt}928 "929"Returning to my example. (he first (wo assumptions allow me to write the II photocetachment rale al adistance 7? from the stars as where L,. the stellar luminosity per unit frequency. is given by the Leithererefal. moclel.","Returning to my example, the first two assumptions allow me to write the $\Hm$ photodetachment rate at adistance $R$ from the stars as where $L_{\nu}$, the stellar luminosity per unit frequency, is given by the \citeauthor{lei} model."930" Using (his value. Iobtain where and where M, is the mass of stars formed in the starburst."," Using this value, Iobtain where and where $M_{*}$ is the mass of stars formed in the starburst."931" Similarly. we can write the IL, photocdissociation rate as and from these rates calculate frau and fi By comparing these values and equation 42.. we can see that formation via IL, contributes at most about of the IH» produced in the gas phase. with the rest coming from II.."," Similarly, we can write the $\mHtp$ photodissociation rate as and from these rates calculate $f_{\rm rad, \Hm}$ and $f_{\rm rad, \mHtp}$ By comparing these values and equation \ref{my_pg}, we can see that formation via $\mHtp$ contributes at most about of the $\mHt$ produced in the gas phase, with the rest coming from $\Hm$."932 To evaluate these numbers. I use the fact that for atruncated isothermal sphere. in regions outside of the core.," To evaluate these numbers, I use the fact that for atruncated isothermal sphere, in regions outside of the core."933" The final unknown. M,. can be written as where ©, is (he star formation efficiency of the protogalaxy. z is ils redshift of Formation and his the IIubble constant in units of 100kms.!Mpe.|."," The final unknown, $M_{*}$, can be written as where $\varepsilon_{*}$ is the star formation efficiency of the protogalaxy, $z$ is its redshift of formation and $h$ is the Hubble constant in units of $100 \: \rm{km} \: \rm{s}^{-1} \: \rm{Mpc}^{-1}$."934" For a protogalaxy (hat formed in a standard ACDM cosmology (Q,,= 0.3. Q,= 0.04. h— 0.7) αἱ a redshilt z= 10. and that formed stars with an ellicieney 2,= 0.01.we find Lad"," For a protogalaxy that formed in a standard $\Lambda$ CDM cosmology $\Omega_{m} = 0.3$ , $\Omega_{b} = 0.04$ , $h = 0.7$ ) at a redshift $z=10$ , and that formed stars with an efficiency $\varepsilon_{*} = 0.01$ ,we find that"935Peacock’s approximation ancl Vietris formulation.,Peacock's approximation and Vietri's formulation.936F'irst. transform Eq. (,"First, transform Eq. ("93724) and Eq. (,24) and Eq. (938"27) as where s)(s2) is the power-law index cerived from Vietri's formulation (Peacock’s approximation) and 4, is the shock velocity which satislies Eq. (",27) as where $s_1(s_2)$ is the power-law index derived from Vietri's formulation (Peacock's approximation) and $\beta_{s_1}$ is the shock velocity which satisfies Eq. (93927).,27).940 Peacock’s approximation (leq. (, Peacock's approximation (Eq. (94124)) ancl Vietri’s formulation (eq. (,24)) and Vietri's formulation (Eq. (942"27)) coincide with each other as long as the following equation is satisLied: Now we introduce the value defined as We use DG3,) as the function which indicates the dillerence. between Peacock’s approximation ancl Vietri's formulation.",27)) coincide with each other as long as the following equation is satisfied: Now we introduce the value defined as We use $D(\beta_{s_1})$ as the function which indicates the difference between Peacock's approximation and Vietri's formulation.943 The averaged value is calculated using. the energv-gain [actor distribution as follows. where D becomes 0 if Peacock’s approximation ancl Vietri's formulation give the same result.," The averaged value is calculated using the energy-gain factor distribution as follows, where $D$ becomes $0$ if Peacock's approximation and Vietri's formulation give the same result."944 Particularly. D approaches O when s approaches 3.," Particularly, $D$ approaches 0 when $s$ approaches 3."945 D becomes larec if the cillerence between Peacock’s approximation and Vietri's formulation becomes conspicuous., $D$ becomes large if the difference between Peacock's approximation and Vietri's formulation becomes conspicuous.946 ow let us see the clleet of the variance in D., Now let us see the effect of the variance in $D$.947 However. ib is dillcult to know the relation between 1 and. the variance.," However, it is difficult to know the relation between $D$ and the variance."948 Here. we use the simple model of the distribution function which shows the distribution function (lq. (," Here, we use the simple model of the distribution function which shows the distribution function (Eq. ("94933)) approximately.,33)) approximately.950 In Fig., In Fig.951 4 the energy-gain factor's distribution function (C) is plotted. for the various shock velocity., 4 the energy-gain factor's distribution function $P(G)$ is plotted for the various shock velocity.952 1n the case of model A. the distribution. becomes wider and rectangular as the shock moves fast.," In the case of model A, the distribution becomes wider and rectangular as the shock moves fast."953 Then we use the rectangular clistribution function for highlv-relativistic shocks in model A. The rectangular distribution function is Written as. On the other hand. the distribution does not become rectangular and seems unsuitable to apply this. simple distribution function in model B. D. which is calculated using the simple distribution mocel. is written as. We expect that the variance which is calculated by the true distribution function (I2q. (," Then we use the rectangular distribution function for highly-relativistic shocks in model A. The rectangular distribution function is written as, On the other hand, the distribution does not become rectangular and seems unsuitable to apply this simple distribution function in model B. $D$, which is calculated using the simple distribution model, is written as, We expect that the variance which is calculated by the true distribution function (Eq. ("95433)) corresponds to the one which is calculated by the rectangular clistribution.,33)) corresponds to the one which is calculated by the rectangular distribution.955 L has a relation to the variance σ΄2 ase=(L.—1/2., L has a relation to the variance $\sigma^2$ as $\sigma=(L-1)/2\sqrt{3}$.956" Using this relation. 2.,,CL.41) is rewritten as. Diy, has the convergence value when @ becomes infinity."," Using this relation, $D_{app}(L,s_1)$ is rewritten as, $D_{app}$ has the convergence value when $\sigma$ becomes infinity."957 The convergence value is written as.," The convergence value is written as,"958Science Foundation (grant 997088[).,Science Foundation (grant 9970884).959"For each point on the i-Q-grid we find the least-square solution by solving a linear equation using matrix inversion, where e, P, To, ω, Κι, i, and Q are fixed.","For each point on the $i$ $\Omega$ -grid we find the least-square solution by solving a linear equation using matrix inversion, where $e$ , $P$ , $T_0$ , $\omega$, $K_1$, $i$, and $\Omega$ are fixed."960 The y? value hence obtained for each grid-point allows us to derive joint confidence intervals on the i-Q-grid., The $\chi^2$ value hence obtained for each grid-point allows us to derive joint confidence intervals on the $i$ $\Omega$ -grid.961" The parallax dependence of the Thiele-Innes constants is removed by writing and defining the new constant Note that a, is expressed in AU and corresponds to the angular semimajor axis a of the astrometric orbit.", The parallax dependence of the Thiele-Innes constants is removed by writing and defining the new constant Note that $a_1$ is expressed in AU and corresponds to the angular semimajor axis $a$ of the astrometric orbit.962 Now we can rewrite Eq., Now we can rewrite Eq.963" 8 as This relation is linear in the five remaining free parameters (a*, 6, το, Max, us) and can easily be solved analytically."," \ref{eq:abscissa1} as This relation is linear in the five remaining free parameters $\alpha^{\star}$, $\delta$, $\varpi$, $\mu_{\alpha^\star}$, $\mu_\delta$ ) and can easily be solved analytically."964" The companion signature is solely contained in an additive modulation Y(i,Q,e,P,To,c»,ΚΙ) of the parallax factor."," The companion signature is solely contained in an additive modulation $\Upsilon(i,\Omega,e,P,T_0,\omega,K_1)$ of the parallax factor."965" It is important to realise that the presence of Y forces the parallax, rather than a parallax offset, to be present in the model function, which originates in the abscissa reconstruction from Eq. 1.."," It is important to realise that the presence of $\Upsilon$ forces the parallax, rather than a parallax offset, to be present in the model function, which originates in the abscissa reconstruction from Eq. \ref{eq:abscrecon}."966" For the remaining parameters it is sufficient to consider the offsets Aa*, Ad, Aug«, and Δμο to the catalogue values, because the abscissa has been constructed with af=69Hax,0Hao 0."," For the remaining parameters it is sufficient to consider the offsets $\Delta \alpha^{\star}$ , $\Delta \delta$, $\Delta \mu_{\alpha^\star}$, and $\Delta \mu_{\delta}$ to the catalogue values, because the abscissa has been constructed with $\alpha^\star_0 = \delta_0 = \mu_{\alpha^\star,0} = \mu_{\delta,0} = 0$ ."967" For every combination of i and © the linear equation= 16 is solved, yielding the five astrometric parameters and the corresponding y?."," For every combination of $i$ and $\Omega$ the linear equation \ref{eq:upsilon} is solved, yielding the five astrometric parameters and the corresponding $\chi^2$."968 The best-fit parameters are identified by the minimum x? value on the i-O-grid., The best-fit parameters are identified by the minimum $\chi^2$ value on the $i$ $\Omega$ -grid.969" The results of the linear adjustment are not directly used in the quoted final solution, but they serve as a consistency check for the results from the non-linear fitting and are used for graphical illustration of the joint confidence intervals as shown in Fig. 12.."," The results of the linear adjustment are not directly used in the quoted final solution, but they serve as a consistency check for the results from the non-linear fitting and are used for graphical illustration of the joint confidence intervals as shown in Fig. \ref{fig:HD167665contour}."970 Low-significance orbits can show several local X-minima corresponding to approximately opposite orbit orientations (see also e.g. ??)).," Low-significance orbits can show several local $\chi^2$ -minima corresponding to approximately opposite orbit orientations (see also e.g. \citealt{Zucker:2001ve, Reffert:2006ly}) )."971 We find that moderate- and high-significance orbits have one global y?