ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 The best-fitting quadratie ephemeris calculated is: and is shown in Fig. 3.., The best-fitting quadratic ephemeris calculated is: and is shown in Fig. \ref{fig:ephem}.3 Xdding a cubic term had little ellect on the quality of the fit and is thus not done., Adding a cubic term had little effect on the quality of the fit and is thus not done.4 Note that this gives a slightly longer period than Mason (1997). and a smaller value for the period change.," Note that this gives a slightly longer period than Mason (1997), and a smaller value for the period change."5 We extractedsource. anc background. spectra. from. the, We extractedsource and background spectra from the6Consequently. the flux associated to the measured photometric quantity can be written as the dot product of the original flux distribution. /(À;) and a weighting function. so that each column of the sensing matrix ® in Eq. (1)),"Consequently, the flux associated to the measured photometric quantity can be written as the dot product of the original flux distribution $f(\lambda_i)$ and a weighting function, so that each column of the sensing matrix $\mathbf{\Phi}$ in Eq. \ref{eq:sensing}) )"7 is given bv: The sparsity constraint of (he spectrum is fulfilled automatically when using a principal component decomposition. with the additional advantage of knowing exactly which coefficients ol (he sparse vector a are non-zero.," is given by: The sparsity constraint of the spectrum is fulfilled automatically when using a principal component decomposition, with the additional advantage of knowing exactly which coefficients of the sparse vector $\mathbf{a}$ are non-zero."8 Therefore. the solution of the problem given by Eq. (3))," Therefore, the solution of the problem given by Eq. \ref{eq:sensing2}) )"9 is simpler than the full CS problem in which the non-zero elements of a have to be identified., is simpler than the full CS problem in which the non-zero elements of $\mathbf{a}$ have to be identified.10 Consequently. the solution to Eq. (3))," Consequently, the solution to Eq. \ref{eq:sensing2}) )"11 is given by the sparse vector that minimizes the following f5-norm: In other words. welook for the sparse vector a with the first AV elements different [rom zero aud the rest set to zero that minimizes (he square difference between (he photonmetric flix on the g. r aud / fillers aud the ones reconstructed using (hie previous formalism. where the [ας is obtained as a linear combination of ἐν principal components.," is given by the sparse vector that minimizes the following $\ell_2$ -norm: In other words, welook for the sparse vector $\mathbf{a}$ with the first $K$ elements different from zero and the rest set to zero that minimizes the square difference between the photometric flux on the $g$, $r$ and $i$ filters and the ones reconstructed using the previous formalism, where the flux is obtained as a linear combination of $K$ principal components."12 We now develop in more detail the steps to be followed., We now develop in more detail the steps to be followed.13 Assume that the signal of interest. F(A) ean be written as a linear combination of A (sparsity) PCA basis functions D;(À). so that: The measurement process produces the following linear combinations: where Af is (he number of wavelength points. NV is the number of measurements ancl the ®;; ave the matrix elements of the sensing matrix 9. given in Eq. (3)).," Assume that the signal of interest $F(\lambda)$ can be written as a linear combination of $K$ (sparsity) PCA basis functions $B_i(\lambda)$, so that: The measurement process produces the following linear combinations: where $M$ is the number of wavelength points, $N$ is the number of measurements and the $\Phi_{ij}$ are the matrix elements of the sensing matrix $\mathbf{\Phi}$ , given in Eq. \ref{eq:sensing_matrix_final}) )."14 Plugging Eq. (10)), Plugging Eq. \ref{eq:develop}) )15 into Eq. (11)).," into Eq. \ref{eq:sensing_linear_combination}) ),"16 we end up with:, we end up with:17for some function q;(r). then the cross power spectrum. will be Η we wish to caleulate the cross power of & between two redshifts. then we see by comparing equations (10)) and (15)) that we do have two projections of the necessary form. with q; given by so we therefore obtain (noting that. the two-point statistics of α and  agree. c.g. Blandford et al 19911. where (is the angular wavenumber.,"for some function $q_i(r)$, then the cross power spectrum will be If we wish to calculate the cross power of $\kappa$ between two redshifts, then we see by comparing equations \ref{eq:kappa}) ) and \ref{eq:pi}) ) that we do have two projections of the necessary form, with $q_i$ given by so we therefore obtain (noting that the two-point statistics of $\kappa$ and $\gamma$ agree, e.g. Blandford et al 1991), where $\ell$ is the angular wavenumber."18 In the case where we wish to examine the power of the shear at one particular redshift. we can simplify this to We can obtain corresponding cross-correlation functions for shears at two clilferent redshifts 24. 22.," In the case where we wish to examine the power of the shear at one particular redshift, we can simplify this to We can obtain corresponding cross-correlation functions for shears at two different redshifts $z_1$ , $z_2$."19" We will use three diferent correlation functions: C, represents (4-7). where ut represents the first shear component of two galaxies. in a coordinate frame where zero position angle lies along the line joining the galaxies (e.g. Bacon et al 2003)."," We will use three different correlation functions: $C_1$ represents $\langle \gamma_1^a \gamma_1^b20\rangle$, where $\gamma_1^{a,b}$ represents the first shear component of two galaxies, in a coordinate frame where zero position angle lies along the line joining the galaxies (e.g. Bacon et al 2003)."21 C2 represents (5555‘1 sand C=Cy|€».," $C_2$ represents $\langle \gamma_2^a \gamma_2^b \rangle$, and $C=C_1+C_2$."22 Given these definitions. the correlation functions are simple transforms of the power: These are the 3-D. shear correlation functions we have been seeking: we will use these functions to compare our data with various evolving cosmological models.," Given these definitions, the correlation functions are simple transforms of the power: These are the 3-D shear correlation functions we have been seeking; we will use these functions to compare our data with various evolving cosmological models."23 ]t is convenient to have a simple means of calculating the shear power spectrum [rom the matter power spectrum: this has been described in the last section., It is convenient to have a simple means of calculating the shear power spectrum from the matter power spectrum; this has been described in the last section.24 However. it is also useful to have a means of calculating the matter power spectrum given the shear power spectrum: here we outline how this can be achieved for theoretical models.," However, it is also useful to have a means of calculating the matter power spectrum given the shear power spectrum; here we outline how this can be achieved for theoretical models."25 Noisy data ave difficult to invert with this procedure: it would be more convenient to fit models to the data and then use the results of this section to invert these models., Noisy data are difficult to invert with this procedure; it would be more convenient to fit models to the data and then use the results of this section to invert these models.26 ln order to show how to invert the shear power spectrum. we start by considering an integral of the form where D(r.r)' is. à smooth. continuous. function.," In order to show how to invert the shear power spectrum, we start by considering an integral of the form where $B(r',r)$ is a smooth, continuous function."27⋅. Carrving out a partial dillerentiation of ο with respect tor. we find This result will be used below in order to untangle the matter power spectrum from its integral projection found in calculating the shear.," Carrying out a partial differentiation of $A$ with respect to $r$, we find This result will be used below in order to untangle the matter power spectrum from its integral projection found in calculating the shear."28 We also require the result which can be easily verified directly from equation (12))., We also require the result which can be easily verified directly from equation \ref{eq:fk}) ).29 Using these two results repeatedly. upon the shear power spectrum (for). we find that we can calculate the matter power spectrum: Alternatively. we can find a similar means of calculating the matter power spectrum from the cross power spectrum. of shear at two clilferent redshifts: These equations therefore permit us to find the matter power spectrum given a model for the shear power spectrum.," Using these two results repeatedly upon the shear power spectrum $P_{\gamma}(l,r)$, we find that we can calculate the matter power spectrum: Alternatively, we can find a similar means of calculating the matter power spectrum from the cross power spectrum of shear at two different redshifts: These equations therefore permit us to find the matter power spectrum given a model for the shear power spectrum."30 Note that upon noisy data. the first and second dilferentials in this equation can lead to unphysical negative power spectra.," Note that upon noisy data, the first and second differentials in this equation can lead to unphysical negative power spectra."31 Thus we reiterate that a better approach is to fit a continuous shear model to the data which can then be inverted with these equations., Thus we reiterate that a better approach is to fit a continuous shear model to the data which can then be inverted with these equations.32 We conclude this section with a discussion of models for the matter and shear power spectra which allow us to directly examine the redshift evolution of the power spectrum., We conclude this section with a discussion of models for the matter and shear power spectra which allow us to directly examine the redshift evolution of the power spectrum.33 Firstly. suppose we have measured the shear cross-correlation function C' between many recshifts. from which we can calculate the shear power spectrum.," Firstly, suppose we have measured the shear cross-correlation function $C$ between many redshifts, from which we can calculate the shear power spectrum."34" We will initially restrict ourselves to power within a redshift shell. 2.2 we will consider £7,» later."," We will initially restrict ourselves to power within a redshift shell, $P_\gamma$; we will consider $P_{\gamma 1 2}$ later."35 We will attempt to use our formalism with a simple model for the shear power spectrum: a power law in both theangular and redshift directions. i.c. The correlation function corresponding to this moclel. calculated from equation (20)) is:," We will attempt to use our formalism with a simple model for the shear power spectrum: a power law in both theangular and redshift directions, i.e. The correlation function corresponding to this model, calculated from equation \ref{ctheta}) ) is:"36Viable optical counterparts have been suggested. for ouly five among the26 sources shown iu roffxlun.. all of them probable cataclesiuic variables.,"Viable optical counterparts have been suggested for only five among the 26 sources shown in \\ref{fxlum}, all of them probable cataclysmic variables."37 We compare the ratio of X-ray flux to optical flux of these sources with the ratios measured for cataclysuic variables and for RS CVu systems in the Galactic Disk in reffeompa.., We compare the ratio of X-ray flux to optical flux of these sources with the ratios measured for cataclysmic variables and for RS CVn systems in the Galactic Disk in \\ref{fcompa}.38 It is seen that the sueeested optical counterparts for the sources ino 66397. and 66752 lead to ratios which are compatible with those of cataclvsiic variables. whereas those i [7 Tuc are too bright in N-ravs. in aerecineut with reffxhun..," It is seen that the suggested optical counterparts for the sources in 6397 and 6752 lead to ratios which are compatible with those of cataclysmic variables, whereas those in 47 Tuc are too bright in X-rays, in agreement with \\ref{fxlum}."39 Tf these sources are indeed catachvsndc variables. their excessive N-rayv luminosity needs to be explained: alternatively. the suggestedOO identifications may be chance coiucideuces (as discussed by Verbuut Wasinger 1998).," If these sources are indeed cataclysmic variables, their excessive X-ray luminosity needs to be explained; alternatively, the suggested identifications may be chance coincidences (as discussed by Verbunt Hasinger 1998)."40 All sugeested counterparts lead to hnieher X-ray o optical flux ratios than those of RS CVu binaries., All suggested counterparts lead to higher X-ray to optical flux ratios than those of RS CVn binaries.41 The accurate positions that we determine for individual sources are valid for separately detected sources in particular., The accurate positions that we determine for individual sources are valid for separately detected sources in particular.42 Iu the case of overlapping sources. we do not lave unique solutious.," In the case of overlapping sources, we do not have unique solutions."43 Thus. iu the core of 66397 fits with 5 and 6 sources are both acceptable. at simular quality: aud we cannot exclude that more sources contribute to the observed flix. which would invalidate our derived positions.," Thus, in the core of 6397 fits with 5 and 6 sources are both acceptable, at similar quality; and we cannot exclude that more sources contribute to the observed flux, which would invalidate our derived positions."44 Binaries mav reside away from the core either because he cluster has uudergouc little mass segresation. or )ocaise a three-body interaction aa close encounter Pa binary with a single star) in the core has expelled the inuv from the core HITut et 11992).," Binaries may reside away from the core either because the cluster has undergone little mass segregation, or because a three-body interaction a close encounter of a binary with a single star) in the core has expelled the binary from the core Hut et 1992)."45 In the latter case the binary is expected to be ecceutric nunuediatelv after beiug expelled: tidal forces iav in time circularize he orbit again., In the latter case the binary is expected to be eccentric immediately after being expelled; tidal forces may in time circularize the orbit again.46 Such binaries are only a minoritv of the overall binary population of a cluster: however. Nouv observations may preforablv select sucht binaries if tical orces act in them.," Such binaries are only a minority of the overall binary population of a cluster; however, X-ray observations may preferably select such binaries if tidal forces act in them."47 Since sources away frou the core can be ore- or background sources. optical identification of thoi is required to settle whether they belong to the cluster or rot.," Since sources away from the core can be fore- or background sources, optical identification of them is required to settle whether they belong to the cluster or not."48 Our accurate positions should help iu finding such counterparts., Our accurate positions should help in finding such counterparts.49"ποιο! of 2.8«10τοσα” by suggesting a breaking strain of 10.2,","moment of $2.8\times5010^{41}$ $\cdot $ $^2$ by suggesting a breaking strain of $10^{-2}$."51 Our estimation is one order ligher than hat of Owen(2005). and shows that the solidified nountains can provide a bigger quadrupole moment thaw clastic mountains do.," Our estimation is one order higher than that of \cite{Owen2005}, and shows that the solidified mountains can provide a bigger quadrupole moment than elastic mountains do."52 Horowitzetal.(2009) have done sole work to show that the breakiug straiu on normal jeutron stars can be as big as LO+., \cite{Horowitz2009} have done some work to show that the breaking strain on normal neutron stars can be as big as $10^{-1}$.53 Our result about the Παπ quadrupole moment on the solid quark stars would agree with Owen's if the breaking strain on solid quark stars can also be as high as 10.+., Our result about the maximum quadrupole moment on the solid quark stars would agree with Owen's if the breaking strain on solid quark stars can also be as high as $10^{-1}$.54 Tt is evideut that th the dependence on radius aud mass are the sanie iu his work auc that of Owen(2005)., It is evident that both the dependence on radius and mass are the same in this work and that of \cite{Owen2005}.55.. What can we coustrain the equation of state ly he CW observations?, What can we constrain the equation of state by the GW observations?56 To compare the theoretical quadrupole moment with the LICO 85 data (Abbottetal. 