-minimum and the confidence contours cover a small area of the i-Q-space (similarly to HD 53680 in Fig. 12))., We find that moderate- and high-significance orbits have one global $\chi^2$ -minimum and the confidence contours cover a small area of the $i$ $\Omega$ -space (similarly to HD 53680 in Fig. \ref{fig:HD167665contour}) ).972" The solution parameters corresponding to an opposite-orientation orbit are always beyond the 4-c contour, i.e. all orbital parameters of significant solutions are unambiguouslydetermined."," The solution parameters corresponding to an opposite-orientation orbit are always beyond the $\sigma$ contour, i.e. all orbital parameters of significant solutions are unambiguouslydetermined."973" While the solution method discussed in the previous section is favourable because the model function is linear, its accuracy is limited by the resolution of the i-Q-grid."," While the solution method discussed in the previous section is favourable because the model function is linear, its accuracy is limited by the resolution of the $i$ $\Omega$ -grid."974" For instance, the resolution of a square grid with 900 points is 6? and 12? in i and Q, respectively."," For instance, the resolution of a square grid with 900 points is $6\degr$ and $12\degr$ in $i$ and $\Omega$, respectively."975" To avoid this limitation, we determine the best solution via y?-minimisation of a model function, where i and © are free parameters and thus can adopt continuous values."," To avoid this limitation, we determine the best solution via $\chi^2$ -minimisation of a model function, where $i$ and $\Omega$ are free parameters and thus can adopt continuous values."976" Therefor, the i-Q-grid is used to define the starting values of a non-linear least-squares fit by the Levenberg-Marquardt method."," Therefor, the $i$ $\Omega$ -grid is used to define the starting values of a non-linear least-squares fit by the Levenberg-Marquardt method."977" The model function is given by Eq. 10,,"," The model function is given by Eq. \ref{eq:abscissa2},"978" however limited to seven free parameters: the 5 astrometric parameters a*, 6, @, µα». µο plus i and Ω."," however limited to seven free parameters: the 5 astrometric parameters $\alpha^{\star}$, $\delta$, $\varpi$, $\mu_{\alpha^\star}$, $\mu_\delta$ plus $i$ and $\Omega$."979 We select the non-linear solution yielding the smallest y? and perform 1000 Monte-Carlo simulations., We select the non-linear solution yielding the smallest $\chi^2$ and perform 1000 Monte-Carlo simulations.980 Every Monte-Carlo realisation consists of generating aset of Hipparcos abscissa measurements and consequent y?-minimisation of the non-linear model and therefore provides 1000 sets of solution elements., Every Monte-Carlo realisation consists of generating aset of Hipparcos abscissa measurements and consequent $\chi^2$ -minimisation of the non-linear model and therefore provides 1000 sets of solution elements.981" To incorporate the uncertainties of the spectroscopic parameters we run the complete analysis for 100 sets of spectroscopic parameters, where each set is randomly drawn from gaussian distributions with mean and standard deviation given by the radial-velocity solution and its error, respectively (similarly to ?))."," To incorporate the uncertainties of the spectroscopic parameters we run the complete analysis for 100 sets of spectroscopic parameters, where each set is randomly drawn from gaussian distributions with mean and standard deviation given by the radial-velocity solution and its error, respectively (similarly to \citealt{Sozzetti:2010nx}) )."982" The final solution accounts for all 1000 Monte-Carlo solutions, which are obtained for each of the 100 sets of spectroscopic parameters."," The final solution accounts for all 1000 Monte-Carlo solutions, which are obtained for each of the 100 sets of spectroscopic parameters."983" To achieve this, we combine all solutions to yield distributions of 1000000 values for each parameter in Eq. 10.."," To achieve this, we combine all solutions to yield distributions of 000 values for each parameter in Eq. \ref{eq:abscissa2}."984" The final parameter value and its error is derived from the mean and the 1-c confidence interval of the associated distribution, respectively."," The final parameter value and its error is derived from the mean and the $\sigma$ confidence interval of the associated distribution, respectively."985" The values and errors of derived quantities, such as the companion mass, are obtained in the same way and thus take into account possible correlations between individual parameters."," The values and errors of derived quantities, such as the companion mass, are obtained in the same way and thus take into account possible correlations between individual parameters."986 Outlying astrometric measurements are examined if they deviate by more than 4-o from the orbital solution., Outlying astrometric measurements are examined if they deviate by more than $\sigma$ from the orbital solution.987" Here, c is calculated as the root-mean-square of the fit residuals."," Here, $\sigma$ is calculated as the root-mean-square of the fit residuals."988 The datapoint is discarded if there are at least three measurements at same satellite orbit number and if it is more than 3-o away from these datapoints., The datapoint is discarded if there are at least three measurements at same satellite orbit number and if it is more than $\sigma$ away from these datapoints.989" If less than three datapoints at same orbit number are present, they are all removed."," If less than three datapoints at same orbit number are present, they are all removed."990 The analysis is then iterated., The analysis is then iterated.991" This procedure is similar to the one applied by ? and in some cases also agrees with the outlier rejection, that is applied by the new Hipparcos reduction itself."," This procedure is similar to the one applied by \cite{Pourbaix:2000sf} and in some cases also agrees with the outlier rejection, that is applied by the new Hipparcos reduction itself."992" Outliers are removed for the following objects: GJ 595, HD 3277, HD 43848, HD 74842, HD 154697, HD 1644274, HD 167665, HD 191760, and HIP 103019."," Outliers are removed for the following objects: GJ 595, HD 3277, HD 43848, HD 74842, HD 154697, HD 164427A, HD 167665, HD 191760, and HIP 103019."993 This never requires more than one iteration., This never requires more than one iteration.994 Orbital solutions can be found for any set of astrometric data and the crucial step in the analysis is to determine the credibility of the derived orbits., Orbital solutions can be found for any set of astrometric data and the crucial step in the analysis is to determine the credibility of the derived orbits.995 We accomplish this byapplying twostatisticaltests: the F-test for its simplicity and the permutation test for its lack of underlying assumptions., We accomplish this byapplying twostatisticaltests: the F-test for its simplicity and the permutation test for its lack of underlying assumptions.996" The F-test is extensively usedfor the statistical analysis of astrometric orbit signatures in Hipparcos data (????),, although it relies on the assumption that the measurement errors are Gaussian."," The F-test is extensively usedfor the statistical analysis of astrometric orbit signatures in Hipparcos data \citep{Pourbaix:2000sf, Pourbaix:2001rt, Pourbaix:2001qe, Reffert:2006ly}, , although it relies on the assumption that the measurement errors are Gaussian."997" That this assumption is not necessarily fulfilled for Hipparcosdata is mentioned by ?,, who do not apply the"," That this assumption is not necessarily fulfilled for Hipparcosdata is mentioned by \cite{Zucker:2001ve}, , who do not apply the"998These SElts. which again are uncorrected [for dust extinction. average 1.61250.37Mvr.