2010).. we are to provide the relationship between Qo and CAV amplitude fy.," To compare the theoretical quadrupole moment with the LIGO S5 data \citep{Abbott2010}, , we are to provide the relationship between $Q_{22}$ and GW amplitude $h_0$."57 Assuniug a density perturbation of 6p=Ro|pz23o2(0. (Ushomirskyetal.2000) aud following the definition 09]of Qo» above. oue comes to where a factor 1/2 before the amplitude of the trace-reversed perturbation is added for fy estimation.," Assuming a density perturbation of $\delta \rho={\rm Re}[\rho_{22}Y_{22}(\theta,\phi)]$ \citep{Ushomirsky2000} and following the definition of $Q_{22}$ above, one comes to where a factor $1/\sqrt{2}$ before the amplitude of the trace-reversed perturbation is added for $h_0$ estimation."58 Similar reatiments can also be found in other eravitational wave iteratures (CJaranowskietal.1998)., Similar treatments can also be found in other gravitational wave literatures \citep{Jaranowski1998}.59. The ouly difference is applviug ellipticity € rather than quadrupole moment Qo»., The only difference is applying ellipticity $\epsilon$ rather than quadrupole moment $Q_{22}$.60 Note the relationship e=VarLiQoofT... it is casy o prove that they are equivalent.," Note the relationship $\epsilon=\sqrt{8\pi/15}Q_{22}/I_{zz}$, it is easy to prove that they are equivalent."61 With our estimation of the maxinuuun quadrupole uonicnt into the equation above. we can obtain the uaxinumn amplitude of the exavitational waves. LIGO i focusing ou the direct detection of eravitational waves.," With our estimation of the maximum quadrupole moment into the equation above, we can obtain the maximum amplitude of the gravitational waves, LIGO is focusing on the direct detection of gravitational waves."62 Recent LIGO $5 data has given an upper bound of the fy for 116 known pulsars (Abbottetal.2010)., Recent LIGO S5 data has given an upper bound of the $h_0$ for 116 known pulsars \citep{Abbott2010}.63. The value of the upper bound of the 116 pulsus varies from 107° to 1077., The value of the upper bound of the 116 pulsars varies from $10^{-26}$ to $10^{-25}$.64 However. from Eq.(5)). it sees that solid quark stars can have mountains high enough to radiate gravitational waves with amplitudes as high as 10.77.," However, from \ref{h0esti}) ), it seems that solid quark stars can have mountains high enough to radiate gravitational waves with amplitudes as high as $10^{-22}$."65 Does this mean that these 116 pulsars cannot be solid quark stars?, Does this mean that these 116 pulsars cannot be solid quark stars?66 Should we believe that the mountains ou solid quar stars have the imaxiumnun heights?, Should we believe that the mountains on solid quark stars have the maximum heights?67 Iu addition. iu our estimation of Eq.(5)). we assune a distribution of 35». which cau attribute most to the exavitational waves.," In addition, in our estimation of \ref{h0esti}) ), we assume a distribution of $Y_{22}$, which can attribute most to the gravitational waves."68 It is surcly quite strange if natural mountains on stars have he exact distribution of 359 im order to produce the ΠαπΙΙ eravitational waves., It is surely quite strange if natural mountains on stars have the exact distribution of $Y_{22}$ in order to produce the maximum gravitational waves.69 The orogeny iu the Earth's crust is powered by the uautle convection and thus the engagement of tectonic ates., The orogeny in the Earth's crust is powered by the mantle convection and thus the engagement of tectonic plates.70 What could be the force to build mountaius onu solid quark stars?, What could be the force to build mountains on solid quark stars?71 Elastic energy develops when a star evolves. and both bulk-iuvariable aud bulk-variable Orces can result in decreases of moment of inertia durimg a star quake (Penge&Xu2008).," Elastic energy develops when a star evolves, and both bulk-invariable and bulk-variable forces can result in decreases of moment of inertia during a star quake \citep{Peng2008}."72 This force would be responsible for mountain building too., This force would be responsible for mountain building too.73 We cau then estimate the real heights of mountains from the elitch phenomena of pulsars below., We can then estimate the real heights of mountains from the glitch phenomena of pulsars below.74 We think elitehes occur if the moment of inertia change suddenly inside a solid quark stars (Zhouetal.2001)., We think glitches occur if the moment of inertia change suddenly inside a solid quark stars \citep{Zhou2004}.75". The pulsus aneular momentum, πιοον the assmuption of sphere. is 3ALR?O/5."," The pulsars' angular momentum, under the assumption of sphere, is $\sim 3MR^2\Omega/5$ ."76" Making a differential of it. we have |RI~5«10""[8(Q/Q)/10""|."," Making a differential of it, we have $\left|\delta R/R\right|\sim775\times 10^{-7}[\delta(\Omega/\Omega)/10^{-6}]$ ."78 Although this consideration could not be the real heights of mountains on pulsars. we think that actually the height of mountains might be of the same order of 62.," Although this consideration could not be the real heights of mountains on pulsars, we think that actually the height of mountains might be of the same order of $\delta R$."79 Therefore. replacing 6R with {μι aud inserting this iuto the estimation of Eq.(1)). we have the estimation of amplitude /y below. We draw Fie.," Therefore, replacing $\delta R$ with $H_{\rm80m}$ and inserting this into the estimation of \ref{Q22h0}) ), we have the estimation of amplitude $h_0$ below, We draw Fig."81 l to show how fy varies as the mass of solid quark stus changes iu the model of Lai&Xu(2009).. for different elitch amplitude 00/0.," 1 to show how $h_0$ varies as the mass of solid quark stars changes in the model of \cite{Lai2009}, for different glitch amplitude $\delta\Omega/\Omega$."82 In the calculations. we choose the numbers of quarks in a quar clusters to be 18 aud the potential Uy to be 50 MeV. We can see that if our estimation of the real height of mountains is valid. it would be natural that LICO still hasn't detect the eravitational waves directly. since the miaxiuuni CAV amplitude preseuted iu Eq.(5)) requires maxim height and a particular Y55-distribution of mountains.," In the calculations, we choose the numbers of quarks in a quark clusters to be $18$ and the potential $U_0$ to be $50$ MeV. We can see that if our estimation of the real height of mountains is valid, it would be natural that LIGO still hasn't detect the gravitational waves directly, since the maximum GW amplitude presented in \ref{h0esti}) ) requires maximum height and a particular $Y_{22}$ -distribution of mountains."83 What if the mountains havent the Y55-distribution?, What if the mountains haven't the $Y_{22}$ -distribution?84 This will be discussed im the next section., This will be discussed in the next section.85 Above we give an approach to the actual amplitude of CAVS using the elitch plenomenon., Above we give an approach to the actual amplitude of GWs using the glitch phenomenon.86 However. the auplitude of GAVs from quark stars depends also ou another factor.," However, the amplitude of GWs from quark stars depends also on another factor."87 Besides the maxinnun height of mountains. the distribution of mountains plavs a kev role as well.," Besides the maximum height of mountains, the distribution of mountains plays a key role as well."88 Iu the previous section. we eive an estimation of the iiaxiumia amplitude of CAs by assinuing a specific distribution described in Eq.," In the previous section, we give an estimation of the maximum amplitude of GWs by assuming a specific distribution described in Eq."89(2).. Such a hypothesis is too strong to approach the physical circtiustances., Such a hypothesis is too strong to approach the physical circumstances.90 Iu this section we will discard this assumption aud consider another Likely distribution., In this section we will discard this assumption and consider another likely distribution.91 Tt is certainly very cdifüeult to kuow the real distribution of imountaius on a solid quark star., It is certainly very difficult to know the real distribution of mountains on a solid quark star.92 Nevertheless. an idea comes out that we can give a random distribution to approach the actual situation.," Nevertheless, an idea comes out that we can give a random distribution to approach the actual situation."93 Yet another problem of the definition of random distribution cmerees., Yet another problem of the definition of random distribution emerges.94 The imost strict and plysical definition should satisfv the following requirements. (, The most strict and physical definition should satisfy the following requirements. (951) The height of mountains should varies frou 0 to the miaxiuun height of mountains. (,1) The height of mountains should varies from 0 to the maximum height of mountains. (962) The surface of the star should be coutimmous. sav the fiction 0.ω) which describe the distribution of iiouutaius should be infinitely differentiable. (,"2) The surface of the star should be continuous, say the function $H(\theta,\phi)$ which describe the distribution of mountains should be infinitely differentiable. ("973) Thethird requireimieut comes uot from imathematics. but from plivsics: the partial derivative of /7(0.0)should not be too high. otherwise a 1nountain which is quite precipitous would tend to fall down.,"3) Thethird requirement comes not from mathematics, but from physics: the partial derivative of $H(\theta,\phi)$should not be too high, otherwise a mountain which is quite precipitous would tend to fall down."98 With all the considerations above. we find it is nupossible or at least ναν hard to use the most," With all the considerations above, we find it is impossible or at least very hard to use the most"99Ix8.,K8.100 All of tjejr Baliner lines are in enilssiol along with the Ca H aud Ix lines., All of their Balmer lines are in emission along with the Ca H and K lines.101 We detect Li I AGTOS line iu the spectrum of idl659 even at OUL ow resolution., We detect Li I $\lambda$ 6708 line in the spectrum of id1659 even at our low resolution.102 There is oue M star in our sample (k113) with weak Ha aud [NU] emission., There is one M star in our sample (id113) with weak $H\alpha$ and [NII] emission.103 To examine the pessljlitw that KlE13 is a dMe star. we estimate the number of nearby «Me stars from the observed stellar density of 0.081 star/pe% (Henryeal.2002).," To examine the possibility that id113 is a dMe star, we estimate the number of nearby dMe stars from the observed stellar density of 0.084 $\rm pc^{-3}$ \citep{henr02}."104. Roughly 70% of nearby stars are M dwarls (Her'οἱal.2002)., Roughly $70\%$ of nearby stars are M dwarfs \citep{henr02}.105. At our completeness imit (V.c11.9). we cau detect M cdwarfs at clistances of 100 ye.," At our completeness limit $V \simeq 14.9$ ), we can detect M dwarfs at distances of 100 pc."106 The number of detectable M dwars towards NGC 6871 is two., The number of detectable M dwarfs towards NGC 6871 is two.107 The number of «Me stars alno& M cdwarfs increases monotonically with spectral type (1% around MO and 9056 M5 and later (Joy&Abt 1971)))., The number of dMe stars among M dwarfs increases monotonically with spectral type $4\%$ around M0 and $90\%$ M5 and later \citep{joy74}) ).108 The overall ratio of dle stars among M cdwarfs is 175€. whieh yields a imocest probability (~ 31%) of detecting oue in our spectroscopic sample.," The overall ratio of dMe stars among M dwarfs is $17\%$, which yields a modest probability $\simeq 34\%$ ) of detecting one in our spectroscopic sample."109 Thus. id113 could be a dMe star.," Thus, id113 could be a dMe star."110 High resolution optical spectra of Li E AGTOS would cliscriminate between a field «Me star and a pre-main sequence star., High resolution optical spectra of Li I $\lambda$ 6708 would discriminate between a field dMe star and a pre-main sequence star.111 There are 15 emission line stars iu this eeroup., There are 15 emission line stars in this group.112 Their spectral tvpes raneeOm from early B to late G. Most are definite emission liue objects., Their spectral types range from early B to late G. Most are definite emission line objects.113 More than half of the 15 cluster members (9 altogether) appear to be PMS stars., More than half of the 15 cluster members (9 altogether) appear to be PMS stars.114 For 8 stars. we base this ideutification ou their position on the HRD.," For 8 stars, we base this identification on their position on the HRD."115 Oue star has [NID] ancl [SII] emission., One star has [NII] and [SII] emission.116 The‘e are three B type stars (dS. 14156. i138) amoung the 11 definite emission liue stars.," There are three B type stars (id8, id186, id38) among the 11 definite emission line stars."117 They show emission ouly in Πα., They show emission only in $H\alpha$.118 Two of them (145 aud id38) were previously known Polcaro 2001).," Two of them (id8 and id38) were previously known \citep[see][]{grig88,bern01}."119.. They could be cassical Be stars., They could be classical Be stars.120 The‘e ape two A stars (10492100. id1691) in this subgroup.," There are two A stars (id2139, id1694) in this subgroup."121 One (id2139) shows sigus of [NII] and [SII] emission., One (id2139) shows signs of [NII] and [SII] emission.122 The Ha emission of id160[ is very weak. but its position on the HRD iudicates that it may be a PMS star.," The $H\alpha$ emission of id1694 is very weak, but its position on the HRD indicates that it may be a PMS star."123 There are three F type stars witl clelinite eiilssion featwes among the cluster members., There are three F type stars with definite emission features among the cluster members.124 Two (i2616. 12631) are PAIS caudidates with [NI aud [SII] emission.," Two (id2646, id2631) are PMS candidates with [NII] and [SII] emission."125 The third one (id12055) shows emission in Ho and lies close to the 1ail secuelce., The third one (id2055) shows emission in $H\alpha$ and lies close to the main sequence.126 Three G type members (12621. i¢12138. id26το) may be PMS stars.," Three G type members (id2621, id2138, id2675) may be PMS stars."127 All lie well above the main sequence., All lie well above the main sequence.128 The spectrum of id2621 coiains [NIL and [SII] emission: we detect Li I AGTOS line in the spectrum of id2138., The spectrum of id2621 contains [NII] and [SII] emission; we detect Li I $\lambda$ 6708 line in the spectrum of id2138.129 The third star of this ο'oup does not show any. particular eature beside the weak emission in the core of the Ha line., The third star of this group does not show any particular feature beside the weak emission in the core of the $H\alpha$ line.130 Based ou their reddening.Om we identify 16 emission line stars as possible backgrouudfon) objects.," Based on their reddening, we identify 16 emission line stars as possible background objects."131"mode, the LAT observes the entire sky every 3 hours.","mode, the LAT observes the entire sky every 3 hours."132" For individual sources, pprovides nearly uniform sky coverage down to a photon flux of 4x1071? cm""? s! between 1 and 100 GeV, except for sources at low Galactic latitude (|b|€ 10?) where the diffuse emission dominates (Abdoetal.2010a)."," For individual sources, provides nearly uniform sky coverage down to a photon flux of $4 \times 10^{-10}$ $^{-2}$ $^{-1}$ between 1 and 100 GeV, except for sources at low Galactic latitude $|b|\leq 10^\circ$ ) where the diffuse emission dominates \citep{abdo}."133". Throughout the paper, we assume an Ho —71 km s! Mpc!, Qm=0.27, Qa=0.73 cosmological model."," Throughout the paper, we assume an $H_0 = $ 71 km $^{-1}$ $^{-1}$, $\Omega_m = 0.27$, $\Omega_{\Lambda} = 0.73$ cosmological model."134" As of 2007 November, the public catalog of UHECRs released by the collaboration contains 27 events with energiesabove 55 EeV collected at their site in Malargüee, Argentina (Abrahametal.2004)."," As of 2007 November, the public catalog of UHECRs released by the collaboration contains 27 events with energiesabove 55 EeV collected at their site in Malargüee, Argentina \citep{abraham}."135. The LLAT 1FGL catalog consists of 1451 sources characterized in the 100 MeV—100 GeV energy range (Abdoetal.2010a)., The LAT 1FGL catalog consists of 1451 sources characterized in the 100 MeV–100 GeV energy range \citep{abdo}.136. The data were obtained in an all-sky scanning mode during 2008 August-2009 July and represents the most extensive map of the gamma-ray sky (>100 MeV) ever obtained., The data were obtained in an all-sky scanning mode during 2008 August–2009 July and represents the most extensive map of the gamma-ray sky $\geq 100$ MeV) ever obtained.137" The entire catalog includes 689 blazars, two starburst galaxies, two radio galaxies, 56 pulsars, 50 supernova remnants, and 630 unidentified sources (Abdoetal.2010a)."," The entire catalog includes 689 blazars, two starburst galaxies, two radio galaxies, 56 pulsars, 50 supernova remnants, and 630 unidentified sources \citep{abdo}."138". Since we are interested in testing for possible correlations of UHECRs with various classes of gamma-ray emitters in the MeV-GeV energy range without anypriori assumption, we take advantage of the complete 1FGL catalog without any redshift or type discrimination."," Since we are interested in testing for possible correlations of UHECRs with various classes of gamma-ray emitters in the MeV-GeV energy range without any assumption, we take advantage of the complete 1FGL catalog without any redshift or type discrimination."139" To test for a possible cross-correlation between UHECRs and ssources in the 1FGL catalog, we checked whether the individual UHECR positions in the sample are clearly contained within the error circle of individual sources listed in the 1FGL catalog."," To test for a possible cross-correlation between UHECRs and sources in the 1FGL catalog, we checked whether the individual UHECR positions in the sample are clearly contained within the error circle of individual sources listed in the 1FGL catalog."140" Specifically, we count correlations whenever an UHECR event is within a circle of 3.P radius around a particular ssource."," Specifically, we count correlations whenever an UHECR event is within a circle of $3.1\!