+.,"These SFRs, which again are uncorrected for dust extinction, average $1.61\pm 0.37 \rm ~M_{\odot}yr^{-1}$."999 There are two wavs in which we can estimate à very approximate cdust-corrected SER., There are two ways in which we can estimate a very approximate dust-corrected SFR.1000 Firstlv. if the emission lines are assumed to be subject to the same dust. extinction as the continuum. then from the Calzetti (2000) reddening curve the OL]. extinction dave;=SSGL(BV)," Firstly, if the emission lines are assumed to be subject to the same dust extinction as the continuum, then from the Calzetti (2000) reddening curve the [OII] extinction $A_{3727}=5.86E(B-V)$."1001" d£ we apply this correction to the SETs in Fable 4. using the value of (D.V) best-fit to the spectrum of cach galaxy. the mean SER of the LO line galaxies increases to 12.6M.vr+ Secondly. i£ we assume that the SER and cust extinction in the star-forming component is truly constant. we can estimate SEIta,=ALi/Pa.."," If we apply this correction to the SFRs in Table 4, using the value of $E(B-V)$ best-fit to the spectrum of each galaxy, the mean SFR of the 10 emission-line galaxies increases to $12.6 \rm ~M_{\odot}yr^{-1}$ Secondly, if we assume that the SFR and dust extinction in the star-forming component is truly constant, we can estimate $\rm SFR_{sb}=M_{sb}/T_{sb}$."1002 Phis will correct. for dust. as this is taken into account in calculating ον. but for an individual ERG this is very approximate πο to the large error bars on ορ," This will correct for dust, as this is taken into account in calculating $M_{sb}$, but for an individual ERG this is very approximate due to the large error bars on $T_{sb}$."1003" For the full sample of ERGs (but excluding the AGN). the mean SER, is 24Aleve +."," For the full sample of ERGs (but excluding the AGN), the mean $\rm SFR_{sb}$ is $24 \rm ~M_{\odot}yr^{-1}$ ."1004value ofX is almost an order of magnitude lower than the standard value.,value of$X$ is almost an order of magnitude lower than the standard value.1005 Thus the Πο abundance ratio should also be ~1 in the inner region., Thus the $_2$ abundance ratio should also be $\sim$ 1 in the inner region.1006 The velocityautcerated emission refFIG.ΝΤΑ ΡΟ) sugeests a variation dn major axis position angle aud perhaps inclination across the ealaxy., The velocity-integrated emission \\ref{FIG.MAPS}b b) suggests a variation in major axis position angle and perhaps inclination across the galaxy.1007 As incutioned carlicr. there appears to be an inner disk with a lower position angle than hat for the outer reeions.," As mentioned earlier, there appears to be an inner disk with a lower position angle than that for the outer regions."1008 To investigate whether the galaxy is warped. we nodeled the cussion with a set of concentric rings (ef.," To investigate whether the galaxy is warped, we modeled the emission with a set of concentric rings (cf."1009 Beecuan 1987: Rogstad et al., Begeman 1987; Rogstad et al.1010" 1971) of width 50” your R=100"" to 650"" aud fitted the uorth-casterm aud soutliwestern sides of the galaxy separately.", 1974) of width $50''$ from $R=100''$ to $650''$ and fitted the north-eastern and south-western sides of the galaxy separately.1011 The resulting oosition angles and inclinations for the rings both vary over less than 107 along the major axis., The resulting position angles and inclinations for the rings both vary over less than $^{\circ}$ along the major axis.1012" Part of this variation is systematic iu that the position angle varies rom 50° in the north-east to 13° in the soutl-west. aud for R> 100"" the inclination appears about 3° higher in the south-west than in the north-east."," Part of this variation is systematic in that the position angle varies from $^{\circ}$ in the north-east to $^{\circ}$ in the south-west, and for $|R|$$>$ $''$ the inclination appears about $^{\circ}$ higher in the south-west than in the north-east."1013 Significant variations in inclination are also found as a function of azimuth aud radius in AL331 (see Draun 1991) aud may be in part attributable to the presence of spiral aruis., Significant variations in inclination are also found as a function of azimuth and radius in 31 (see Braun 1991) and may be in part attributable to the presence of spiral arms.1014 It has been pointed out already. that the distributious of the GGIIz conutimmun.ILL. and CO in refFIC.AIAPS.. and also the optical image (for optica nuages nof contaminated by radio contours. see e.g. Nakai 1989: Ehuouttie et al.," It has been pointed out already that the distributions of the GHz continuum, and CO in \\ref{FIG.MAPS}, and also the optical image (for optical images not contaminated by radio contours, see e.g. Nakai 1989; Elmouttie et al."1015 1997) show a conmuuon exteude enission ridee which is above the major axis at positive offsets. and below the major axis at negative offsets.," 1997) show a common extended emission ridge which is above the major axis at positive offsets, and below the major axis at negative offsets."1016 There are nian enission features associated with the ridge. arc he most prominent are listed in refTAB TILATANINIA..," There are many emission features associated with the ridge, and the most prominent are listed in \\ref{TAB.HI.MAXIMA}."1017 Several ciission peaks are locatec at COMMON major axis offsets. aud are prestunably relates plivsically.," Several emission peaks are located at common major axis offsets, and are presumably related physically."1018" The distribution shows clistiuctive features at cach eud of the galaxy. at offsets of 6207 and οδοί”,"," The distribution shows distinctive features at each end of the galaxy, at offsets of $''$ and $-580''$."1019 They extend away frou he major axis and resectable the aueential locations of outer trailing spiral arias of a highly inclined galaxy., They extend away from the major axis and resemble the tangential locations of outer trailing spiral arms of a highly inclined galaxy.1020" At the rorth-castern cud of the galaxy. which is moving away from us. the arm eudiug at the uear side extends around behind the plane. above the major axis. aud joius an iuncer disk at the location of tle eissiou features at offset ~250"","," At the north-eastern end of the galaxy, which is moving away from us, the arm ending at the near side extends around behind the plane, above the major axis, and joins an inner disk at the location of the emission features at offset $\sim-250''$."1021" At the south-western cucl. rotating owards us. the arm extends around he front of the galaxy. below the major axis. joining the iuner disk at the location of tle cussion peak at offse 230""."," At the south-western end, rotating towards us, the arm extends around the front of the galaxy, below the major axis, joining the inner disk at the location of the emission peak at offset $''$."1022 The o»roninen dust lane present in the optical image would vc associated with this arm., The prominent dust lane present in the optical image would be associated with this arm.1023 This interpretation accounts or the auti-svnunetrv of the immer emission ridee (see also Dahlem et al., This interpretation accounts for the anti-symmetry of the inner emission ridge (see also Dahlem et al.1024 1993 for the immer part of the galaxy)., 1993 for the inner part of the galaxy).1025" It is noteworthy that stroug IRAS point sources are ocated at R~210"" on cach side of the uucleus.", It is noteworthy that strong IRAS point sources are located at $R\sim240''$ on each side of the nucleus.1026" At these ocations he PCO? D//7CO(1 line inteusitv ratio ἵνα, ", At these locations the $^{12}$ $^{12}$ line intensity ratio is $>$ 1.1027These features are consisteut with regions of cuhanced star formation. which may reside in spiral aris viewed near their taugeutial point.," These features are consistent with regions of enhanced star formation, which may reside in spiral arms viewed near their tangential point."1028" The interpretation could be extended to include the regions of enhanced cussion at offsets of about 120"" and 1207 as additional tangential locatious of the two spiral arms.", The interpretation could be extended to include the regions of enhanced emission at offsets of about $''$ and $''$ as additional tangential locations of the two spiral arms.1029" Then oue ari would extend through offsets Γον 250"" aud 120"". aud the other through oMets 58a 230 and 120,"," Then one arm would extend through offsets $''$, $''$ and $''$, and the other through offsets $''$, $''$ and $''$."1030 Tuterpreting the distributious in in terms of a feo-uin spiral structure. we can test whether the designated tangential locations are consistent with an overall regular spiral pattern.," Interpreting the distributions in \\ref{FIG.MAPS} in terms of a two-arm spiral structure, we can test whether the designated tangential locations are consistent with an overall regular spiral pattern."1031 We therefore consider a spiral described by R=Ry«exped. with the pitch angle c in degrees given by e=tauc and the azimuth anele ) in radians.," We therefore consider a spiral described by $R=R_0 \times \exp a\vartheta$, with the pitch angle $\psi$ in degrees given by $a=\tan \psi$ and the azimuth angle $\vartheta$ in radians."1032 Cousideration of the two inner tangential offsets for cach arm vields c=127 aud37., Consideration of the two inner tangential offsets for each arm yields $\psi=12\degr$ and.1033 For a pair of positions consisting of the outermost xd central offsets. c=16° ffor both arms.," For a pair of positions consisting of the outermost and central offsets, $\psi=16$ for both arms."1034 The results are plausible two major spiral arnis with pitch angles of about 120013° Hu the mner region aud 16 in the outer region., The results are plausible – two major spiral arms with pitch angles of about $12-13$ in the inner region and $16$ in the outer region.1035" They are consistent with aris iu other spiral galaxies (6.ο, Pucrari Dottor 1992) and might also be detectable by near infrared imagine.", They are consistent with arms in other spiral galaxies (e.g. Puerari Dottori 1992) and might also be detectable by near infrared imaging.1036 A conmmonly used relation to describe the rotation curve of a galaxy is (see 226 aud 28 of Draudt et al., A commonly used relation to describe the rotation curve of a galaxy is (see 26 and 28 of Brandt et al.1037 1960). where 1 Is a ineasure of the steepness of the rotation curve and Hs the radius at which the maxima rotation velocity," 1960), where $n$ is a measure of the steepness of the rotation curve and is the radius at which the maximum rotation velocity"1038estimates of the lifetimes of the evolutionary stages of young stars strongly favour episodic accretion lasting for ~LOO.000 years (see?.andreferencestherein)...,"estimates of the lifetimes of the evolutionary stages of young stars strongly favour episodic accretion lasting for $\sim100,000$ years \cite[see][and references1039therein]{baraffe09}."1040" The heavy accretion rates in the assembly phase drive stars away from thermal equilibrium,", The heavy accretion rates in the assembly phase drive stars away from thermal equilibrium.1041 Luminosity spreads are introduced because stars accrete different actions of their tinal mass during this phase: stars which accrete a large fraction of their final mass are further from. thermal equilibrium. and are much smaller than stars which aecrete a small Traction of their tinal mass during this phase.," Luminosity spreads are introduced because stars accrete different fractions of their final mass during this phase; stars which accrete a large fraction of their final mass are further from thermal equilibrium, and are much smaller than stars which accrete a small fraction of their final mass during this phase."1042 We assume that all stars emerge from the assembly phase ocked to their dises. and at similar rotation rates. and consider he ensuing spin-u» towards the main sequence once disc-locking ceases.," We assume that all stars emerge from the assembly phase locked to their discs, and at similar rotation rates, and consider the ensuing spin-up towards the main sequence once disc-locking ceases."1043 Stars whic1 rapidly accrete large fractions of their mass during the assemby phase are already quite small. and undergo imited contraction and spin up as they approach the main sequence.," Stars which rapidly accrete large fractions of their mass during the assembly phase are already quite small, and undergo limited contraction and spin up as they approach the main sequence."1044 A star Wlich accretes a smaller fraction of its final mass during the assembly phase undergoes much more contraction. and jenee spins up significantly as it approaches the main sequence.," A star which accretes a smaller fraction of its final mass during the assembly phase undergoes much more contraction, and hence spins up significantly as it approaches the main sequence."1045 Case A thus naturally produces small. faint stars which are rotating more slowly than their larger. brighter counterparts.," Case A thus naturally produces small, faint stars which are rotating more slowly than their larger, brighter counterparts."1046 In this scenario. we assume that the stars which accrete large actions of their final mass during the assembly phase are likely to be those in dense environments surrounded by massive discs.," In this scenario, we assume that the stars which accrete large fractions of their final mass during the assembly phase are likely to be those in dense environments surrounded by massive discs."1047 We ‘urther assume that these stars are more likely to emerge from the assembly phase surrounded by massive dises which will in turn be onger-lived and supply the pre-main-sequence star with material at a higher accretion rate., We further assume that these stars are more likely to emerge from the assembly phase surrounded by massive discs which will in turn be longer-lived and supply the pre-main-sequence star with material at a higher accretion rate.1048 These stars are most likely to remain ocked to their dises and will show slow rotation rates., These stars are most likely to remain locked to their discs and will show slow rotation rates.1049 Since they experienced heavy assembly phases. they are also the smallest. uintest stars.," Since they experienced heavy assembly phases, they are also the smallest, faintest stars."1050" By contrast. stars which are rotating rapidly at a few Myr must. according to the dise-locking model. have been released from heir discs after ~10"" yr."," By contrast, stars which are rotating rapidly at a few Myr must, according to the disc-locking model, have been released from their discs after $\sim10^5$ yr."1051 The most rapidly rotating stars in an association are therefore those stars with shortest dise lifetimes., The most rapidly rotating stars in an association are therefore those stars with shortest disc lifetimes.1052 Under scenario B. these stars also accreted a small fraction of their tinal mass during the assembly phase and are therefore the largest. brightest stars.," Under scenario B, these stars also accreted a small fraction of their final mass during the assembly phase and are therefore the largest, brightest stars."1053 Some authors have suggested (e.g.22). that. contrary to the results of ? phases of rapid accretion can dramaticallyincrease the size (and luminosity) of a young star.," Some authors have suggested \cite[e.g.][]{hartmann96,kley99} that, contrary to the results of \cite{baraffe09}1054 phases of rapid accretion can dramatically the size (and luminosity) of a young star."1055 Such a star would look much younger in à CMD than a non-acereting counterpart with the same initial mass and radius., Such a star would look much younger in a CMD than a non-accreting counterpart with the same initial mass and radius.1056 The accreting stars. Kelvin-Helmholtz timescale drops as a result of the increased size and luminosity., The accreting star's Kelvin-Helmholtz timescale drops as a result of the increased size and luminosity.1057 Thus. over a given time period the accreting star contracts and spins up more than it's non-accreting counterpart.," Thus, over a given time period the accreting star contracts and spins up more than it's non-accreting counterpart."1058 Thus. some time after the accretion event. the accreting star looks younger. and will be rotating more rapidly than. the non-accreting star.," Thus, some time after the accretion event, the accreting star looks younger, and will be rotating more rapidly than, the non-accreting star."1059 In other words. such a scenario can also explain the correlations presented here.," In other words, such a scenario can also explain the correlations presented here."1060 In summary. there are three plausible scenarios which explain the correlation between luminosity and rotation.," In summary, there are three plausible scenarios which explain the correlation between luminosity and rotation."1061 Each starts from a co-eval population into which luminosity spreads are injected through varying accretion histories., Each starts from a co-eval population into which luminosity spreads are injected through varying accretion histories.1062 We therefore argue that the observed correlation between luminosity and rotation is strong evidence that luminosity spreads in star forming region are primarily caused by a range of accretion histories. instead of a spread in ages.," We therefore argue that the observed correlation between luminosity and rotation is strong evidence that luminosity spreads in star forming region are primarily caused by a range of accretion histories, instead of a spread in ages."1063 In principle. it ought to be possible to determine if accretion-induced luminosity spreads can explain the full extent of the observed luminosity spreads in star forming regions by simultaneously modelling the affects of accretion on the stellar luminosity and spin rate.," In principle, it ought to be possible to determine if accretion-induced luminosity spreads can explain the full extent of the observed luminosity spreads in star forming regions by simultaneously modelling the affects of accretion on the stellar luminosity and spin rate."1064 The difficulty with such an analysis at present lies in the fact we do not know how accretion at a given rate effects the spin of the central object., The difficulty with such an analysis at present lies in the fact we do not know how accretion at a given rate effects the spin of the central object.1065 Proper modelling of this result will therefore require a fuller understanding of the physical mechanisms) by which the star-dise interaction governs stellar rotation., Proper modelling of this result will therefore require a fuller understanding of the physical mechanism(s) by which the star-disc interaction governs stellar rotation.1066 In addition. some of the scatter seen in figure | results from variabiity. extinction and binarity.," In addition, some of the scatter seen in figure \ref{fig:age_sel} results from variability, extinction and binarity."1067 This scatter might also explain some «of the substantial overlap between the period distribution of bright and faint samples., This scatter might also explain some of the substantial overlap between the period distribution of bright and faint samples.1068 Any analysis would have to include a careful reatment of these confounding factors., Any analysis would have to include a careful treatment of these confounding factors.1069 Can any other mechanisms plausibly explain the sense of the correlation we observe here?, Can any other mechanisms plausibly explain the sense of the correlation we observe here?1070 One potential mechanism is the effect of magnetic activity on stellar radius., One potential mechanism is the effect of magnetic activity on stellar radius.1071 Observations of low-mass stars in eclipsing binaries show that they are over-sized by some 5— percent (see?.forareview).., Observations of low-mass