^\circ$ radius around a particular source."141 This radius is in line with the value predicted by conventional models of cosmic ray trajectories that consider the full effect of the Galactic magnetic field (Abrahametal.2008a).., This radius is in line with the value predicted by conventional models of cosmic ray trajectories that consider the full effect of the Galactic magnetic field \citep{abraham5}.142" In order to avoid “multiple” counts, we only consider one match per individual UHECR event."," In order to avoid “multiple” counts, we only consider one match per individual UHECR event."143" Within the 27 UHECR events, we find 12 matches with 1FGL sources."," Within the 27 UHECR events, we find 12 matches with 1FGL sources."144" To examine the likelihood of such correlation, we used the BATSE 4B gamma-ray burst (GRB) catalog (Paciesasetal.1999) in place of a random generator of isotropic sky positions that allows us to generate artificial samples of simulated UHECRs."," To examine the likelihood of such correlation, we used the BATSE 4B gamma-ray burst (GRB) catalog \citep{paciesas} in place of a random generator of isotropic sky positions that allows us to generate artificial samples of simulated UHECRs."145 The BATSE 4B catalog consists of 1637 GRB positions localized by the BATSE instrument on board the Compton Gamma Ray Observatory (CGRO) in the period between 1991 April 19 and 1996 August 29., The BATSE 4B catalog consists of 1637 GRB positions localized by the BATSE instrument on board the Compton Gamma Ray Observatory (CGRO) in the period between 1991 April 19 and 1996 August 29.146" For our work, we restricted our analysis to events that would be accessible from the southern site at a declination < 24.8 (Abrahametal.2004)."," For our work, we restricted our analysis to events that would be accessible from the southern site at a declination $<$ $24.8\!^\circ$ \citep{abraham}."147". In addition, we assume that the fraction of exposure is the same accross the declination range as stated in Abrahametal.(2008a)."," In addition, we assume that the fraction of exposure is the same accross the declination range as stated in \citet{abraham5}."148". After the proper cuts were applied, we drew 100 random sets of 27 events from the resulting “southern” BATSE 4B catalog to match the UHECR sample."," After the proper cuts were applied, we drew 100 random sets of 27 events from the resulting “southern” BATSE 4B catalog to match the UHECR sample."149 We next proceeded to correlate each of the 100 random sets with the 1451 ssources in the same manner as with the original dataset., We next proceeded to correlate each of the 100 random sets with the 1451 sources in the same manner as with the original dataset.150 Figure 1 shows the distribution of matches between the artificial samples of UHECRs constructed from the BATSE 4B catalog and the 1FGL catalog., Figure \ref{figure1} shows the distribution of matches between the artificial samples of UHECRs constructed from the BATSE 4B catalog and the 1FGL catalog.151" In particular, 63% of the artificial samples have 12 or more matches consistent with ppositions."," In particular, $\%$ of the artificial samples have 12 or more matches consistent with positions."152 Allowing for larger circles (6° and 8° radii) only increases the number of false positives when compared with the BATSE sample to 71% and 73% respectively., Allowing for larger circles $6^\circ$ and $8^\circ$ radii) only increases the number of false positives when compared with the BATSE sample to $\%$ and $\%$ respectively.153" If the position of events were strongly correlated with ssources, we would expect a greater number of coincidences when compared with the outcomes of randomly-generated artificial sets of UHECR events drawn from the BATSE 4B GRB catalog."," If the position of events were strongly correlated with sources, we would expect a greater number of coincidences when compared with the outcomes of randomly-generated artificial sets of UHECR events drawn from the BATSE 4B GRB catalog."154 We find no evidence for such an association and subsequently cannot claim a positive cross-correlation between UHECRs and the 1FGL catalog., We find no evidence for such an association and subsequently cannot claim a positive cross-correlation between UHECRs and the 1FGL catalog.155" In summary, we find no cross-correlation between UHECRs and 1FGL sources that cannot be reproduced by chance alignment."," In summary, we find no cross-correlation between UHECRs and 1FGL sources that cannot be reproduced by chance alignment."156" This differs from the findings reported by Abrahametal. (2009),, using a different AGN sample (see 2007).."," This differs from the findings reported by \citet{abraham3}, , using a different AGN sample \citep[see also][]{abraham2}. ."157 Examining the matches between, Examining the matches between158bar causes the scale length. of the disk to increase with time as well.,bar causes the scale length of the disk to increase with time as well.159 Measured. with a double exponential fit to the surface density. profile. this increase in the disk scale length is fairly rapid initially. jumping to 2.3 from 1.0 between |—50 and /=110. and slowly increasing to 2.8 hy the end of the simulation.," Measured with a double exponential fit to the surface density profile, this increase in the disk scale length is fairly rapid initially, jumping to 2.3 from 1.0 between $t=50$ and $t=110$, and slowly increasing to 2.8 by the end of the simulation."160 This increase more than olfsets the pattern speed slow-clown. with only one comparison still too low at /=110 while two are higher than observed. and the rest are within the accepted ranges.," This increase more than offsets the pattern speed slow-down, with only one comparison still too low at $t=110$ while two are higher than observed, and the rest are within the accepted ranges."161 By the end of the simulation three are again too low. only one is too high. and the rest are acceptable (with two at the lower limit of the error bars. anc two well within the measured. range)," By the end of the simulation three are again too low, only one is too high, and the rest are acceptable (with two at the lower limit of the error bars, and two well within the measured range)."162 Therefore. for à considerable duration. these long-lived. bar is rotating at speeds. comparable to those observed.," Therefore, for a considerable duration, these long-lived bar is rotating at speeds comparable to those observed."163 This reiterates the corotation to bar length ration finding above: both the simulated. and observed. bars are “fast” (ratio less than 1.5).," This reiterates the corotation to bar length ration finding above: both the simulated and observed bars are ""fast"" (ratio less than 1.5)."164 Some attention has recently been placed on the identification of cclge-on barred galaxies., Some attention has recently been placed on the identification of edge-on barred galaxies.165 MM. Athanassoula Bureau (1999) (ΑΦ). and BAA have studied: the. line-ol-sight. velocity. profile. of peanut-shaped. edge-on galaxies and have shown that thei kinematics are explained by the presence of a bar.," M, Athanassoula Bureau (1999) B), and A have studied the line-of-sight velocity profile of peanut-shaped, edge-on galaxies and have shown that their kinematics are explained by the presence of a bar."166 The characteristic plot. of position versus velocity gives a unique figure-eight pattern for barred ealaxies. since some orbits are depleted in these systems.," The characteristic plot of position versus velocity gives a unique figure-eight pattern for barred galaxies, since some orbits are depleted in these systems."167 Our simulation results have been similarly plotted., Our simulation results have been similarly plotted.168 After initial xw formation. the plot appears similar to the unbarred dots: as the bar develops. the central positions darken while the clensity increases. and the areas immediately to he outside of this central pole suller some depopulation. similar to the observational plots in WaAIAL and DD. With bar buckling. though. comes increased scatter in he plot. removing any forming pattern. and once again caving a plot which would be considered unbarred i£ viewed observationallv.," After initial bar formation, the plot appears similar to the unbarred plots; as the bar develops, the central positions darken while the density increases, and the areas immediately to the outside of this central pole suffer some depopulation, similar to the observational plots in M and B. With bar buckling, though, comes increased scatter in the plot, removing any forming pattern, and once again leaving a plot which would be considered unbarred if viewed observationally."169 Plots at /250 and /—76 are shown in Fig., Plots at $t$ =50 and $t$ =76 are shown in Fig.170 12., 12.171 The original simulation is composed only of a disc and halo anc was constructed to be in equilibrium. with a JToomre (OQ greater. than 1., The original simulation is composed only of a disc and halo and was constructed to be in equilibrium with a Toomre Q greater than 1.172 This generates a higher velocity. dispersion. than would be observed: 0.23. (times maximum velocity) tangential ancl 0.215 radial dispersion at 2.4 scale lengths., This generates a higher velocity dispersion than would be observed: 0.23 (times maximum velocity) tangential and 0.215 radial dispersion at 2.4 scale lengths.173 Phe radial dispersion increases to 0.258 by £216., The radial dispersion increases to 0.258 by $t$ =76.174 “Phis blurs the Geure-cight pattern in the IK&MM plot., This blurs the figure-eight pattern in the M plot.175 Since all the observational results used. cool gas to determine velocities. our results would be much closer to the analytically predicted orbits. and the distinctive figure-cight plot.," Since all the observational results used cool gas to determine velocities, our results would be much closer to the analytically predicted orbits, and the distinctive figure-eight plot."176 ‘To counter part of the possible velocity. dispersion problem statec above. a model containing a small. compact bulge was constructed in the lower resolution range (0001 particles). keeping a similar halo and rotation curve (see Section 2 for a more complete description).," To counter part of the possible velocity dispersion problem stated above, a model containing a small, compact bulge was constructed in the lower resolution range (500K particles), keeping a similar halo and rotation curve (see Section 2 for a more complete description)."177 The evolution of the disc is similar to the earlier model in that the bar is initiated. a little before. 7-20 (540 Myr): it differs in that the initial bar is about 20 per cent smaller. with dumbbell-shaped inner isophotes when viewed [face-on.," The evolution of the disc is similar to the earlier model in that the bar is initiated a little before $t$ =20 (540 Myr); it differs in that the initial bar is about 20 per cent smaller, with dumbbell-shaped inner isophotes when viewed face-on."178 The bar remains smaller than the the previous model. by about the same amount for the duration of the simulation.," The bar remains smaller than the the previous model, by about the same amount for the duration of the simulation."179 This is in clirect contrast with the findings of MM who found their bulge model to have a longer bar. although the shape is similar.," This is in direct contrast with the findings of M who found their bulge model to have a longer bar, although the shape is similar."180 Llowever. their bulge is more massive in comparison to the disk. and more extended than ours.," However, their bulge is more massive in comparison to the disk, and more extended than ours."181 Fig., Fig.182 13 shows /—26 o 250., 13 shows $t$ =26 to 250.183 The initial velocity. dispersion (0.146. versus 0.23 above for tangential and 0.18. versus 0.215 for racial) was ower than our original simulation: however. the line-of-sight velocity distribution (LOSVD) plots remained similar.," The initial velocity dispersion (0.146 versus 0.23 above for tangential and 0.18 versus 0.215 for radial) was lower than our original simulation; however, the line-of-sight velocity distribution (LOSVD) plots remained similar."184 The veh resolution simulation showed much more detail and ollowecl trends toward the figure-cight shape not seen in he lower resolution plots for the same initial conditions., The high resolution simulation showed much more detail and followed trends toward the figure-eight shape not seen in the lower resolution plots for the same initial conditions.185 Creating a simulation of the bulge mass model with higher resolution. with its lowered. velocity dispersion. should vield clearer LOSVD plots than the original high resolution run. therefore we cannot make anv conclusions as to whether or not the inflated velocity dispersion in the original sipiulation is responsible for masking the figure-eight. pattern.," Creating a simulation of the bulge mass model with higher resolution, with its lowered velocity dispersion, should yield clearer LOSVD plots than the original high resolution run, therefore we cannot make any conclusions as to whether or not the inflated velocity dispersion in the original simulation is responsible for masking the figure-eight pattern."186 The pattern speed of the bulge model is higher than, The pattern speed of the bulge model is higher than187represent discrete physical structures.,represent discrete physical structures.188 Columns (2) and (3) are the coordinates of the sources. and column (4) is the relative positions of the these sources will respect to the strongest component.," Columns (2) and (3) are the coordinates of the sources, and column (4) is the relative positions of the these sources with respect to the strongest component."189 Column (5) lists the surface brightnesses of these sources. and column (6) their integrated. [lux densities.," Column (5) lists the surface brightnesses of these sources, and column (6) their integrated flux densities."190 Column (7) gives the nominal deconvolved sizes of the Gaussian components at EWIIM as given by JMETT. aud column 8 lists the position angles of the fitted Gaussians.," Column (7) gives the nominal deconvolved sizes of the Gaussian components at FWHM as given by JMFIT, and column 8 lists the position angles of the fitted Gaussians."191 The corresponding intrinsic brightness temperatures of (hese compact sources are on the order of 10* to 103 IK. and are listed in column 9.," The corresponding intrinsic brightness temperatures of these compact sources are on the order of $10^7$ to $10^8$ K, and are listed in column 9."192 Dased on the VLBA results. the source is composed of (wo dominant structures separated bv ~31 mas.," Based on the VLBA results, the source is composed of two dominant structures separated by $\sim 31$ mas."193 The stronger of (hese is consistent will (wo Gaussians (components 1 and 3 in Table 3). while the second dominant source is represented by one Gaussian (component 2 in Table 3).," The stronger of these is consistent with two Gaussians (components 1 and 3 in Table 3), while the second dominant source is represented by one Gaussian (component 2 in Table 3)."194 Including a possible faint component to the east (component + in Table 3). gives a total [lux density of 1.7780.109 mJy.," Including a possible faint component to the east (component 4 in Table 3), gives a total flux density of $1.778 \pm 1950.109$ mJy."196 This value is consistent with the 1.73£0.13 mJv obtained with the VLA FIRST survev (Decker.White.&Ilelfand1995).. and with the 1.316x:0.021 mJv obtained with the VLA ELAIS survey (Ciliegietal.1999).," This value is consistent with the $1.73 \pm 0.13$ mJy obtained with the VLA FIRST survey \citep{BWH95}, and with the $1.816 \pm 0.021$ mJy obtained with the VLA ELAIS survey \citep{CP99}."197. The 1.4 GIIz flux densities measured with the VLA in 1995 and 1997 (Becker.Cilieeietal.1999) and the VLBA in 2007 (this paper) are equal to better than5%... implvine that this source is not highly variable on time scales of vears.," The 1.4 GHz flux densities measured with the VLA in 1995 and 1997 \citep{BWH95,CP99} and the VLBA in 2007 (this paper) are equal to better than, implying that this source is not highly variable on time scales of years."198" We have also svnthesized larger images (2""x 2"") using the VLBA and found no other radio components al >5e level (140 (Jy. +) in the field other than those seen in Figure 4 and listed in Table 3.", We have also synthesized larger images $2'' \times 2''$ ) using the VLBA and found no other radio components at $\ge 5\sigma$ level $140~\mu$ Jy $^{-1}$ ) in the field other than those seen in Figure 4 and listed in Table 3.199 We have detected the z=6.12 QSO J14272-3312 at 8.4 GIIz with the VLA A-array and al 1.4 GllIz with the VLBA., We have detected the $z=6.12$ QSO J1427+3312 at 8.4 GHz with the VLA A-array and at 1.4 GHz with the VLBA.200 The source is unresolved as seen in the 8.4 GIIz VLA results. and has a steep spectrum wilh a spectral index value of a1=--.1.," The source is unresolved as seen in the 8.4 GHz VLA results, and has a steep spectrum with a spectral index value of $\alpha^{8.4}_{1.4}=-1.1$."201 At mas resolution. the VLBA observations show that this QSO is comprised of two dominant continuum components separated by 31 mas (174 pe: Table 3) with a flux density ratio of ~3:1.," At mas resolution, the VLBA observations show that this QSO is comprised of two dominant continuum components separated by 31 mas (174 pc; Table 3) with a flux density ratio of $\sim 3:1$."202 The Gaussian fitting suggests that both components are resolved with sizes ol ~4—6 mas (22—34 pe)., The Gaussian fitting suggests that both components are resolved with sizes of $\sim 4-6$ mas $22-34$ pc).203 The physical properties observed in this source suggest (hat this high-: QSO could be a Compact Sxiinetric Object (CSO) with two distinct. steep spectra. radio lobes that are confined) by a dense ISM in the host galaxy. (Conway2002).," The physical properties observed in this source suggest that this $z$ QSO could be a Compact Symmetric Object (CSO) with two distinct, steep spectra, radio lobes that are confined by a dense ISM in the host galaxy \citep{CO02}."204.. CSOs are radio sources that have sizes on scales of 1 pe to 1 kpe. and are thought to be verv voung (X10! vi: Reaclheacl (1998))).," CSOs are radio sources that have sizes on scales of 1 pc to 1 kpc, and are thought to be very young $\leq 10^4$ yr; \citet{RTXPWP96,OC98}) )."205 Moreover. because CSOs are highly confined," Moreover, because CSOs are highly confined"206Dress Gunn (1973) were the first to propose that a COSELOogical abundance of dark compact objects could be detected. by gravitational lensing of more clistant sources.,Press Gunn (1973) were the first to propose that a cosmological abundance of dark compact objects could be detected by gravitational lensing of more distant sources.207 Ifa point mass lies along the observer-source line of sight. the relative motion tween. the lens. source ancl observer produces a change in the magnifications of two lensed images.," If a point mass lies along the observer-source line of sight, the relative motion between the lens, source and observer produces a change in the magnifications of two lensed images."208 The presence of foreground. compact objects. is therefore. detected. through a change in the observed. Dux of the background source (termed microlensing)., The presence of foreground compact objects is therefore detected through a change in the observed flux of the background source (termed microlensing).209 This οσοι has been used successfully in the search for compact objects in the halo of the Milky Way galaxy (e.g. cock et a., This effect has been used successfully in the search for compact objects in the halo of the Milky Way galaxy (e.g. Alcock et al.210 2000)., 2000).211 Also. microlensing «ue to stars in a galaxy at moderate redshift has been observed. in the. gravitationally lensed quasar Q2237|0305 (Lewin et al.," Also, microlensing due to stars in a galaxy at moderate redshift has been observed in the gravitationally lensed quasar Q2237+0305 (Irwin et al."212 1989: Corriganet al., 1989; Corrigan et al.213 1991)., 1991).214 The short durations of gamma rav bursts (CBs) oller an alternativo way to study microlensing and hence search [or à cosmological population of compact objects. through observation of repeating bursts.," The short durations of gamma ray bursts (GRBs) offer an alternative way to study microlensing and hence search for a cosmological population of compact objects, through observation of repeating bursts."215 In this paper we assume GRBs to be at cosmological distances (Paczynski 1995). and therefore probable sources for gravitational lensing (Lurner. Ostriker Cott 1984).," In this paper we assume GRBs to be at cosmological distances (Paczynski 1995), and therefore probable sources for gravitational lensing (Turner, Ostriker Gott 1984)."216 Paczyvuski (1986. LOST) noted that while multiple images of a single GRB cannot be angularly resolved: by present clay detectors. their relative ἅσίαν may be longer than the burst duration so that the lensecl images could be resolved temporally (a pair of lensed GiB images that are produced bv a single mass (Ade) have a relative time delay that is AL~5Oscc(Ade10AL.) (Mao 1992)).," Paczynski (1986, 1987) noted that while multiple images of a single GRB cannot be angularly resolved by present day detectors, their relative delay may be longer than the burst duration so that the lensed images could be resolved temporally (a pair of lensed GRB images that are produced by a single mass $(M_{CO})$ have a relative time delay that is $\Delta t\sim 50 sec\times(M_{CO}/10^{6}M_{\odot})$ (Mao 1992))."217 Microlensing of aGkB by a compact object is therefore observed as a GRB that repeats., Microlensing of a GRB by a compact object is therefore observed as a GRB that repeats.218 Phe utility. of GRBs to explore cosmological dark matter. as well as the possible inference of properties of the GIU population itself was cliscussed in detail by Blaes Webster (1992).," The utility of GRBs to explore cosmological dark matter, as well as the possible inference of properties of the GRB population itself was discussed in detail by Blaes Webster (1992)."219 The short event duration. as well as the transparcney of the universe to ganmuna ravs make GRBs ideal probes of dark matter in the form of compact objects over à wide range of masses.," The short event duration, as well as the transparency of the universe to gamma rays make GRBs ideal probes of dark matter in the form of compact objects over a wide range of masses."220 Alicrolensing of existing ancl potential catalogues of GRBs have been used to discuss the cosmological abundance of compact objects., Microlensing of existing and potential catalogues of GRBs have been used to discuss the cosmological abundance of compact objects.221 Marani et al. (, Marani et al. (2221999) use non-detections of lensed images from the BATSE and Ulysses catalogues to set conservative limits on dark compact objects with masses between LO15 and LOAZ...,1999) use non-detections of lensed images from the BATSE and Ulysses catalogues to set conservative limits on dark compact objects with masses between $10^{-16}$ and $10^{-7}M_{\odot}$.223 Also a universe proposed. by Gnedin Ostriker (1992) with Meo107A. and O3;=Oco—(015 was ruled out at a confidence level of., Also a universe proposed by Gnedin Ostriker (1992) with $M_{CO}\sim10^{6.5}M_{\odot}$ and $\Omega_{M}=\Omega_{CO}=0.15$ was ruled out at a confidence level of.224. This scenario had. been previously investigated. in detail. using a 3-D lensing code by Mao (1993).," This scenario had been previously investigated in detail, using a 3-D lensing code by Mao (1993)."225 He found results that did not depart significantly from those obtained. by a single- approximation., He found results that did not depart significantly from those obtained by a single-screen approximation.226 Mao (1992) and Crossman Nowak, Mao (1992) and Grossman Nowak227We lave analysed the distribution of various ‘imematical aspects of our sample.,We have analysed the distribution of various kinematical aspects of our sample.228 To ect the information for the overall kinematics of the and to attempt to come to a separation of disk and halo we calculated their orbits., To get the information for the overall kinematics of the and to attempt to come to a separation of disk and halo we calculated their orbits.229 The observational parameters 0.0.4.fy.fs.rad Were transformed iuto ἂν}.ZEW (for details see de Boer 1997b).," The observational parameters $\alpha,\delta,d,\mu_{\alpha},\mu_{\delta},v_{\rm rad}$ were transformed into $X,Y,Z,U,V,W$ (for details see de Boer 1997b)."230 Also the orbital velocity projected to the ealactic plane. O. and the velocity towards the ealactic ceutre. ®. were calculated.," Also the orbital velocity projected to the galactic plane, $\Theta$, and the velocity towards the galactic centre, $\Phi$, were calculated."231 Orbits were calculated over a time span of 10 taking steps of LATIN., Orbits were calculated over a time span of 10 taking steps of Myr.232" Following de Doer (1997) the eccentricity. cece. of the orbit aud the apo- aud perigalactic distances. Ry aud fé were calculated as well as the maxima -dstauce reached. μιας. ad its ealactic radial distance normalised z-extenut. nic. For the valuesIh, for our stars sec Table available in electrouic form."," Following de Boer (1997b) the eccentricity, $ecc$, of the orbit and the apo- and perigalactic distances, $R_{\rm a}$ and $R_{\rm p}$, were calculated as well as the maximum $z$ -distance reached, $z_{\rm max}$, and its galactic radial distance normalised $z$ -extent, $nze$, For the values for our stars see Table \\ref{tablecds} available in electronic form."233 The meridional sections of the orbits of ({sec reforhits.fig)) show very different shapes., The meridional sections of the orbits of (see \\ref{orbits.fig}) ) show very different shapes.234" About half of the stars of our sample have perigalactic distances fü,x 3kkpc."," About half of the stars of our sample have perigalactic distances $R_{\rm p}235\leq 3$ kpc."236 65 rroach a perigalactic distance Ryx Lkkpe., 65 reach a perigalactic distance $R_{\rm p}\leq 1$ kpc.237 Three stars AAnd. VVir and VVir) reach perigalactic distances less than 0.1 kpe.," Three stars And, Vir and Vir) reach perigalactic distances less than 0.1 kpc."238 The other extreme is represented by 5 (CTAAnd. ALCCAG. LLyu. PPer and PPsc) which have perigalactic distances more than 9 Ipc aud always stav bevoud the solar circle.," The other extreme is represented by 5 And, CMi, Lyn, Per and Psc) which have perigalactic distances more than 9 kpc and always stay beyond the solar circle."239 Of the 217 663 have boxy orbits auc stay close to the plane., Of the 217 63 have boxy orbits and stay close to the plane.240 A subset of 29 inakes only nall excursions in a reforbits.fig top row). 31 have planar but very ecceutric orbits 2. iuiddle row).," A subset of 29 makes only small excursions in $\varpi$ \\ref{orbits.fig} top row), 34 have planar but very eccentric orbits \ref{orbits.fig} middle row)."241" The orbit of itself is not like that of a disk population star (oven although its 444 is only kkpe aud its το= 0.01). because its orbit has ecc=OS with 4,= δρ aud R=9.1 kkpe."," The orbit of itself is not like that of a disk population star (even although its $z_{\rm max}$ is only kpc and its $nze = 0.01$ ), because its orbit has $ecc =0.8$ with $R_{\rm a}=18.4$ kpc and $R_{\rm p}= 2.1$ kpc."242 151 of the sshow orbits resenibliug those of he bottoni row., 154 of the show orbits resembling those of the bottom row.243 The shape of these orbits is really chaotic. aud shows movements perpendicular to the plane.," The shape of these orbits is really chaotic, and shows movements perpendicular to the plane."244" These stars partly have orbits geome to vorv small ealactocentric distances and some of them reach very laree apogalactic distances. with as an extreme Ih,Si kkpe (for AAÀqr)."," These stars partly have orbits going to very small galactocentric distances and some of them reach very large apogalactic distances, with as an extreme $R_{\rm p} \simeq 51$ kpc (for Aqr)."245 The statistics of the circular componcut O of the velocity is shown in 1tthetalist.fig.., The statistics of the circular component $\Theta$ of the velocity is shown in \\ref{thetahist.fig}.246 In nr suuple we have 87 wwitl retrograde orbits., In our sample we have 87 with retrograde orbits.247 We compared the characteristics of these stars with the prograde ones., We compared the characteristics of these stars with the prograde ones.248 Among the retrograde part of our sample there are no stars with a iietallicity [Fe/TI] >0.9 (see rofanavel upper eft panel)., Among the retrograde part of our sample there are no stars with a metallicity [Fe/H] $>-0.9$ (see \\ref{anavel} upper left panel).249 Considering the retrograde eroup separately shows that the peak at high eccentricities in refeccuzehistfig (eft panel) is nearly completely due to the retrogradeLxis.. while the stars with prograde orbits show a flat distribution over the hole metallicity ranee.," Considering the retrograde group separately shows that the peak at high eccentricities in \\ref{eccnzehist.fig} (left panel) is nearly completely due to the retrograde, while the stars with prograde orbits show a flat distribution over the hole metallicity range."250 The ecceutzricities ecc of the orbits as well as the values of ize span a large range (see rofeccuzelist.fig))., The eccentricities $ecc$ of the orbits as well as the values of $nze$ span a large range (see \\ref{eccnzehist.fig}) ).251 The eccentricity of the orbit of the majority ofour stars is ccc.>0.15., The eccentricity of the orbit of the majority of our stars is $ecc~>0.45$.252 The distribution has an absolute maxima at cece=0.9 and a shallow local τή at eeczz0.6., The distribution has an absolute maximum at $ecc= 0.9$ and a shallow local minimum at $ecc\simeq 0.6$.253" The distribution of the uormalised z-exteuts shows a nani at low values neκ0,9, a local nunuuuuni at nie=0.4 followed by another peak at niez0.6."," The distribution of the normalised $z$ -extents shows a maximum at low values $nze<0.2$, a local minimum at $nze =0.4$ followed by another peak at $nze \simeq 0.6$."254 There are 100 wwith sies0 12d only 15 mreach niecol., There are 109 with $nze \leq 0.4$ and only 45 reach $nze \geq 1$.255 A separation in stars with prograde aud retrograde orbits does not chauge the appearance of the Dic diagram., A separation in stars with prograde and retrograde orbits does not change the appearance of the $nze$ diagram.256 Both eroups show Ligh peaks at low values of nie anda oug flat tail., Both groups show high peaks at low values of $nze$ and a long flat tail.257 The shape of a stellar orbit gives an indication of the population a star belongs to., The shape of a stellar orbit gives an indication of the population a star belongs to.258 stars have orbits simular to those of the younger galactic stars. deine rather circular and staving close to the plane.," stars have orbits similar to those of the younger galactic stars, being rather circular and staying close to the plane."259 These are the ones nost likely haviug been bora iu the disk., These are the ones most likely having been born in the disk.260 It is. from our data. not easy to discriminate between so-called thin- aud thick-clisk stars. a distinction which is uot well defined auvway.," It is, from our data, not easy to discriminate between so-called thin- and thick-disk stars, a distinction which is not well defined anyway."261 The cousists of stars whose orbits are not akin to disk-like galactic rotation., The consists of stars whose orbits are not akin to disk-like galactic rotation.262 They most likely have been born outside he disk of the Allkv Wav., They most likely have been born outside the disk of the Milky Way.263 Using the above criteria (which were largely set by the distribution of the parameters of our stars as discussed above uxiug aud 5)). one can now roughly sort the stars according to populations.," Using the above criteria (which were largely set by the distribution of the parameters of our stars as discussed above using \\ref{thetahist.fig} and \ref{eccnzehist.fig}) ), one can now roughly sort the stars according to populations."264 We define halo stars as those having O-100 oor ecce>OL or nie> 0.L., We define halo stars as those having $\Theta<100$ or $ecc > 0.4$ or $nze>0.4$ .265 Each one of the criteria alone, Each one of the criteria alone266textscii] 46548 A and [N textscii] 46584 A transitions must exhibit identical non-thermal motions since both lines are emitted by the same ions.,$]$ $\lambda$ 6548 $\mbox{\AA}$ and $[$ $]$ $\lambda$ 6584 $\mbox{\AA}$ transitions must exhibit identical non-thermal motions since both lines are emitted by the same ions.267 The same argument also applies to the [S textscii] 46716 A and [S textscii] 46731 A lines., The same argument also applies to the $[$ $]$ $\lambda$ 6716 $\mbox{\AA}$ and $[$ $]$ $\lambda$ 6731 $\mbox{\AA}$ lines.268" Finally, specific line ratios of the [N textscii]and[S textscii] transitions must agree with standard theoretical models of ionized nebulae."," Finally, specific line ratios of the $[$ $]$ and $[$ $]$ transitions must agree with standard theoretical models of ionized nebulae."269" All conditions taken in consideration, only 30057 emission-line profiles were retained, most of them being associated to the bright, central structure found in the overlapping region between the eastern and western field (see 8 5.2.1)."," All conditions taken in consideration, only 057 emission-line profiles were retained, most of them being associated to the bright, central structure found in the overlapping region between the eastern and western field (see $\S$ 5.2.1)."270" Obviously, the summation of both cubes largely contributes to increase the data quality for duplicated pixels not only by increasing the peak signal for all lines but also by flattening noise fluctuations in empty channels (see Figure 2)."," Obviously, the summation of both cubes largely contributes to increase the data quality for duplicated pixels not only by increasing the peak signal for all lines but also by flattening noise fluctuations in empty channels (see Figure 2)."271" Considering the very large number of emission-line profiles available in our initial data set (more than 0000), we are fully aware that the conditions listed above drastically reduce the size of the retained sample."," Considering the very large number of emission-line profiles available in our initial data set (more than 000), we are fully aware that the conditions listed above drastically reduce the size of the retained sample."272" On the other hand, these conditions assure that the retained profiles are undoubtedly the most reliable available."," On the other hand, these conditions assure that the retained profiles are undoubtedly the most reliable available."273 We reiterate that a S/N greater than 6 is required to appropriately conduct an investigation on line ratios., We reiterate that a S/N greater than 6 is required to appropriately conduct an investigation on line ratios.274" However, a *physical detection"" [of a given line] is considered when Z33 (Rola&Pelat 1994).."," However, a “physical detection” [of a given line] is considered when $\gtrsim$ 3 \citep{Rol1994}. ."275" This will be used in a later subsection to investigate notable, although not necessarily reliable, line ratios for particular structures in 11805 (see 8 5.2.2.2)."," This will be used in a later subsection to investigate notable, although not necessarily reliable, line ratios for particular structures in 1805 (see $\S$ 5.2.2.2)."276" The [S[Su]u]A6716A6731 line ratios were computed and used as input values for the Fivel procedure (DeRobertisetal.1987) adapted, for convenience, inIDL."," The $\frac{[\textnormal{S}\,\textsc{ii}]\,\lambda6716}{[\textnormal{S}\,\textsc{ii}]\,\lambda6731}$ line ratios were computed and used as input values for the Fivel procedure \citep{DeR1987} adapted, for convenience, in."277. Assuming a constantelectron temperature of 74400 K throughout, Assuming a constantelectron temperature of 400 K throughout278al progressively longer wavelengths (Meszaros&ReesL997).,at progressively longer wavelengths \citep{Meszaros1997}.279. Ever since the discovery of the first afterglows. these have been modeled succeshilly by combining a model for the blast wave ονπας wilh a svehirotron radiation model. where shock-accelerated particles radiate by interacting with a shock-generated magnetic field (e.g. Wijersetal.1997:&Galama1999:Frailetal.2000:Panaiteseu&Ixirunar. 