stars in eclipsing binaries show that they are over-sized by some 5--10 percent \cite[see][for a review]{ribas06}.1072 Several authors have argued that this could be the result of magnetic activity (22).. and ? showed that this discrepancy could be explained by magnetic effects. including starspots.," Several authors have argued that this could be the result of magnetic activity \citep{lopez-morales07,1073 ribas08}, and \cite{chabrier07} showed that this discrepancy could be explained by magnetic effects, including starspots."1074 Since pre-main-sequence stars are magnetically highly active (e.g.2) it is plausible this mechanism operates in pre-main-sequence stars too., Since pre-main-sequence stars are magnetically highly active \citep[e.g.][]{donati10} it is plausible this mechanism operates in pre-main-sequence stars too.1075 We can speculate that the influence of magnetic fields on stellar structure might cause a correlation similar in to that presented in this paper., We can speculate that the influence of magnetic fields on stellar structure might cause a correlation similar in to that presented in this paper.1076 The effect of starspot coverage is to increase the stellar radius and reduce the effective temperature. at roughly constant luminosity (2)..," The effect of starspot coverage is to increase the stellar radius and reduce the effective temperature, at roughly constant luminosity \citep{chabrier07}."1077 If the lower effective temperature produces redder V-I colour. and if rapid rotators have larger spot coverage than slower rotators. this could explain the correlation observed here.," If the lower effective temperature produces redder V-I colour, and if rapid rotators have larger spot coverage than slower rotators, this could explain the correlation observed here."1078 However. neither of these conditions are likely to be satistied.," However, neither of these conditions are likely to be satisfied."1079 So far. there is little evidence for a link between rotation and activity for pre-main-sequence stars ?:: it is likely that most pre-main-sequence stars show saturated levels of activity across a wide range of rotation rates.," So far, there is little evidence for a link between rotation and activity for pre-main-sequence stars \cite{scholz07}; it is likely that most pre-main-sequence stars show saturated levels of activity across a wide range of rotation rates."1080 Even if rapid rotators did have higher spot coverages. it is far from clear that the ensuing drop in effective temperature would cause a change in V-I colour.," Even if rapid rotators did have higher spot coverages, it is far from clear that the ensuing drop in effective temperature would cause a change in V-I colour."1081 At the typical effective temperatures within our sample (Thur~3500 KK). a cool starspot reduces both the V-band and I-band flux. and can leave V-T unchanged.," At the typical effective temperatures within our sample $_{\rm eff} \sim10823500$ K), a cool starspot reduces both the V-band and I-band flux, and can leave V-I unchanged."1083 Good evidence that this in fact the case comes from the CMD of intermediate age clusters like NGC 2547 (e.g.2).. which have a very tightly defined pre-main-sequence locus in a V. V-I CMD. and contain many stars with saturated levels of magnetic activity (2)..," Good evidence that this in fact the case comes from the CMD of intermediate age clusters like NGC 2547 \citep[e.g.][]{jeffries04}, which have a very tightly defined pre-main-sequence locus in a V, V-I CMD, and contain many stars with saturated levels of magnetic activity \citep{jeffries06}."1084 Therefore. we believe it is unlikely that starspots are the origin of the correlation presented within this paper.," Therefore, we believe it is unlikely that starspots are the origin of the correlation presented within this paper."1085 We have presented an analysis of the rotation of young stars in the associations Cepheus OB3b. NGC 2264. NGC 2362 and the Orion Nebula Cluster (ONC).," We have presented an analysis of the rotation of young stars in the associations Cepheus OB3b, NGC 2264, NGC 2362 and the Orion Nebula Cluster (ONC)."1086 The rotation rate shows a significant correlation with position in a CMD. in the sense that stars with below average luminosity are rotating more slowly than stars with above average luminosity.," The rotation rate shows a significant correlation with position in a CMD, in the sense that stars with below average luminosity are rotating more slowly than stars with above average luminosity."1087 If position within the CMD is interpreted as being due to genuine age spreads within a cluster. then the implication is that the youngest stars in the cluster (those. with the largest moments of inertia and highest likelihood of ongoing accretion) are the most rapidly rotating.," If position within the CMD is interpreted as being due to genuine age spreads within a cluster, then the implication is that the youngest stars in the cluster (those with the largest moments of inertia and highest likelihood of ongoing accretion) are the most rapidly rotating."1088 Such a result is in conflict, Such a result is in conflict1089(Sellgrenetal.1983:Sellgren1984): vibrational fluorescence of many overtone bands and combination bands of PAH molecules blended together to form a pseudo-continuum (Léger&Puget1984:Allamandolaetal.1985):: continuous electronic fluorescence from PAH molecules (Allamandolaetal.1989):; and continuous photoluminescent electron-band transitions of solid-state particles. most notably HAC grains or carbon nanoparticles 2001).,"\citep{SWD83,Se84}; vibrational fluorescence of many overtone bands and combination bands of PAH molecules blended together to form a pseudo-continuum \citep{LP84,ATB85}; continuous electronic fluorescence from PAH molecules \citep{ATB89}; and continuous photoluminescent electron-band transitions of solid-state particles, most notably HAC grains or carbon nanoparticles \citep{DW88,Du88,Du01}."1090. Both the stochastically heated grains and the PAH molecules are proposed to have a size of ~ 1 nm. with 50 to 100 constituent atoms.," Both the stochastically heated grains and the PAH molecules are proposed to have a size of $\sim$ 1 nm, with 50 to 100 constituent atoms."1091 Photoluminescence from carbon nanoparticles would require a range of 220 to 260 atoms per nanoparticle to provide the correct bandgap energy (cf.Seahra&Duley1999;'2001) to explain the observed 2.0-2.2 econtinuum.," Photoluminescence from carbon nanoparticles would require a range of 220 to 260 atoms per nanoparticle to provide the correct bandgap energy \citep[cf.][]{SD99,Du01} to explain the observed 2.0-2.2 continuum."1092 While the origin of the 2 ccontinuum emission is uncertain. the assignment of the 3.29 IIEF to the stretching mode of aromatic C—H is generally agreed upon among the community.," While the origin of the 2 continuum emission is uncertain, the assignment of the 3.29 IEF to the stretching mode of aromatic H is generally agreed upon among the community."1093 Proposed laboratory analogs or identifications for the IEF earrier(s) mainly involve hydrocarbon species: carbyne (Webster1980):: an aromatic C—H stretch (Duley&Williams1981): PAH molecules (Léger&Puget1984;Allanandolaetal.1985.1989): quenched carbonaceous composite. amorphous carbon. or coal with varying degrees of hydrogenation (Sakataetal.1984.1987;Blanco.Bussoletti. 1989):; partially or fully hydrogenated fullerenes (Webster1992.1993;Stoldtetal. 2001): nanodiamonds (Guillois.Ledoux.&Reynaud1999:Joresd'Hendecourt2000:DuleyGrishko2001):: nonlinear pphotoexcitation (Glownia&Sorokin200001: and Rydberg matter (Holnlid2000.2001)..," Proposed laboratory analogs or identifications for the IEF carrier(s) mainly involve hydrocarbon species: carbyne \citep{We80}; ; an aromatic H stretch \citep{DW81}; PAH molecules \citep{LP84,ATB85,ATB89}; quenched carbonaceous composite, amorphous carbon, or coal with varying degrees of hydrogenation \citep*{SWT84,SWO87,BBC88,Du88,PCG89}; partially or fully hydrogenated fullerenes \citep{We92,We93,SMC01}; nanodiamonds \citep*{GLR99,JD00,DG01}; nonlinear photoexcitation \citep{GS00}; and Rydberg matter \citep{Ho00,Ho01}."1094 Neutral or ionized gas-phase warm (~1000 K) PAH molecules (seereviewsbyAllamandolaetal.1989:Puget&Léger1989;Salama1999) are currently the leading candidate carrier for the 3.29 HEF. in the view of many researchers.," Neutral or ionized gas-phase warm $\sim$ 1000 K) PAH molecules \citep[see reviews by][]1095{ATB89,PL89,Sa99} are currently the leading candidate carrier for the 3.29 IEF, in the view of many researchers."1096 Our high-resolution images demonstrate that the distributions of the 3.294 IIEF emission and the 2 ccontinuum emission are spatially distinct in ((Fig. 6))., Our high-resolution images demonstrate that the distributions of the 3.29 IEF emission and the 2 continuum emission are spatially distinct in (Fig. \ref{f6}) ).1097 The 2 ccontinuum emission ts strongest in the σσας close to the star. and is brightest at a projected distance of - 50 mpe from the star. although faint 2 ccontinuum emission Is also seen in the ffilaments at a projected distance of ~ 100 mpe from the star.," The 2 continuum emission is strongest in the gas close to the star, and is brightest at a projected distance of $\sim$ 50 mpc from the star, although faint 2 continuum emission is also seen in the filaments at a projected distance of $\sim$ 100 mpc from the star."1098 On the other hand. the 3.294 HEF emission is strongest in the ffilaments. with a projected separation from the peak of the 2 ccontinuum emission of ~50 mpe.," On the other hand, the 3.29 IEF