2002)).," Ever since the discovery of the first afterglows, these have been modeled succesfully by combining a model for the blast wave dynamics with a sychrotron radiation model, where shock-accelerated particles radiate by interacting with a shock-generated magnetic field (e.g. \citealt{Wijers1997, Wijers1999, Frail2000, PK2002}) )."280 AnalvGecally tractable solutions for the dvnamies are the self-similar Blandford-MeIxee (BAI. Blandford&Melee1976)). and sedov-von Neumann-Tavlor (ST. Sedov1959:Tavlor1950:VouNeumann 1961)) solutions describing. respectively. (he ulira-relativistic ancl non-relativistic phase of the blast wave evolution.," Analytically tractable solutions for the dynamics are the self-similar Blandford-McKee (BM, \citealt{Blandford1976}) ) and Sedov-von Neumann-Taylor (ST, \citealt{Sedov1959, Taylor1950, vonNeumann1961}) ) solutions describing, respectively, the ultra-relativistic and non-relativistic phase of the blast wave evolution."281 At early time lateral spreading of the collimated jet has not vet set in and the outflow is purely radial. while al late times the jet will have become (uly spherical. allowing the application of spherically svmmetrie solutions in both cases.," At early time lateral spreading of the collimated jet has not yet set in and the outflow is purely radial, while at late times the jet will have become truly spherical, allowing the application of spherically symmetric solutions in both cases."282 As of vet. no analvtieal solution exists that fully captures the intermediate stage of the blast wave evolution. where the blast wave becomes trausrelativistic. inhomogenous along the shock front (Zhang&Mac-Facdven2009;VanEerten&MacFadven2011) and decollimates.," As of yet, no analytical solution exists that fully captures the intermediate stage of the blast wave evolution, where the blast wave becomes transrelativistic, inhomogenous along the shock front \citep{Zhang2009, vanEerten2011jetspreading} and decollimates."283 Early attempts assumed a homogeneous shock front (Rhoads1999). or spherical outflow (παςetal.1999).. while even recently studies (e.g. Granot&Piran 2011)) do not account [or the radial structure of the jet.," Early attempts assumed a homogeneous shock front \citep{Rhoads1999} or spherical outflow \citep{Huang1999}, while even recently studies (e.g. \citealt{Granot2011}) ) do not account for the radial structure of the jet."284 The practical implications of the fact that the blast wave evolution is determined by a very small number of variables such that scalings between different explosion energies and circumbiurst density are possible were not fully realized until verv recently., The practical implications of the fact that the blast wave evolution is determined by a very small number of variables such that scalings between different explosion energies and circumburst density are possible were not fully realized until very recently.285 The scalings apply in the asvimptolic sell-similar limits. but also in the intermediate regime where the two-dimensional nature of jet decollimation is in full effect.," The scalings apply in the asymptotic self-similar limits, but also in the intermediate regime where the two-dimensional nature of jet decollimation is in full effect."286 This made it possible to use only a small set of simulations for different initial jel opening angles as a basis lor a fit code that can be applied to broadband aftereglow data (VanEertenetal.2011).., This made it possible to use only a small set of simulations for different initial jet opening angles as a basis for a simulation-based fit code that can be applied to broadband afterglow data \citep{vanEerten2011boxfit}.287 Bul even though a complete recalculation of the dynamics of the blast wave is no longer necessary. (here remained the equations of radiative Urausfer of (a representative number of) ravs (rough (he evolving jet. that have to be solved for each datapoint fit iteration.," But even though a complete recalculation of the dynamics of the blast wave is no longer necessary, there remained the equations of radiative transfer of (a representative number of) rays through the evolving jet, that have to be solved for each datapoint fit iteration."288 For a large nuniber of iterations and datapoints this procedure remains computationally expensive and requires the use of a parallel computer., For a large number of iterations and datapoints this procedure remains computationally expensive and requires the use of a parallel computer.289 The current study shows (hat the calculation (ime for a given light curve or spectrum can be futher reduced., The current study shows that the calculation time for a given light curve or spectrum can be further reduced.290 We demonstrate that scalability between blast waves has straightforward implications for scalability between light curves., We demonstrate that scalability between blast waves has straightforward implications for scalability between light curves.291 In 82. we describe how the scaling relations for the clvnamics of blast waves can be used (o scale between light curves as well., In \ref{scalings_section} we describe how the scaling relations for the dynamics of blast waves can be used to scale between light curves as well.292 We show that the sealings remain unchanged. between the DM. ancl ST regimes. and in 33 we demonstrate numerically that the sealings also hold in the intermediate regime and [or off-axis observers.," We show that the scalings remain unchanged between the BM and ST regimes, and in \ref{numerics_section} we demonstrate numerically that the scalings also hold in the intermediate regime and for off-axis observers."293 We discuss our findings in 84.., We discuss our findings in \ref{discussion_section}. .294"grid along its cardinal directions, necessary to maximise the usage of the cubic simulation volume.","grid along its cardinal directions, necessary to maximise the usage of the cubic simulation volume."295 We focus on the thermal state of the gas surrounding the central source before and after the II-front passes., We focus on the thermal state of the gas surrounding the central source before and after the I-front passes.296 The evolution of the temperature in slice through the simulation is shown in Figure 1.., The evolution of the temperature in a slice through the simulation is shown in Figure \ref{fig:temperature}.297 The role aplayed by dense structures surrounding the source in restraining the growth of the aand ILfronts is apparent in the highly anisotropic temperature patterns., The role played by dense structures surrounding the source in restraining the growth of the and I-fronts is apparent in the highly anisotropic temperature patterns.298" For comparison, the density field at z—2.6 is shown in Figure 2.. ("," For comparison, the density field at $z=2.6$ is shown in Figure \ref{fig:overdensity}. ("299"Since the overdensities change very little over the redshift interval 2.6«z4.6, only the image at z—2.6 is shown.)","Since the overdensities change very little over the redshift interval $2.6<z<4.6$, only the image at $z=2.6$ is shown.)"300" The gas temperature increases sharply behind the ILfronts, then relaxes to lower values as the gas achieves equilibrium between photoionization heating and atomic radiative losses."," The gas temperature increases sharply behind the I-fronts, then relaxes to lower values as the gas achieves equilibrium between photoionization heating and atomic radiative losses."301" As a consequence, the highest temperatures tend to lie furthest from the source in regions behind the Il-front."," As a consequence, the highest temperatures tend to lie furthest from the source in regions behind the I-front."302" Thus, whilst the gas temperature is increased within the rregion surrounding the QSO compared with the gas temperature outside, the temperature of the gas within the rregion decreases towards the QSO itself."," Thus, whilst the gas temperature is increased within the region surrounding the QSO compared with the gas temperature outside, the temperature of the gas within the region decreases towards the QSO itself."303" As will be discussed in below, another important contributing factor to the trend is the hardening of the radiation field by the intervening gas between the source and the more distant regions."," As will be discussed in below, another important contributing factor to the trend is the hardening of the radiation field by the intervening gas between the source and the more distant regions."304 Figure 3 shows azimuthal averages of the median gas temperature along lines of sight drawn around the source with varying impact parameter., Figure \ref{fig:los-temperature} shows azimuthal averages of the median gas temperature along lines of sight drawn around the source with varying impact parameter.305" Once the power-law source turns on, a steep rise in the temperature with decreasing redshift is found."," Once the power-law source turns on, a steep rise in the temperature with decreasing redshift is found."306 The rise occurs over a much narrower redshift interval than the transition redshift interval of the source spectrum as the source becomes sufficiently hard to photoionizeHerr., The rise occurs over a much narrower redshift interval than the transition redshift interval of the source spectrum as the source becomes sufficiently hard to photoionize.307" The associated photoionization heating occurs over a redshift interval of approximately Az~0.4, with the temperature peaking at the centre of the transition redshift interval."," The associated photoionization heating occurs over a redshift interval of approximately $\Delta308z\simeq0.4$, with the temperature peaking at the centre of the transition redshift interval."309 The median averages show a trend of increasing temperature with increasing impact parameter of the lines of sight after helium is fully ionized., The median averages show a trend of increasing temperature with increasing impact parameter of the lines of sight after helium is fully ionized.310 The, The311orbits is determined that best fits the observed. kincniatics. using the observed surface brightness and selt-consistency as constraints.,"orbits is determined that best fits the observed kinematics, using the observed surface brightness and self-consistency as constraints."312" This wav. the viewing directions. stellar mass- ratio Al,L. central black hole mass Al. as well as the internal orbital structure can be determined. (see also van de Ven. de Zeeuw van den Boseh 2008: van den Bosch van de Ven 2008))."," This way, the viewing directions, stellar mass-to-light ratio $M_*/L$, central black hole mass $M_\bullet$ as well as the internal orbital structure can be determined (see also van de Ven, de Zeeuw van den Bosch \nocite{2008MNRAS.385..614V}; van den Bosch van de Ven \nocite{2008arXiv0811.3474V}) )."313 Within the limits of the observed. photometry and LOSVD. the velocity. anisotropy of the galaxy can vary [reely.," Within the limits of the observed photometry and LOSVD, the velocity anisotropy of the galaxy can vary freely."314 We extended. the triaxial Schwarzschild code by acting a dark matter halo to the gravitational potential. which already consisted of a stellar. contribution inferred fron the observed. photometry and a Plummer potential for the contribution of the central black bole (see van den Bosch et al.," We extended the triaxial Schwarzschild code by adding a dark matter halo to the gravitational potential, which already consisted of a stellar contribution inferred from the observed photometry and a Plummer potential for the contribution of the central black hole (see van den Bosch et al."315 for more details)., \nocite{2008MNRAS.385..647V} for more details).316 We parametrise the dark halo with a spherical NEW profile (Navarro. Frenk White 1996)): with p. the characteristic density of the halo and. rs a characteristic radius.," We parametrise the dark halo with a spherical NFW profile (Navarro, Frenk White \nocite{1996ApJ...462..563N}) ): with $\rho_s$ the characteristic density of the halo and $r_s$ a characteristic radius."317 The potential generated. by. this density. distribution is then given by: where € is the gravitational constant., The potential generated by this density distribution is then given by: where $G$ is the gravitational constant.318 We are interested in the presence and. acceptable mass range of the halo: modeling the shape of the halo in detail is bevond. the scope of this paper., We are interested in the presence and acceptable mass range of the halo; modeling the shape of the halo in detail is beyond the scope of this paper.319 We therefore fix. the concentration e=rego£r; of the halo to 10. as indicated by cosmological simulations (Bullock et al. 2001)).," We therefore fix the concentration $c = r_{200}/r_s$ of the halo to 10, as indicated by cosmological simulations (Bullock et al. \nocite{2001MNRAS.321..559B}) )."320 Llere 17200 is the radius of the halo within which the mean density has dropped. to 200 times the critical densitypoji., Here $r_{200}$ is the radius of the halo within which the mean density has dropped to 200 times the critical density$\rho_{\mathrm{crit}}$.321" Le can be shown that such that e determines p, in the potential of Equation 6..", It can be shown that such that $c$ determines $\rho_s$ in the potential of Equation \ref{eq:NFWpot}.322" We vary the halo mass. which is the enclosed mass within roug. vielding r,."," We vary the halo mass, which is the enclosed mass within $r_{200}$, yielding $r_s$."323 We only [it lor Alsou ancl keep AL./L fixed to the maximum: value allowed by the data. therefore fitting a minimal halo or maximalspheroid?.," We only fit for $M_{200}$ and keep $M_*/L$ fixed to the maximum value allowed by the data, therefore fitting a minimal halo or maximal."324. The influence of the black hole is negligible at [large racii and therefore we also do not fit [or Ad. but keep its value fixed., The influence of the black hole is negligible at large radii and therefore we also do not fit for $M_\bullet$ but keep its value fixed.325 NGC 3379 has a small kinematic misalignment of 5+3° (e.g. Statler Smecker-Hane 1990)) and shows signs of a kinematic twist (Ixrajnovié et al. 2008)..," NGC 3379 has a small kinematic misalignment of $5 \pm 3^\circ$ (e.g. Statler Smecker-Hane \nocite{1999AJ....117..839S}) ) and shows signs of a kinematic twist (Krajnović et al. \nocite{2008MNRAS.390...93K},"326 which indicate that the galaxy is not perfectly axisvnimetric (see also C'apaccioli et al. 1991:, which indicate that the galaxy is not perfectly axisymmetric (see also Capaccioli et al. \nocite{1991ApJ...371..535C};327 Statler 90011)., Statler \nocite{2001AJ....121..244S}) ).328 Van den Bosch de Zeeuw therefore constructed triaxial Schiwarzschild mocdels of this galaxy., Van den Bosch de Zeeuw \nocite{2009MNRAS.subm} therefore constructed triaxial Schwarzschild models of this galaxy.329 Vhei best-fitting triaxial model (axis ratios p= 0.95. q- = OSI) is nearly [ace-on. with an inclination of ~40°.," Their best-fitting triaxial model (axis ratios $p$ = 0.95, $q$ = 0.81) is nearly face-on, with an inclination of $\sim40^\circ$."330 This model is nearly spherical in the centre anc becomes close to oblate at large radii. which is in agreemen with Statler and De Lorenzi et al. (2009)..," This model is nearly spherical in the centre and becomes close to oblate at large radii, which is in agreement with Statler \nocite{2001AJ....121..244S} and De Lorenzi et al. \nocite{2009MNRAS.395...76D}."331 We adopt the best-fit model of van den Bosch de Zeeuw for our halo moceline., We adopt the best-fit model of van den Bosch de Zeeuw \nocite{2009MNRAS.subm} for our halo modeling.332" The mode has a black hole mass of Al,=4.010AJ. and a dynamical mass-to-light ratio M/L,; = 2.9 M./Lj,.. which we adopt as the maximally allowed: stellar mass-to-ligh ratio Ad,/L."," The model has a black hole mass of $M_\bullet = 4.0 \times 10^8 M_\odot$ and a dynamical mass-to-light ratio $M/L_I$ = 2.9 $M_\odot/L_{I,\odot}$, which we adopt as the maximally allowed stellar mass-to-light ratio $M_*/L$."333 The stellar potential is represented by a Multi-Gaussian Expansion. (MGIZ. Emsellem. Monnet Bacon 1994: Cappellari model based upon /-band. ing.. presented by Cappellari et al. (2006)..," The stellar potential is represented by a Multi-Gaussian Expansion (MGE, Emsellem, Monnet Bacon \nocite{1994A&A...285..723E}; ; Cappellari \nocite{2002MNRAS.333..400C} model based upon $I$ -band, presented by Cappellari et al. \nocite{2006MNRAS.366.1126C}."334 We use the sanie central SAURON kinematics (up to fe) extracted with the ALLLES library (see Shapiro et al. 2006::, We use the same central SAURON kinematics (up to $h_6$ ) extracted with the MILES library (see Shapiro et al. \nocite{2006MNRAS.370..559S};335 C'appellari et al. 2007:, Cappellari et al. \nocite{2007MNRAS.379..418C};336 van den Bosch de Zeeuw 2009)) to cover the inner I of NGC 3379 and add our measure points at large radii., van den Bosch de