emission is strongest in the filaments, with a projected separation from the peak of the 2 continuum emission of $\sim$ 50 mpc."1099 Somewhat fainter 3.294 HEF emission. however. is also detected in the vicinity of the peak 2 ccontinuum emission.," Somewhat fainter 3.29 IEF emission, however, is also detected in the vicinity of the peak 2 continuum emission."1100 This suggests that the 3.29 IIEF carriers and the 2 ccontinuum emitters either are distinct and/or are excited by different physical mechanisms., This suggests that the 3.29 IEF carriers and the 2 continuum emitters either are distinct and/or are excited by different physical mechanisms.1101 Molecular hydrogen ts both excited by and photodissociated by photons between 91.2 nm and 110 nm., Molecular hydrogen is both excited by and photodissociated by photons between 91.2 nm and 110 nm.1102 We observe both 2.4m ccontinuum emission and 3.29 HEF emission in the eclump near the 2 ccontinuum emission peak. and in the ffilaments. although their relative intensities are different.," We observe both 2 continuum emission and 3.29 IEF emission in the clump near the 2 continuum emission peak, and in the filaments, although their relative intensities are different."1103 This suggests that both the 2 ccontinuum emitters and the 3.29 IIEF carriers. whether or not they aredistinct. should be able to survive in aand warm H»..," This suggests that both the 2 continuum emitters and the 3.29 IEF carriers, whether or not they aredistinct, should be able to survive in and warm ."1104Using Eqns.,Using Eqns.1105" | and 2 one can show that, K*(W), of the linearly combined map follows, where W denotes a 1xn; vector whose f"" entry is given by wy and T=MT "," \ref{K} and \ref{lc} one can show that, $\mathcal K^c({\bf W})$, of the linearly combined map follows, where $\bf W$ denotes a $1 \times n_b$ vector whose $f^{th}$ entry is given by $w_f$ and ${\bf T} = \sum_{j=1}^{n} {\bf T}_j$ ."1106"Here T; is a npXn; symmetric matrix for pixel j, = where ATy; denotes the temperature at Tj;p,pixel j ofAT;j;ATp; frequency index f after the mean temperature corresponding to this frequency has been subtracted from actual pixel temperature."," Here ${\bf T}_j$ is a $n_b \times n_b$ symmetric matrix for pixel $j$, ${\bf T}_{j(ff')} = \Delta \bar T_{fj} \Delta \bar T_{f'j}$ where $\Delta \bar T_{fj}$ denotes the temperature at pixel $j$ of frequency index $f$ after the mean temperature corresponding to this frequency has been subtracted from actual pixel temperature."1107" In principle, the solution for W for minimum X*(W) satisfying our conditions can be obtained by employing a Lagrange's undetermined multiplier approach."," In principle, the solution for $\bf W$ for minimum $\mathcal K^c({\bf W})$ satisfying our conditions can be obtained by employing a Lagrange's undetermined multiplier approach."1108" However, because of nontrivial nature of dependency of K* on W we find that such an approach is not feasible for our problem."," However, because of nontrivial nature of dependency of $\mathcal K^c$ on $\bf W$ we find that such an approach is not feasible for our problem."1109" Instead, we find the minimum of K*(W) by invoking a non-linear search algorithm due to Powell."," Instead, we find the minimum of $\mathcal K^c({\bf W})$ by invoking a non-linear search algorithm due to Powell."1110 The distributions of pixel temperatures due to diffuse galactic foregrounds are shown in top panel of Fig. 1.., The distributions of pixel temperatures due to diffuse galactic foregrounds are shown in top panel of Fig. \ref{Kvals}.1111" Each of these foreground distributions is strongly asymmetric and exhibits a long tail towards positive temperature direction indicating a variation slower than ~eT, which is the case for a Gaussian distribution."," Each of these foreground distributions is strongly asymmetric and exhibits a long tail towards positive temperature direction indicating a variation slower than $\sim e^{-T^2}$, which is the case for a Gaussian distribution."1112" The peak for the synchrotron distribution shows that at 23GHz most likely contamination due to synchrotron occurs at a temperature ~75j:K, although contaminations at high (>400μΚ) and low (e.g., as low as «254K) pixel temperature are also likely."," The peak for the synchrotron distribution shows that at $23$ GHz most likely contamination due to synchrotron occurs at a temperature $\sim 75\mu K$, although contaminations at high $> 400 \mu K$ ) and low (e.g., as low as $ < 25\mu K$ ) pixel temperature are also likely."1113 How does K vary with foreground contamination in CMB maps at different WMAP frequencies?, How does $\mathcal K$ vary with foreground contamination in CMB maps at different WMAP frequencies?1114 To answer this question we generate 150 random full sky CMB maps using WMAP's LCDM power spectrum., To answer this question we generate $150$ random full sky CMB maps using WMAP's LCDM power spectrum.1115 With each of these random realization of CMB map we add WMAP's MEM foreground templates at various strengths., With each of these random realization of CMB map we add WMAP's MEM foreground templates at various strengths.1116 The resulting behavior of the K with foreground strength is shown in Fig., The resulting behavior of the $\mathcal K$ with foreground strength is shown in Fig.1117 1 for all WMAP frequency bands., \ref{Kvals} for all WMAP frequency bands.1118 For each band K increases as the amount of foreground contamination increases., For each band $\mathcal K$ increases as the amount of foreground contamination increases.1119" For K band the variation takes a shape of a plateau, characterized by a slow increase of K, as the foreground level reaches ~20% of its full level."," For K band the variation takes a shape of a plateau, characterized by a slow increase of $\mathcal K$, as the foreground level reaches $\sim 20\%$ of its full level."1120 For all bands K becomes more than 150 when all foregrounds are operative at their 100% level., For all bands $\mathcal K$ becomes more than $150$ when all foregrounds are operative at their $100\%$ level.1121 It is interesting to note that the Q band (not the K band which has the highest level of synchrotron and free free contamination) shows the largest K value among all the 5 bands at the maximum foreground strength., It is interesting to note that the Q band (not the K band which has the highest level of synchrotron and free free contamination) shows the largest $\mathcal K$ value among all the $5$ bands at the maximum foreground strength.1122 We validate the methodology by performing Monte-Carlo simulations., We validate the methodology by performing Monte-Carlo simulations.1123" We use MEM foreground maps for synchrotron, free free and thermal dust available from LAMBDA website."," We use MEM foreground maps for synchrotron, free free and thermal dust available from LAMBDA website."1124 These maps are provided in a common resolution of 1? and at pixel resolution parameter nside=256 in antenna millikelvin temperature unit., These maps are provided in a common resolution of $1^\circ$ and at pixel resolution parameter $nside = 256$ in antenna millikelvin temperature unit.1125 We upgrade the pixel resolution of each map to nside=512 and convert them to thermodynamic microkelvin unit., We upgrade the pixel resolution of each map to $nside = 512$ and convert them to thermodynamic microkelvin unit.1126 We add the composite foreground map of each WMAP frequency with a random realization of CMB compatible to LCDM model to make foreground contaminated CMB maps at each of the WMAP frequencies., We add the composite foreground map of each WMAP frequency with a random realization of CMB compatible to LCDM model to make foreground contaminated CMB maps at each of the WMAP frequencies.1127" Finally, we mask the position of the known point sources using the WMAP's 7 year point source mask."," Finally, we mask the position of the known point sources using the WMAP's 7 year point source mask."1128 We develop a C code (hereafter GaussMap) to implement constrained Powell's conjugate gradient method., We develop a C code (hereafter ) to implement constrained Powell's conjugate gradient method.1129 We perform 200 Monte-Carlo simulations of foreground removal method., We perform $200$ Monte-Carlo simulations of foreground removal method.1130 From these simulations we find that the foreground removal is effective over almost all parts of the sky., From these simulations we find that the foreground removal is effective over almost all parts of the sky.1131" However, we find visible signature of some residual foreground emission in the inner plane of the galaxy."," However, we find visible signature of some residual foreground emission in the inner plane of the galaxy."1132 To find out the sky regions where the residual foreground could be significant compared to the expected CMB signal we subtract average of input CMB maps from the average of foreground cleaned maps., To find out the sky regions where the residual foreground could be significant compared to the expected CMB signal we subtract average of input CMB maps from the average of foreground cleaned maps.1133 Then we form an initial mask by assigning zero values to all pixels with absolute temperature values more than 204K of this map and unity at all other pixels., Then we form an initial mask by assigning zero values to all pixels with absolute temperature values more than $20\mu$ K of this map and unity at all other pixels.1134 This mask contains a set of scattered pixels in the inner galactic plane., This mask contains a set of scattered pixels in the inner galactic plane.1135 To remove these pixels we first smooth the initial mask by a Gaussian window of 1?., To remove these pixels we first smooth the initial mask by a Gaussian window of $1^\circ$.1136 We transform this smoothed mask to a new mask by assigning all pixels of smoothed mask with values greater than or equal to 0.9 to a new value of unity and the all other pixelsto zero., We transform this smoothed mask to a new mask by assigning all pixels of smoothed mask with values greater than or equal to $0.9$ to a new value of unity and the all other pixelsto zero.1137 To exclude position of the known point sources from the analysis we make the final mask multiplying this mask by the WMAP's point source mask., To exclude position of the known point sources from the analysis we make the final mask multiplying this mask by the WMAP's point source mask.1138 We call the resulting mask as G20 mask., We call the resulting mask as G20 mask.1139 This, This1140emitting regions as 48+L1 and 7S+19 mas respectively (see Paper I for a description of the method).,emitting regions as $48\pm11$ and $78\pm19$ mas respectively (see Paper I for a description of the method).1141 The large relative uncertainty in these sizes is a direct consequence of the high rms uncertainty per visibility at 22 11., The large relative uncertainty in these sizes is a direct consequence of the high rms uncertainty per visibility at 22 GHz.1142 The fluxes fron the VLA observations were determined by Gaussian source fitting using the routineJMETFT., The fluxes from the VLA observations were determined by Gaussian source fitting using the routine.1143 Phe measured IHuxes are given in Table L.., The measured fluxes are given in Table \ref{tab:fluxes}.1144 The final synthesized AMERLIN image at 5 Gllz is shown in Fig 1.., The final synthesized MERLIN image at 5 GHz is shown in Fig \ref{fig:MERLIN}.1145 The image reveals two components of emission. identified as INz and σι," The image reveals two components of emission, identified as $_5$ and $_5$."1146 In the MEBRLIN observation. the Hux and size of component Nz were determined by Gaussian model fitting of the visibility data.," In the MERLIN observation, the flux and size of component $_5$ were determined by Gaussian model fitting of the visibility data."1147 The derived diameter for Ns is 42£1 mas., The derived diameter for $_5$ is $42\pm1$ mas.1148 Gaussian fitting to the image cata were used for the source parameters of S given in Table 1., Gaussian fitting to the image data were used for the source parameters of S given in Table 1.1149 Qualitatively. the 1992. ALERLIN image is consistent with the 5-CGllz observation from 1995 April 29 (Paper 1) hough there is some evidence that Ns may have decreased in lux by ~3 mJy between 1992 anc 1995.," Qualitatively, the 1992 MERLIN image is consistent with the 5-GHz observation from 1995 April 29 (Paper I) though there is some evidence that $_5$ may have decreased in flux by $\sim3$ mJy between 1992 and 1995."1150 The tux of S- appears to have decreased between the two epochs., The flux of $_5$ appears to have decreased between the two epochs.1151 Llowever. he difference is only 2o. much less than the Se threshold vpically adopted: as evidence for variation.," However, the difference is only $2\sigma$, much less than the $5\sigma$ threshold typically adopted as evidence for variation."1152 Therefore. we adopt the mean value of 2.0+0.2 mJv for the flux of 85.," Therefore, we adopt the mean value of $2.0\pm0.2$ mJy for the flux of $_5$."1153 Variations in the total 5-Gilz emission from WIUII46 have en observed. using the WS over the last decade that are attributed to variations in the non-thermal component (Setia-Gunawan et al., Variations in the total 5-GHz emission from 146 have been observed using the WSRT over the last decade that are attributed to variations in the non-thermal component (Setia-Gunawan et al.1154 2000)., 2000).1155 Both our MEBRLIN 5-CLllz otal flux values are consistent with the WSR observations., Both our MERLIN 5-GHz total flux values are consistent with the WSRT observations.1156 Variability could account for the slightly higher 5-Cillz Hux at the epoch of the VLA observations., Variability could account for the slightly higher 5-GHz flux at the epoch of the VLA observations.1157 The positions of the components observed at 5 112 and 22 Cllz are quoted in Table 2.., The positions of the components observed at 5 GHz and 22 GHz are quoted in Table \ref{tab:positions}.1158 The absolute position of the northern component in the various observations was deduced. from the phase-reference only calibrated: images., The absolute position of the northern component in the various observations was deduced from the phase-reference only calibrated images.1159 Absolute position information is lost curing the sclf- process. though the relative position is preserved.," Absolute position information is lost during the self-calibration process, though the relative position is preserved."1160 These were deduced from the images shown in Fig., These were deduced from the images shown in Fig.1161 1. and Pie. 2.., \ref{fig:MERLIN} and Fig. \ref{fig:22GHz}.1162 The nominal resolution of A-conliguration at 22-Cillz observations is very similar to that of ALERLIN at 5 Gills. allowing direct. comparison of these data.," The nominal resolution of A-configuration at 22-GHz observations is very similar to that of MERLIN at 5 GHz, allowing direct comparison of these data."1163 At 22 Cllz. the VLA observations reveal two components No» and So». very similar in appearance to the AUERLIN 5-ClIz data.," At 22 GHz, the VLA observations reveal two components $_{22}$ and $_{22}$, very similar in appearance to the MERLIN 5-GHz data."1164 However. the relative positions of the two 22-CGllIz components show them to be significantly further apart than those from the ALERLIN 5-Cillz data. leading to the question of whether the 22-Cillz sources are the same as those observed at 5 Cllz.," However, the relative positions of the two 22-GHz components show them to be significantly further apart than those from the MERLIN 5-GHz data, leading to the question of whether the 22-GHz sources are the same as those observed at 5 GHz."1165" The brightness temperatures of Nos. Sez and S; are L610 EK. ~5000 E and ~4008 1 respectively. all consistent with an origin in a photo-ionized circumstellar envelope. where the photo-ionization equilibrium temperature is typically ~107 Ix. In contrast. this is about two orders of magnitude lower than the brightness temperature of 1.3:10"" Ix for Ns. which clearly indicates a non-thermal origin."," The brightness temperatures of $_{22}$ , $_{22}$ and $_5$ are $1.6\times10^4$ K, $\sim5000$ K and $\sim4000$ K respectively, all consistent with an origin in a photo-ionized circumstellar envelope where the photo-ionization equilibrium temperature is typically $\sim10^4$ K. In contrast, this is about two orders of magnitude lower than the brightness temperature of $1.3\times10^6$ K for $_5$, which clearly indicates a non-thermal origin."1166 The separation of S»» and No» (16248 at a position angle of 22 44°) is very close to that (168+31 mas at position angle 21 44°) of the optical components (No and So) observed with the LIST., The separation of $_{22}$ and $_{22}$ $162\pm8$ at a position angle of $22\pm4^\circ$ ) is very close to that $168\pm31$ mas at position angle $21\pm4^\circ$ ) of the optical components $_{\rm O}$ and $_{\rm O}$ ) observed with the HST.1167 There is no evidence of intrinsic proper motion in the source at. 22 Cllz in recent (1999) observations of the source CX. Fink. private communication).The coincidence of the optical and. 22-CGlLIz positions. the lack of evidence of intrinsic proper motion. and the thermal," There is no evidence of intrinsic proper motion in the source at 22 GHz in recent (1999) observations of the source (A. Fink, private communication).The coincidence of the optical and 22-GHz positions, the lack of evidence of intrinsic proper motion, and the thermal"1168well separated polarization spheres. cach of which coutains a static charee sumrounded by mauy medium charges. with au overall excess of the opposite charec.,"well separated polarization spheres, each of which contains a static charge surrounded by many medium charges, with an overall excess of the opposite charge."1169 When the heavy quarks are brought still closer to cach other. the polarization spheres begin to overlap |," When the heavy quarks are brought still closer to each other, the polarization spheres begin to overlap \cite{KZ-lat05}."1170 The overlapping spheres coutiuue to attract cach other. but this interaction uow has two componcuts and can no longer be described by a pure Debve-scereened poteutial.," The overlapping spheres continue to attract each other, but this interaction now has two components and can no longer be described by a pure Debye-screened potential."1171 On oue hand. there is the direct interaction between the Q aud the Q. which in the limit of sinall ¢ becomes just the Coulombic vacuum form ofr.," On one hand, there is the direct interaction between the $Q$ and the $\bar Q$, which in the limit of small $r$ becomes just the Coulombic vacuum form $\alpha/r$."1172 Ou the other haud. the charged constitucuts inside the overlapping polarization spheres also attract cach other directly. with a streneth determined by the deviation of the region from the state without a QQ pair.," On the other hand, the charged constituents inside the overlapping polarization spheres also attract each other directly, with a strength determined by the deviation of the region from the state without a $\Q$ pair."1173 Once the spheres no longer