Zeeuw \nocite{2009MNRAS.subm}) ) to cover the inner $R_e$ of NGC 3379 and add our measure points at large radii.337 For extra spatial coverage. we also include the svnunetrized data of the four long-slit observations of Statler Smecker-Lane (see Figure 10)).," For extra spatial coverage, we also include the symmetrized data of the four long-slit observations of Statler Smecker-Hane \nocite{1999AJ....117..839S} (see Figure \ref{fig:foot}) )."338 The Large mosaic of central SAURON data provides many more kinematic constraints in he central region than the four slits., The large mosaic of central SAURON data provides many more kinematic constraints in the central region than the four slits.339 We therefore exclude he inner 20 aresee of cach slit from the fit., We therefore exclude the inner 20 arcsec of each slit from the fit.340 The planetary nebulae measurements are not. based. on integrated. stellar ight. as our SAURON and long-slit data. and therefore for consistency not included.," The planetary nebulae measurements are not based on integrated stellar light, as our SAURON and long-slit data, and therefore for consistency not included."341 We use a similar procedure to construct mass mocels of GO S21., We use a similar procedure to construct mass models of NGC 821.342 This galaxy is a very [lattened system (190) and shows no signs of non-axisvmmetry in its central part. even hough planetary nebulae kinematics suggest twists at larger radii (Coceato ct al. 2009)).," This galaxy is a very flattened system (E6) and shows no signs of non-axisymmetry in its central part, even though planetary nebulae kinematics suggest twists at larger radii (Coccato et al. \nocite{2009MNRAS.394.1249C}) )."343 Our dataset however provides no constraints on the behaviour of the velocity field at these scales., Our dataset however provides no constraints on the behaviour of the velocity field at these scales.344 We therefore deproject this galaxy axisvmmetrically. assuming an edge-on view and use the triaxial code in the axisvmmetric limit.," We therefore deproject this galaxy axisymmetrically, assuming an edge-on view and use the triaxial code in the axisymmetric limit."345 We adopt the edge-on. ALG mocel of NGC 821 based upon ground-based -band. ancl space-basecl imaging with HIST/WEDPC2 in. FSIAW-band. as in MeDermid and Cappellari et al. (2006)..," We adopt the edge-on MGE model of NGC 821 based upon ground-based $R$ -band and space-based imaging with HST/WFPC2 in F814W-band, as in McDermid \nocite{2002PhD} and Cappellari et al. \nocite{2006MNRAS.366.1126C}."346 We first construct a model without a dark halo. based only on kinematics (up to fe) of the central SAURON dataset. extracted with the MILISS library (Cappellari ct al. 20073).," We first construct a model without a dark halo, based only on kinematics (up to $h_6$ ) of the central SAURON dataset, extracted with the MILES library (Cappellari et al. \nocite{2007MNRAS.379..418C}) )."347" Our best fit has a stellar mass-to-light ratio of 2.5 M.fLj. with a black hole mass of A4,—2.1.107. from the AA- 7 relation."," Our best fit has a stellar mass-to-light ratio of 2.5 $M_\odot/L_{I,\odot}$ with a black hole mass of $M_\bullet = 2.1 \times 10^8 M_\odot$ from the $M_\bullet$ $\sigma$ relation."348 We then add a dark NEW halo to this model. with a fixed concentration of e=10.," We then add a dark NFW halo to this model, with a fixed concentration of $c=10$."349 The SAURON central dataset is used to cover the central part of the galaxy. while our four measurepoints at large raclii are included to cover the outerparts.," The SAURON central dataset is used to cover the central part of the galaxy, while our four measurepoints at large radii are included to cover the outerparts."350 To avoid a possible conflict between the central. SAURON data and the long-slit cata of Forestell Gobhardt (2008)... we decided to not include the latter in our model. as there seem to be some deviations between the two datasets(see Figure 6)).," To avoid a possible conflict between the central SAURON data and the long-slit data of Forestell Gebhardt \nocite{2008arXiv0803.3626F}, , we decided to not include the latter in our model, as there seem to be some deviations between the two datasets(see Figure \ref{fig:kin_ngc821}) )."351 Our best fitting mocdel for NGC 3379 requires a halo, Our best fitting model for NGC 3379 requires a halo352In1.. we have seen (hat BS(Q./) of CEV model has multiple solutions.,"In, we have seen that $BS(Q,f)$ of CEV model has multiple solutions."353 We continue this model to demonstrate5.. a solution smaller than V. must. be unbounded from below.," We continue this model to demonstrate, a solution smaller than $V$ must be unbounded from below."354 Recall that the domain of the value function V is given on the domain Q of(2.4).. aud its related truncated domain Q is given by," Recall that the domain of the value function $V$ is given on the domain $\overline Q$ of, and its related truncated domain $Q_\beta$ is given by."355(3.5).. Let 2:(Q—IR. be a measurable function., Let $\varphi: \overline Q \to \mathbb{\bar R^+}$ be a measurable function.356 We introduce the truncated value function V* for convenience. where the stopping time 7? of is the first hitting time to the barrier 2.," We introduce the truncated value function $V^{\beta,357 \varphi}$ for convenience, where the stopping time $\tau^\beta$ of is the first hitting time to the barrier $\beta$."358 By the above definition. for the V of(3.2). if we set With the above setup. to prove Theorem 1.. our goal is toestimate |V?—V| as ο—x with 424 of and the constraint on g given in Theorem 1..," By the above definition, for the $V^\beta$ of, if we set With the above setup, to prove Theorem \ref{thm:conv}, our goal is toestimate $|V^{\beta, \varphi_1} - V|$ as $\beta \to \infty$ with $\varphi_1$ of and the constraint on $g$ given in Theorem \ref{thm:conv}. ."359 We emphasize here. jy may not be continuous up to the boundary. ie. 424€C(Q) when gr)<flr) for somex> 0.," We emphasize here, $\varphi_1$ may not be continuous up to the boundary, i.e. $\varphi_1 \notin C(\overline{Q})$ when $g(x)< f(x)$ for some$x>0$ ."360Alternatively. by performing the O-integral over the 6 function. one obtains where the final expression is obtained by partially integrating twice.,"Alternatively, by performing the $\Theta$ -integral over the $\delta$ function, one obtains ^2(z) ^2(z_c), where the final expression is obtained by partially integrating twice."361 Noting that the inlegral over O in (3.3)) is equal to 4/15. the two results agree.," Noting that the integral over $\Theta$ in \ref{eta5}) ) is equal to $4/15$, the two results agree."362 An alternative form is , An alternative form is P _c).363The power per unit frequency. (o). is identiliel bywriting the right hand side οἱ οςa ). (3.3)) or (3.3)) as the integral of P(e) over dic.," The power per unit frequency, $P(\omega)$, is identified bywriting the right hand side of \ref{eta5}) ),\ref{eta5a}) ) or \ref{eta5b}) ) as the integral of $P(\omega)$ over $\rmd\omega$ ."364 One finds, One finds ^2(z_c) _c).365WolfRavet (WR) stars are evolved massive stars characterized by hieh mass loss ratos (107<LONLxy5λίτρο1019 37.3. driven in fast (es~ewosB0) ln/s) stella winds.,"Wolf–Rayet (WR) stars are evolved massive stars characterized by high mass loss rates $10^{-5}\le\dot{M}\le10^{-4}\:\msun\:\mathrm{yr}^{-1};366\dot{M}_{WR}\sim10^{10}\:\dot{M}_\odot$ ), driven in fast $v_\infty \sim367\mathrm{few} \times 10^3\,\mathrm{km/s}$ ) stellar winds."368 The deuse WR winds obscure their underlying cores aud the region from which ιο outflowiusg wind material is initially accelerated., The dense WR winds obscure their underlying cores and the region from which the outflowing wind material is initially accelerated.369 The difficulty iu quautifiug bulk parameters of WR stars which arises due to this obscuration is tvpified hy jio uncertaintv reearding the appropriate photospheric cluperature to assign them., The difficulty in quantifying bulk parameters of WR stars which arises due to this obscuration is typified by the uncertainty regarding the appropriate photospheric temperature to assign them.370 When the most commonly used definition of the plotosphere is adopted (the ocation of optical depth 7~ 2/3). a temperature degeneracy arises in the models of WR atmospheres or all WR subtypes. the effective plotoxpleric cluperature derived is Doe;~30.000TS. for reasons uuknown (?)..," When the most commonly used definition of the photosphere is adopted (the location of optical depth $\tau\sim2/3$ ), a temperature degeneracy arises in the models of WR atmospheres — for all WR subtypes, the effective photospheric temperature derived is $T_{2/3}\sim30,000\,\mathrm{K}$, for reasons unknown \citep*{Schmutz1992}."371 More effective for predicting luuinesity and αμασοι flux distribution is the interred cluperature. but this assignment depends critically on he choice of a velocity structure of the wiud. the conumionlv asstucd form of which ?. showed to be largely invalid in the single WR star (IID 50896 66) for which the optically thin. supersonic portion of the wiud as been modeled lvdrocwnamically.," More effective for predicting luminosity and emergent flux distribution is the inferred temperature, but this assignment depends critically on the choice of a velocity structure of the wind, the commonly assumed form of which \citet{Schmutz1997} showed to be largely invalid in the single WR star (HD 50896 – 6) for which the optically thin, supersonic portion of the wind has been modeled hydrodynamically."372 Testing models of WR core evolution. aud the advanced unclear reactions which occur there. is complicated by this disconnect vetween the observable bulk properties of the wind. aud he wind-driving core buried beneath it.," Testing models of WR core evolution, and the advanced nuclear reactions which occur there, is complicated by this disconnect between the observable bulk properties of the wind, and the wind-driving core buried beneath it."373 A powerful technique for probing WR core evolution which sidesteps these difficulties is available iu the ueasured abundances of wind-borue nuclear processed elements, A powerful technique for probing WR core evolution which sidesteps these difficulties is available in the measured abundances of wind-borne nuclear processed elements.374" Neon iu particular undergoes a remarkable abuudance change divine the later stages of a WR stars Ποιο,", Neon in particular undergoes a remarkable abundance change during the later stages of a WR star's lifetime.375" By the eud of the more evolved WC phase (characterized by wind material dominated by a-burnuiug by-products. carbon im. particular).H DOAXA-Nethe7 becomes fourth: most abundant element. after: Πο,FC.»aud MO."," By the end of the more evolved WC phase (characterized by wind material dominated by $\alpha$ -burning by-products, carbon in particular), } becomes the fourth most abundant element, after }, }, and }."376" : The reactions of interest contributing to the creation of neon during IHe-buruiug im massive stars are (2): of the tN produced via the CN brauch of the CNQO evele which dominates the carlier WN evolutionary phase to ??Ne, ", The reactions of interest contributing to the creation of neon during He-burning in massive stars are \citep{Maeder1983}: Essentially all of the } produced via the CN branch of the CNO cycle which dominates the earlier WN evolutionary phase is converted to }.377The further conversion of neon Meaudto 7°Meis7? iuefficieut except at the highest temperatures (achieved only iu stars with LOOAT..). and the production of20NG via initial100)Gsmassesalsoneglieible2 except iu the most advanced WC and WO stages of the highest mass stars.," The further conversion of neon to } and } is inefficient except at the highest temperatures (achieved only in stars with initial masses $\gtrsim100\textrm{M}_\odot$ ), and the production of } via } is also negligible except in the most advanced WC and WO stages of the highest mass stars."378 The two main consequences of these critical neon production cliains are a strong increase in the overall abundance of neon by a factor of ~200 over the course of the WR aud a rise in the isotopic abundance ratio 72Ne/79phase.Nefrom ~0.1 to 35.," The two main consequences of these critical neon production chains are a strong increase in the overall abundance of neon by a factor of $\sim$ 200 over the course of the WR phase, and a rise in the isotopic abundance ratio } from $\sim$ 0.1 to $\sim$ 35."379 Both of these changes to the neon abundance occur quite rapidly (in the course of several thousaud vears) at he onset of the WC phase., Both of these changes to the neon abundance occur quite rapidly (in the course of several thousand years) at the onset of the WC phase.380" Late-stage depletion of 2Ne W conversion to maenesmaa is only diving the final 109 ve of the 11ost massive stars lives. with the overwhehuine majority of WRs αλαιο heir full neon excess. thanks to the combined effects of he interior mixing and mass-loss which bring material o the surface,"," Late-stage depletion of } by conversion to magnesium is only during the final $10^6$ yr of the most massive stars' lives, with the overwhelming majority of WRs maintaining their full neon excess, thanks to the combined effects of the interior mixing and mass-loss which bring material to the surface."381 Asstuing normal p-p nuclear processing of hydrogen eutirelv to Lelimu. the cosmic abundance of 10011 by umber is Ne/Ile23.7«10! (see," Assuming normal p-p nuclear processing of hydrogen entirely to helium, the cosmic abundance of neon by number is $\nehe=3.7\times 10^{-4}$ (see"382of the mocdels includes ΝΤΟ cllects) ancl all radiative transfer calculations.,of the models includes NLTE effects) and all radiative transfer calculations.383 For cach primary NLTE line we adel 3 to 5 wavelength points to the overall wavelength erid., For each primary NLTE line we add 3 to 5 wavelength points to the overall wavelength grid.384 This procedure typically leads το about 55.000150.000. wavelength points for the model computations and the svnthetie spectrum calculations.," This procedure typically leads to about 55,000--150,000 wavelength points for the model computations and the synthetic spectrum calculations."385 Test. calculations have shown that the resulting overall wavelength: eric is completely adequate for NLTIE caleulations in static and expanding media (Llauschildt&Baron1995)., Test calculations have shown that the resulting overall wavelength grid is completely adequate for NLTE calculations in static and expanding media \cite{fe2pap}.386. We have also calculated LYE continuum and line blanketed: models. [or comparison., We have also calculated LTE continuum and line blanketed models for comparison.387 In figure LO we show a svnthetic spectrum at the nominal resolution. illustrating the effect. of. low resolution on the appearance of the spectrum.," In figure \ref{hr} we show a synthetic spectrum at the nominal resolution, illustrating the effect of low resolution on the appearance of the spectrum."388 We compare our LTE and NLTE models to. the Ixurucz 92 LTE set of svnthetic spectra in Figs., We compare our LTE and NLTE models to the Kurucz 92 LTE set of synthetic spectra in Figs.389 I1. and 12.., \ref{comp1} and \ref{comp2}.390 The sspectra have been convolved with a Gaussian kernel of GA half-width to make the resolutions of the cillerent sets of spectra comparable., The spectra have been convolved with a Gaussian kernel of $6\ang$ half-width to make the resolutions of the different sets of spectra comparable.391 In general the spectra are very similar., In general the spectra are very similar.392 We use an updated version of the Ixurucz atomic line lists: this could explain the dillerences between the LVL mocels., We use an updated version of the Kurucz atomic line lists; this could explain the differences between the LTE models.393 In addition. the mmodels allow for line scattering and. NLTE (Fig. 12))," In addition, the models allow for line scattering and NLTE (Fig. \ref{comp2}) )"394 whereas the Ixurucz models are caleulated: using complete LYE (no line scattering)., whereas the Kurucz models are calculated using complete LTE (no line scattering).395 All model atmospheres presented. in this paper have og(g)= 4.0., All model atmospheres presented in this paper have $\log(g)=4.0$ .396" Three elfective temperatures CX. D. and € respectively) Lop,=38.000. 45.000. ancl 55.000Ix... have »en considered."," Three effective temperatures (A, B, and C respectively) $T_{eff}=38,000$, 45,000, and $55,000\,$ K, have been considered."397 For cach of these Zip; we have computed models with104... and solar metal abundances(1-3. 4-6. 7-9 respectively).," For each of these $\Teff$ we have computed models with, and solar metal abundances(1-3, 4-6, 7-9 respectively)."398 In. each case NLPE and ETE ine blanketecl models as well as LYE continuum moclels were calculated., In each case NLTE and LTE line blanketed models as well as LTE continuum models were calculated.399 “Phe models and the resulting ionization xwameters qu: the base ten-Iogarithm of the emission rate of LUE Lyman continuum photons and qi (helium. continuum) are presented. in table 1., The models and the resulting ionization parameters $q_{0}$: the base ten-logarithm of the emission rate of HI Lyman continuum photons and $q_{1}$ (helium continuum) are presented in table 1.400 In addition we have computed for cach temperature a line blanketed LEE solar metallicity model (AS. BS. CS). to assess quantitative clillerenees which could result. from a contaminating population of of voung evolved stars that may be present in the LIE region.," In addition we have computed for each temperature a line blanketed LTE solar metallicity model (AS, BS, CS), to assess quantitative differences which could result from a contaminating population of of young evolved stars that may be present in the HII region."401 We start by considering low metallicity mocels., We start by considering low metallicity models.402 As expected. the resulting ionization photon Iluxes are most sensitive to the temperature.," As expected, the resulting ionization photon fluxes are most sensitive to the temperature."403 The dependence in qi; on the metallicity is typically weak., The dependence in $q_{1}$ on the metallicity is typically weak.404 The strongest variation is among the different mocdel type themselves (LVL vs. NLTIE)., The strongest variation is among the different model type themselves (LTE vs. NLTE).405 For the higher temperatures the cilfercnees in qu ancl qi are typically of order. 0.02. or less., For the higher temperatures the differences in $q_0$ and $q_1$ are typically of order 0.02 or less.406 For models 1-9. the dillerences in qj between LTE and. NLTIS models can be as large as 0.19. meaning that the amount of Le ionizing flux ολους bv a factor of 1077.," For models A1-9, the differences in $q_1$ between LTE and NLTE models can be as large as 0.19, meaning that the amount of He ionizing flux differs by a factor of $10^{0.19}$."407 As the dillerences in qu is only about 0.02. the implied dillerence is the ratio of helium-ionizing Ilux to hveirogen-ionizing Hux is about LO~1.45.," As the differences in $q_{o}$ is only about 0.02, the implied difference is the ratio of helium-ionizing flux to hydrogen-ionizing flux is about $10^{0.17}\sim 1.45$."408 We compare the spectra of the -LPE. LYE line rlanketed anc LTE continuum models for three effective emperatures in Figs.," We compare the spectra of the NLTE, LTE line blanketed and LTE continuum models for three effective temperatures in Figs."409 13 to 15.., \ref{tim1} to \ref{tim3}.410 Phe effects of line blanketing on the overall shape of the spectra is significant. even at the owest metallicity that we have considered.," The effects of line blanketing on the overall shape of the spectra is significant, even at the lowest metallicity that we have considered."411 The cdilferences tween LTIS and NLETIS spectra are smaller than the effects of line blanketing by itself, The differences between LTE and NLTE spectra are smaller than the effects of line blanketing by itself.412 Loneware of 1000. X... NLTE elfects on the spectra are small. especially near the thireshold emperature of Zi;=38.000. and would thus have small if any impact on near-UV observations.," Longward of 1000 , NLTE effects on the spectra are small, especially near the threshold temperature of $\Teff=38,000\,$ and would thus have small if any impact on near-UV observations."413 In figures 16 to 18. we show comparisons between solar metallicity spectra and. spectra computed. for 1/10 of the solar metallicity., In figures \ref{mh1} to \ref{mh3} we show comparisons between solar metallicity spectra and spectra computed for 1/10 of the solar metallicity.414 La the solar metallicity spectra the metal lines are always stronger than in the spectra for 1/10 solar metallicity (though the Lyman edge is typically not. quite as strong as in the 1/10 solar metallicity spectra), In the solar metallicity spectra the metal lines are always stronger than in the spectra for 1/10 solar metallicity (though the Lyman edge is typically not quite as strong as in the 1/10 solar metallicity spectra).415 The dillerences in the value of qj areαι., The differences in the value of $q_{1}$ are.416 This implies that if of the stars are vounger higher metallicity stars. the iferenees in the total ionizing number of photons exciting 16 surrounding nebula would be about14.," This implies that if of the stars are younger higher metallicity stars, the differences in the total ionizing number of photons exciting the surrounding nebula would be about."417.. However. 1e differences between the spectra are considerably. more pronounced.," However, the differences between the spectra are considerably more pronounced."418 “Phe resulting ellects from this fact have been μαuciied recently by (Garacta-Vargaset.al.LOOT)... who found iu the Woll-Ravet contribution typically dominates this cllect.," The resulting effects from this fact have been studied recently by \cite{gar97}, who found that the Wolf-Rayet contribution typically dominates this effect."419 Our synthetic spectra show that the predicted. degree of helium ionization in (Ισ could. vary significantly: epending on cdillerent model assumptions about the stellar umospheres., Our synthetic spectra show that the predicted degree of helium ionization in GEHR could vary significantly depending on different model assumptions about the stellar atmospheres.420" In the end. the computed value of Hc]/MH] in 1e nebula depends on the fraction of ionization contributed w the ""relatively cool” hot stars. as well as the geometry of 1e LEE region."," In the end, the computed value of [He]/[H] in the nebula depends on the fraction of ionization contributed by the “relatively cool” hot stars, as well as the geometry of the HII region."421 As the number of recombinations in an LLL region equals the number of ionization. one might expect wt the depths of the ionization zones for He and LE would scale roughly as the cube root of the ionizing fluxes (only roughly because Lle-ionizing radiation can also ionize LE).," As the number of recombinations in an HII region equals the number of ionization, one might expect that the depths of the ionization zones for He and H would scale roughly as the cube root of the ionizing fluxes (only roughly because He-ionizing radiation can also ionize H)."422 On 16 other hand. the uncertainties discussed in this paper. i.e. jose due to the assumption of asfafic atmosphere. might x: augmented by additional uncertainties in line blanketing ellects. such as the existence of winds (Gabler et al.," On the other hand, the uncertainties discussed in this paper, i.e. those due to the assumption of a atmosphere, might be augmented by additional uncertainties in line blanketing effects, such as the existence of winds (Gabler et al.,"423 1989. 901. 1992: Najarro et al.," 1989, 1991, 1992; Najarro et al."424 1996). shocks. etc..," 1996), shocks, etc.,"425 which are ond the scope of this paper., which are beyond the scope of this paper.426 The existence of additional uncertainties in the nebular cvnanmies. such as those implied w the presence of filaments. also need to be investigatedther.," The existence of additional uncertainties in the nebular dynamics, such as those implied by the presence of filaments, also need to be investigatedfarther."427 Phe extent to which the theoretical uncertainty can x gauged by scatter in the data is also hard toassess here. »ecause much o£ it may. be systematic.," The extent to which the theoretical uncertainty can be gauged by scatter in the data is also hard toassess here, because much of it may be systematic."428are equally space on either side of the rotation axis).,are equally spaced on either side of the rotation axis).429 They fall aloic a curve that is closely aligued with the rotation axis. the minor axis of the ceutral torus (Αιonuccietal.1991:Callimoreetal—1996:Cueenhillal.1996) aud the inner radio jet (€tallimorectal.1996) and counter-jet.," They fall along a curve that is closely aligned with the rotation axis, the minor axis of the central torus \citep{ant94,gal96,gre96} and the inner radio jet \citep{gal96} and counter-jet."430 Althoreh the center of mass points do rot coincide exactvo with the rotation axis. their departure frou it varies smoothly from triplet A o D aud this departure can be explained if NGC LOGS itself has some proper motion perpendicular o the Lo-s over the time period covered by the ejection eveuts. (," Although the center of mass points do not coincide exactly with the rotation axis, their departure from it varies smoothly from triplet A to D and this departure can be explained if NGC 1068 itself has some proper motion perpendicular to the l-o-s over the time period covered by the ejection events. ("431This is discussed in detail in a ater paper).,This is discussed in detail in a later paper).432 The N-S offset between the galaxw aud each riplet’s center of mass. whether in the jet or counter-jet direction. is asstuued to indicate that conrponeut of the trplet’s motion. resulting from its respective ejection event. that is directed along he rotation axis and perpendicular to the 1-o-s.," The N-S offset between the galaxy and each triplet's center of mass, whether in the jet or counter-jet direction, is assumed to indicate that component of the triplet's motion, resulting from its respective ejection event, that is directed along the rotation axis and perpendicular to the l-o-s."433 In Fig., In Fig.434 4 the sources in cach triplet have con. re-plotted after removing the N-S offsets of heir respective centers of mass., 4 the sources in each triplet have been re-plotted after removing the N-S offsets of their respective centers of mass.435 The plot shows he relative triplet orieutation more clearly., The plot shows the relative triplet orientation more clearly.436 Each riplet is identified by an A. D. C. or D adjaceut ο its associated pai.," Each triplet is identified by an A, B, C, or D adjacent to its associated pair."437 The triplet position angle > and related rotation angle 6 (defined below) rotate sinoothlv about the rotation axis iu a counter-clockwise direction frou A to D (again this continuous rotation for triplets A to D is achieved oulv if source 10 is chosen for the singlet in triplet D)., The triplet position angle $\beta$ and related rotation angle $\theta$ (defined below) rotate smoothly about the rotation axis in a counter-clockwise direction from A to D (again this continuous rotation for triplets A to D is achieved only if source 10 is chosen for the singlet in triplet D).438 This rotation direction is the same as the galaxy rotation direction and may sugeest that the triplet position angele is fixed relative to the co-ordinates of the ceutral object., This rotation direction is the same as the galaxy rotation direction and may suggest that the triplet position angle is fixed relative to the co-ordinates of the central object.439 The chanec in triplet position angle is thus a measure of the rotation of the central object., The change in triplet position angle is thus a measure of the rotation of the central object.440 This possibility is used below to estimate the rotation period ofthe central objec, This possibility is used below to estimate the rotation period of the central object.441 Tn all four triplets in Fig., In all four triplets in Fig.442 L. the pair orientation auele w (defined by the position angle ou the sky of the line counecting between the two sources 1u cach pair) rotates continuously with the triplet position angle ./ and. im so doing. maintains a siuilar oricutation relative to the siuglet/pair midpoiut/rotation axis plane.," 4, the pair orientation angle $\omega$ (defined by the position angle on the sky of the line connecting between the two sources in each pair) rotates continuously with the triplet position angle $\beta$ and, in so doing, maintains a similar orientation relative to the singlet/pair midpoint/rotation axis plane."443 In effect. alb four triplets are similarly structured. differius onlv iu their rotation angles and sizes.," In effect, all four triplets are similarly structured, differing only in their rotation angles and sizes."444 To obtain this result bv chance seems extremely unlikely if it is remembered that the sources m each triplet were, To obtain this result by chance seems extremely unlikely if it is remembered that the sources in each triplet were445an H-index below around 7.5 pm. the average profiles show only weak emission features.,"an H-index below around 7.5 pm, the average profiles show only weak emission features."446 If the H-index exceeds 7.5 pm. a pronounced asymmetry of Hay and Hog is seen.," If the H-index exceeds 7.5 pm, a pronounced asymmetry of $_{\rm 2V}$ and $_{\rm 2R}$ is seen."447 Profiles with a strongly enhanced Hy peak cover around of the area. in agreement with S96.," Profiles with a strongly enhanced $_{\rm 2V}$ peak cover around of the area, in agreement with S96."448 If however the area fractions of all profiles with emission signatures (H-index >7.5 pm) are added up. the ratio of profiles in emission to those without is 60:40.," If however the area fractions of all profiles with emission signatures (H-index $>$ 7.5 pm) are added up, the ratio of profiles in emission to those without is 60:40."449 Taking the full FOV. the area fraction of profiles with an H-index above 7.5 pm is 64%.," Taking the full FOV, the area fraction of profiles with an H-index above 7.5 pm is 64."450. Another estimate can be made from Fig. 18:, Another estimate can be made from Fig. \ref{fig21}:451: a shock event affects usually three to four profiles. Le. it leads to emission for 60 to 80 seconds afterwards.," a shock event affects usually three to four profiles, i.e. it leads to emission for 60 to 80 seconds afterwards."452 If the next shock happens 180 seconds after the first one. the fraction of time spent in emission is around 70/180~40 %.," If the next shock happens 180 seconds after the first one, the fraction of time spent in emission is around $\sim$ 40."453. This definition of the emission from the appearance of any Hay peak then suggests in all estimates that the chromosphere. or more precisely. the core of the Ca II H line spends around half of the time in emission instead of 10%.," This definition of the emission from the appearance of any $_{\rm 2V}$ peak then suggests in all estimates that the chromosphere, or more precisely, the core of the Ca II H line spends around half of the time in emission instead of 10."454. If this emission can by modeled by a static temperature rise. or reflects a temperature rise at all. is another question.," If this emission can by modeled by a static temperature rise, or reflects a temperature rise at all, is another question."455 On locations with detected photospheric fields. a quasi-permanent increase of intensity in both emission peaks is present. in addition to similar repetitive bright grains as happen outside fields.," On locations with detected photospheric fields, a quasi-permanent increase of intensity in both emission peaks is present, in addition to similar repetitive bright grains as happen outside fields."456 Near to. but still outside strong photospheric magnetic. fields. the emission is generally increased (cf.," Near to, but still outside strong photospheric magnetic fields, the emission is generally increased (cf."457 Figs., Figs.458 4. or 16))., \ref{fig5} or \ref{fig19}) ).459 Interestingly. the maximum H-index observed in the time series is located outside of magnetic fields. which could fit with the suggestion of ? that collisions between flux concentrations and granules are responsible for the creation of bright grains.," Interestingly, the maximum H-index observed in the time series is located outside of magnetic fields, which could fit with the suggestion of \citet{kalkofen1996} that collisions between flux concentrations and granules are responsible for the creation of bright grains."460 We note however that in our case it would be the interaction of a strong uni-polar network element with granulation instead of the weaker mixed-polarity fields suggested by ?.., We note however that in our case it would be the interaction of a strong uni-polar network element with granulation instead of the weaker mixed-polarity fields suggested by \citet{kalkofen1996}.461 The areas with least chromospheric emission in our time series are located furthest away (> 10%) from any magnetic fields. in the middle of the observed field of view.," The areas with least chromospheric emission in our time series are located furthest away $>10^{\prime\prime}$ ) from any magnetic fields, in the middle of the observed field of view."462 The spatial distribution of emission in our ]-D slit observations would comply very well with a cut through the FOV observed by οςVO7.. if the slit would be placed across one of the field concentrations. visible in their Fig.," The spatial distribution of emission in our 1-D slit observations would comply very well with a cut through the FOV observed by \citet[][V07]{vecchio+etal2007}, if the slit would be placed across one of the field concentrations visible in their Fig."463 2., 2.464 The halo of enhanced emission close to the fields found in the present paper would correspond to one high-emission fibril seen in the Ca II nm line by VO7., The halo of enhanced emission close to the fields found in the present paper would correspond to one high-emission fibril seen in the Ca II nm line by V07.465 These fibrils are interpreted to reflect the chromospheric magnetic field topology by V07. and enc after around 10 in low-emission dark regions.," These fibrils are interpreted to reflect the chromospheric magnetic field topology by V07, and end after around $10^{\prime\prime}$ in low-emission dark regions."466 Like ?.. we do not see an one-to-one correlation ofemissiot in calcium and photospheric fields or Stokes V signal as claimed by ?.. in none of the Figs. 1.. 