overlap. this interaction becomes by Crass’ lav just the Debye-screened Coulomb form with a reduced effective charge.," Once the spheres no longer overlap, this interaction becomes by Gauss' law just the Debye-screened Coulomb form with a reduced effective charge."1174 Iu order to determine the behavior of QQ binding iu a decoufined mecitim. we shall first consider the large and small distance linüts of the thermodvuamics potcutials.," In order to determine the behavior of $\Q$ binding in a deconfined medium, we shall first consider the large and small distance limits of the thermodynamics potentials."1175 Iu the limit of large QQ separation. for r>oc. we have two fully screened. and lence non-interacting charges.," In the limit of large $\Q$ separation, for $r \to \infty$, we have two fully screened and hence non-interacting charges."1176 Nevertheless. the thermodyvuamic potential differeuces £C aud 59 do not vanish: they specify the effect of the interaction of cach of the two independent charges with the medium.," Nevertheless, the thermodynamic potential differences $F,U$ and $S$ do not vanish: they specify the effect of the interaction of each of the two independent charges with the medium."1177 This is uot related, This is not related1178have systematically different (redshift dependent) SEDs.,have systematically different (redshift dependent) SEDs.1179" At fixed redshift the quasar apparent magnitude distribution is equivalent to the absolute magnitude distribution,M;."," At fixed redshift the quasar apparent magnitude distribution is equivalent to the absolute magnitude distribution,$M_i$."1180" The large density of objects inthem; versus z plane allows the control sample to be defined using magnitudes close to that of the target quasar, minimising the effect of any systematic magnitude-dependent SED changes."," The large density of objects inthe$m_i$ versus $z$ plane allows the control sample to be defined using magnitudes close to that of the target quasar, minimising the effect of any systematic magnitude-dependent SED changes."1181" The control spectrum was generated for each target quasar, by taking the median value (at each wavelength) of the 50 immediately brighter and 50 immediately fainter quasar spectra within a fixed redshift interval of Az—0.1 centred on the redshift of the targetquasar?."," The control spectrum was generated for each target quasar, by taking the median value (at each wavelength) of the 50 immediately brighter and 50 immediately fainter quasar spectra within a fixed redshift interval of $\Delta z=0.1$ centred on the redshift of the target."1182". The median was chosen instead of the mean, as it was less sensitive to flux outliers arising from intrinsic variation among quasar SEDs."," The median was chosen instead of the mean, as it was less sensitive to flux outliers arising from intrinsic variation among quasar SEDs."1183" A control spectrum is created for each of the 97719 quasars with associated aabsorbers, but only quasars without a detected aabsorber are allowed to contribute to the control spectra."," A control spectrum is created for each of the 719 quasars with associated absorbers, but only quasars without a detected absorber are allowed to contribute to the control spectra."1184" Using a fixed number of quasars to define the control spectrum, rather than a fixed magnitude interval, means that the control sample is not biased due to the systematic mismatch between the luminosity of the target quasar and median luminosity of the control quasars."," Using a fixed number of quasars to define the control spectrum, rather than a fixed magnitude interval, means that the control sample is not biased due to the systematic mismatch between the luminosity of the target quasar and median luminosity of the control quasars."1185" The flux ratio for an absorber is calculated by dividing the target quasar spectrum by the control spectrum in the quasar rest-frame, removing, statistically, the signature of the quasar SED."," The flux ratio for an absorber is calculated by dividing the target quasar spectrum by the control spectrum in the quasar rest-frame, removing, statistically, the signature of the quasar SED."1186 The resulting flux ratio spectrum is then moved to the absorber rest-frame (Fig. 2))., The resulting flux ratio spectrum is then moved to the absorber rest-frame (Fig. \ref{cap:medianext}) ).1187" We have used a parameterisation of the MW, LMC and SMC extinction curves, due to ?,, and fit a curve of the form: to the flux ratio spectrum, where Α(λ) is the extinction at a particular wavelength given by where Exν/ΕΗ.ν is given by ?, and Ry is the ratio of total to selective extinction."," We have used a parameterisation of the MW, LMC and SMC extinction curves, due to \citet{1992ApJ...395..130P}, and fit a curve of the form: to the flux ratio spectrum, where $A\left(\lambda \right)$ is the extinction at a particular wavelength given by where $E_{ \lambda - V }/ E_{B - V}$ is given by \citeauthor{1992ApJ...395..130P}, and $R_{V}$ is the ratio of total to selective extinction."1188" We have adopted R, 3.0, which is representative of the value in the MW andS"," We have adopted $R_{v}=3.0$ , which is representative of the value in the MW and."1189"MC?.. Fo and the reddening parameter E(B—V) are left as free parameters in the fit, which is carried out using the non-linear ‘Levenburg-Marquardt’ algorithm (?).."," $F_{0}$ and the reddening parameter $E(B-V)$ are left as free parameters in the fit, which is carried out using the non-linear `Levenburg-Marquardt' algorithm \citep{marquardt:431}."1190" The wavelength intervals corresponding to the strong telluric sky emission lines at AA5578.5,6301.7, and to the prominent absorption ofFeIL,AlIL, AIIIL, MgL, CaIL, which may be present inthe absorber spectrum, are excluded from the fit."," The wavelength intervals corresponding to the strong telluric sky emission lines at $\lambda\lambda5578.5,6301.7$, and to the prominent absorption of, , , which may be present inthe absorber spectrum, are excluded from the fit."1191hot columns or pixels in the CCD detectors. which require extremely accurate calibration nmeasurenienis for a proper modeling (e.g.Cagnonietal.2003).,"hot columns or pixels in the CCD detectors, which require extremely accurate calibration measurements for a proper modeling \citep[e.g.][]{cag03}."1192. Current. RGS calibration uncertainties are as accurate as e5—1056 between 7 and 36 and. as à consequence. false absorption/enmission features wilh such relative intensities. are expected in the RGS spectra in physical units. in proximitv of the known instrumental features.," Current RGS calibration uncertainties are as accurate as $\sim 5-10$ between 7 and 36 and, as a consequence, false absorption/emission features with such relative intensities, are expected in the RGS spectra in physical units, in proximity of the known instrumental features."1193 The strongest resonant absorption lines from neutral and/or highly ionized O and Ne. [all im wavelength ranges d.e. 13-14À.. 18-20À.. 20-24 A)) in which RGS-2 spectra either do not exist. (20-24A.. due to the failure of a CCD chip) or contain strong line-like shaped instrumental features (seeCagnonietal.2003).," The strongest resonant absorption lines from neutral and/or highly ionized O and Ne, fall in wavelength ranges (i.e. 13-14, 18-20, 20-24 ) in which RGS-2 spectra either do not exist (20-24, due to the failure of a CCD chip) or contain strong line-like shaped instrumental features \citep[see][]{cag03}."1194. Therefore I rely on RGS-1 spectra. which. instead are relatively instrmental-[eature-Iree in these wavelength ranges. and use RGS-2 to double check the reality of a line. when possible. ancl to cover the 10.5-14.2 region. where RGS-1 has a adled CCD chip.," Therefore I rely on RGS-1 spectra, which, instead are relatively instrumental-feature-free in these wavelength ranges, and use RGS-2 to double check the reality of a line, when possible, and to cover the 10.5-14.2 region, where RGS-1 has a failed CCD chip."1195 I also restrict our analysis to the first order spectra only., I also restrict our analysis to the first order spectra only.1196 ] reprocessed the data using (SAS) version 5.3.0 and the latest calibration files as of December 3. 2002.," I reprocessed the data using (SAS) version 5.3.0 and the latest calibration files as of December 3, 2002."1197 Since the wavelength: calibration of XMM erating spectra strongly depends on the position of the Oth order. I used the VLBI position as centroid of the Oth order source (Maetal.1998).," Since the wavelength calibration of XMM grating spectra strongly depends on the position of the 0th order, I used the VLBI position as centroid of the 0th order source \citep{ma98}."1198. Extraction regions. lor source and background. were chosen to be. respectively. within the and outside the of the PSF.," Extraction regions, for source and background, were chosen to be, respectively, within the and outside the of the PSF."1199 To exclude high particle background periods caused by solar activitv. I extracted the background lighteurves from CCD-9 ancl excluded. all the time intervals for which the background count rate was higher than 1.5x10?oE count !.," To exclude high particle background periods caused by solar activity, I extracted the background lightcurves from CCD-9 and excluded all the time intervals for which the background count rate was higher than $1.5 \times 10^{-3}$ count $^{-1}$."1200 The net exposures [or each observation are reported in Table 1., The net exposures for each observation are reported in Table 1.

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