4..," Like \citet{lites+etal1999}, we do not see an one-to-one correlation of emission in calcium and photospheric fields or Stokes $V$ signal as claimed by \citet{sivaraman+etal2000}, in none of the Figs. \ref{fig2}, \ref{fig5},"467 or 16.., or \ref{fig19}.468 ? employed data very similar to ours. spectro-polarimetry in nm and spectroscopy in Ca IL H. There are several occurrences of H»y brightenings on locations without any polarization signal above our detection limit of 0.15 of the continuum intensity.," \citet{lites+etal1999} employed data very similar to ours, spectro-polarimetry in nm and spectroscopy in Ca II H. There are several occurrences of $_{\rm 2V}$ brightenings on locations without any polarization signal above our detection limit of 0.15 of the continuum intensity."469" The relation in the other direction is however rather tight: 1f photospheric fields are present. the emission is enhanced and often also affects the Ho, peak as well (Figs."," The relation in the other direction is however rather tight: if photospheric fields are present, the emission is enhanced and often also affects the $_{\rm 2R}$ peak as well (Figs."470 1. and 4))., \ref{fig2} and \ref{fig5}) ).471 To quantify the visual impression. we use the scatter plot of integrated unsigned Stokes V signal vs the H-index (Fig. 21)).," To quantify the visual impression, we use the scatter plot of integrated unsigned Stokes $V$ signal vs the H-index (Fig. \ref{fig23}) )."472 The scatter plot of the full FOV shows the usual behavior (e.g.22??).. a general increase of chromospheric emission with polarization signal. 1e.. with total magnetic flux.," The scatter plot of the full FOV shows the usual behavior \citep[e.g.][]{skumanich+etal1975,schrijver1987,schrijver+etal1989,reza+etal2007}, a general increase of chromospheric emission with polarization signal, i.e., with total magnetic flux."473 To substantiate the claim that emission can occur without fields. we overplotted the values of the quiet region in the middle of the FOV (cf.," To substantiate the claim that emission can occur without fields, we overplotted the values of the quiet region in the middle of the FOV (cf."474Table 2.. 2nd row) separately t light grey.,"Table \ref{tab2}, 2nd row) separately in light grey."475 It can be clearly seen that the emission in this part of the FOV covers the as the full FOV. from 6 to around 11 pm. but shows only weak polarization signals.," It can be clearly seen that the emission in this part of the FOV covers the as the full FOV, from 6 to around 11 pm, but shows only weak polarization signals."476 We emphasize also again the conclusion of ?. that the presence of magnetic flux influences the minimum H-index. but that the maximum emission seems to be independent of the magnetic flux.," We emphasize also again the conclusion of \citet{reza+etal2007} that the presence of magnetic flux influences the minimum H-index, but that the maximum emission seems to be independent of the magnetic flux."477" This gives another indirect argument that photospheric fields increase the chromospheric emission. but do not actually deliver the main contribution to it,"," This gives another indirect argument that photospheric fields increase the chromospheric emission, but do not actually deliver the main contribution to it."478 For the strongest concentration of magnetic flux in. the field of view observed. a stable long-lasting (>1 hr) network element. we find a displacement of 1” between magnetic flux and highest emission. and Jess pronounced photospheric power.," For the strongest concentration of magnetic flux in the field of view observed, a stable long-lasting $>1$ hr) network element, we find a displacement of $^{\prime\prime}$ between magnetic flux and highest emission, and less pronounced photospheric power."479 The displacement ts only in one direction along the slit. which we ascribe to the field topology in the FOV.," The displacement is only in one direction along the slit, which we ascribe to the field topology in the FOV."480 The strongest field concentration could be connected to one of opposite polarity nearby in the direction of the displacement., The strongest field concentration could be connected to one of opposite polarity nearby in the direction of the displacement.481 The chromospheric intensity oscillations show power at all frequencies from 0 to about 10 mHz., The chromospheric intensity oscillations show power at all frequencies from 0 to about 10 mHz.482 We do not find a pronounced peak of power at 3 minutes. but a broad distribution over several frequencies.," We do not find a pronounced peak of power at 3 minutes, but a broad distribution over several frequencies."483 However. to address the question of heating. the average power spectrum alone is of less interest than the power spectrum of locations with strong chromospheric emission.," However, to address the question of heating, the average power spectrum alone is of less interest than the power spectrum of locations with strong chromospheric emission."484 Comparing the spatially resolved chromospheric intensity with chromospheric and photospheric oscillation power. or with the locations of photospheric fields. it can be seen that strong emission in the chromosphere is always related to one of two things (or both): magnetic fields. or high power in the photospheric velocity oscillations.," Comparing the spatially resolved chromospheric intensity with chromospheric and photospheric oscillation power, or with the locations of photospheric fields, it can be seen that strong emission in the chromosphere is always related to one of two things (or both): magnetic fields, or high power in the photospheric velocity oscillations."485 These photospheric oscillations are due to isolated small-scale power sources in the frequency range up to the acoustic cutoff frequency of around 5 mHz (cf., These photospheric oscillations are due to isolated small-scale power sources in the frequency range up to the acoustic cutoff frequency of around 5 mHz (cf.486 Fig. 7..," Fig. \ref{fig9},"487 lowermost panel)., lowermost panel).488 This agrees with the finding of ? that the large-scale photospheric 3 mHz oscillations are less important for the generation of H»y bright grains than localized 5 mHz oscillations (seealso?).., This agrees with the finding of \citet{kamio+kurokawa2006} that the large-scale photospheric 3 mHz oscillations are less important for the generation of $_{\rm 2V}$ bright grains than localized 5 mHz oscillations \citep[see also][]{hoekzema+etal2002}.489 The result would also be in agreement with both an impulsive excitation of waves. or a stochastic generation by the (random) superposition of large-scale wave patterns. which again would interfere positively only on some locations.," The result would also be in agreement with both an impulsive excitation of waves, or a stochastic generation by the (random) superposition of large-scale wave patterns, which again would interfere positively only on some locations."490 The analysis of the phase differences between the oscillations of the Hay peak and the intensities at other wavelengths gives evidence that the acting agent between photosphere and chromosphere are propagating waves with frequencies above 2 mHz.," The analysis of the phase differences between the oscillations of the $_{\rm491 2V}$ peak and the intensities at other wavelengths gives evidence that the acting agent between photosphere and chromosphere are propagating waves with frequencies above 2 mHz."492 Below 2 mHz. constant phase shifts," Below 2 mHz, constant phase shifts"493fast timing of black hole candidates in their low states and atoll sources in hard island states.,fast timing of black hole candidates in their low states and atoll sources in hard island states.494a given line is likely to be blended to some extent. resulting in additional uncertainty in an EW analvsis.,"a given line is likely to be blended to some extent, resulting in additional uncertainty in an EW analysis."495 We therefore used (he current version of the LTE line analysis program MOOG (Sneclen1973) to fit à svnthetie spectrum toa 10 wavelength region wound the 5782.14 Cul transition., We therefore used the current version of the LTE line analysis program MOOG \citep{moog} to fit a synthetic spectrum to a 10 wavelength region around the 5782.14 Cu I transition.496 For those clusters lor which we had sulficient wavelength coverage. a LO spectrum svnthesis was also emploved to derive an abundance from the Cu I line at 5105.5À.," For those clusters for which we had sufficient wavelength coverage, a 10 spectrum synthesis was also employed to derive an abundance from the Cu I line at 5105.5."497. The model atiosphleres and parameters used in the spectrum svntliesis are identical to (hose derived by the Calilornia/Texas eroup., 	The model atmospheres and parameters used in the spectrum synthesis are identical to those derived by the California/Texas group.498 We have adopted those previously determined abundances. particularly Mg and C. since the 5105 region contains a laree number of Mell and Cs lines in the cooler and higher metallicity stars.," We have adopted those previously determined abundances, particularly Mg and C, since the 5105 region contains a large number of MgH and $_2$ lines in the cooler and higher metallicity stars."499 Though these molecular lines have been (reated as a simple parameter of fit. in only one case has it been necessary io alter either of these abundances.," Though these molecular lines have been treated as a simple parameter of fit, in only one case has it been necessary to alter either of these abundances."500 In the M4 star L2208 the Mg abundance derived from atomic Me lines by. Ivausetal.(1999). did not seem to reproduce the strong Mell features surrounding the 5105 line., In the M4 star L2208 the Mg abundance derived from atomic Mg lines by \citet{Ivans1999} did not seem to reproduce the strong MgH features surrounding the 5105 line.501 In this ease. an increase of 0.3 dex (o Ivans et al," In this case, an increase of 0.3 dex to Ivans et al."502is Meg abundance better fit the observed features.,'s Mg abundance better fit the observed features.503 This star was problematic in the Ivans el al., This star was problematic in the Ivans et al.504 study (see (heir 844.2.2. for a discussion of the anomalies found in (his stars alpha and light odd-elements., study (see their 4.2.2 for a discussion of the anomalies found in this star's alpha and light odd-elements.505 The data for this star are of lower resolution and lower S/N than most of the saaple)., The data for this star are of lower resolution and lower S/N than most of the sample).506 However. since the Mg abundance serves here only as a parameter of the spectrum svnthesis fit. it does not affect the Cu abundance we derive.," However, since the Mg abundance serves here only as a parameter of the spectrum synthesis fit, it does not affect the Cu abundance we derive."507 A line list was prepared bv using MOOG (Sneden1973) to fit lines taken [rom the πο(1993). line list ina region around each επι line to the solar spectrum., 	 A line list was prepared by using MOOG \citep{moog} to fit lines taken from the \citet{KurCD1993} line list in a region around each Cu line to the \citet{Kurucz1984} solar spectrum.508 While (he fit was in general quite good with the initial line parameters. gf values For a few Fe lines were modified empirically to produce a better fit.," While the fit was in general quite good with the initial line parameters, $gf$ values for a few Fe lines were modified empirically to produce a better fit."509 The Cu I gf , The Cu I $gf$ 510Under the assumption that the X-ray spectrum of Cyg X-I is not substantially more complex than what has already been found in theChandra observation. eV-level spectral resolution observations of the system (as those that will be carried out by the satellite) can be used to constrain the dynamics of the disk and establish whether the accretion disk of Cygnus X-] actually precesses. and if so. to determine its dynamics.,"Under the assumption that the X-ray spectrum of Cyg X-1 is not substantially more complex than what has already been found in the observation, eV-level spectral resolution observations of the system (as those that will be carried out by the satellite) can be used to constrain the dynamics of the disk and establish whether the accretion disk of Cygnus X-1 actually precesses, and if so, to determine its dynamics."511 Several X-ray binaries present periodic behavior in their light curves on timescales longer than the orbital period., Several X-ray binaries present periodic behavior in their light curves on timescales longer than the orbital period.512 Among these systems we can mention Her X-1. SS 433. and LMC X-4.," Among these systems we can mention Her X-1, SS 433, and LMC X-4."513 It has been suggested that these long periods correspond to the precession of the accretion disk (e.g. Katz 1973)., It has been suggested that these long periods correspond to the precession of the accretion disk (e.g. Katz 1973).514 In the case of SS 433 the precession is directly measured in the jets. so if these are attached to the accretion disk it is reasonable to expect that the disk will also display precession (Katz 1980).," In the case of SS 433 the precession is directly measured in the jets, so if these are attached to the accretion disk it is reasonable to expect that the disk will also display precession (Katz 1980)."515 Although there is no reported compelling evidence yet for disk precession in black hole binaries. it is reasonable that the same mechanisms responsible for this phenomenon in neutron binaries will apply.," Although there is no reported compelling evidence yet for disk precession in black hole binaries, it is reasonable that the same mechanisms responsible for this phenomenon in neutron binaries will apply."516 The mechanism that produces the precession might be the instability of the response of the disc to the radiation reaction force from the illumination by the central source (e.g. Wijers Pringle 1999. Ogilvie Dubus 2001). or the tidal force of the companion star on a disk which is not coplanar with the binary orbit (Katz 1973. Larwood 1998. Kaufman Bernadó et al.," The mechanism that produces the precession might be the instability of the response of the disc to the radiation reaction force from the illumination by the central source (e.g, Wijers Pringle 1999, Ogilvie Dubus 2001), or the tidal force of the companion star on a disk which is not coplanar with the binary orbit (Katz 1973, Larwood 1998, Kaufman Bernadó et al."517 2002)., 2002).518 Uniform disk precession will occur in this case only if the sound crossing time through the disk is considerably shorter than the characteristic precession period induced by the perturbing star., Uniform disk precession will occur in this case only if the sound crossing time through the disk is considerably shorter than the characteristic precession period induced by the perturbing star.519 The precession angular velocity is given by (e.g. Romero et al., The precession angular velocity is given by (e.g. Romero et al.520" 2000): 1ο)5:Om-cos. where G is the gravitational constant. 7j, 1s the orbital radius. wy Is the inner disk angular velocity. ϐ is the half-opening angle of the precession cone. and 7 is the mass of the star that exerts the torque upon the disk."," 2000): $ \left|\Omega_{\rm p}\right|\approx \frac{3}{4}521\frac{Gm}{r_{\rm m}^3} \frac{1}{\omega_{\rm d}} \cos\theta, $ where $G$ is the gravitational constant, $r_{\rm m}$ is the orbital radius, $\omega_{\rm d}$ is the inner disk angular velocity, $\theta$ is the half-opening angle of the precession cone, and $m$ is the mass of the star that exerts the torque upon the disk."522 The orbital period 7; 1s related with the involved masses and the size of the orbit by Kepler's law: Fa.30ΗMY where M ∣↼is the mass ofκ the accreting. object.," The orbital period $T_{\rm m}$ is related with the involved masses and the size of the orbit by Kepler's law: $ r_{\rm523m}^3=\frac{G(m+M)T_{\rm m}^2}{4\pi^2}, $ where $M$ is the mass of the accreting object."524". The ratio between the orbital and the precessing periods can be related through the disk angular velocity wy—(GM/rjyey where 7,= and #2ry/r,."," The ratio between the orbital and the precessing periods can be related through the disk angular velocity $\omega_{\rm d}=(GM/r_{\rm d}^3)^{1/2}$: where $T_{\rm p}=2\pi/\Omega_{\rm p}$ and $\kappa=r_{\rm d}/r_{\rm525m}$."526" Since &«I. normally Ti/T,<1."," Since $\kappa<1$, normally $T_{\rm m}/T_{\rm p}<1$."527 In the 27/Qp)case of Cygnus X-I. Brocksopp et al. (," In the case of Cygnus X-1, Brocksopp et al. ("5281999) have reported multrwavelength evidence for the existence of a period of 142.0+7.1 days.,1999) have reported multiwavelength evidence for the existence of a period of $142.0\pm7.1$ days.529 Similar precessing periods have been caleulated by Larwood (1998). Katz (1973. 1980) and Katz et al. (," Similar precessing periods have been calculated by Larwood (1998), Katz (1973, 1980) and Katz et al. ("5301982) for other X-ray binaries on the basis of the same model.,1982) for other X-ray binaries on the basis of the same model.531 As shown by Romero et al. (, As shown by Romero et al. (5322002) in the case of Cygnus X-]. such a period can be obtained from tidally-induced precession for an accretion disk with a size ~4«10!! cm. If the half opening angle of the precession cone is ~157.,"2002) in the case of Cygnus X-1, such a period can be obtained from tidally-induced precession for an accretion disk with a size $\sim 4\times 10^{11}$ cm, if the half opening angle of the precession cone is $\sim 15^{\circ}$."533 For a purely wind-fed system. this size might be too large and other mechanism may be in operation to generate the observed timescales.," For a purely wind-fed system, this size might be too large and other mechanism may be in operation to generate the observed timescales."534 In particular. radiation-driven precession (Pringle 1996. Maloney Begelman 1997. Ogilvie Dubus 2001). wind-driven warping and precession (Schandl Meyer 1994. Quillen 2001). and spin-spin precession (Bardeen Petterson 1975. Armitage Natarajan 1999) can yield precession periods of several weeks to a few months.," In particular, radiation-driven precession (Pringle 1996, Maloney Begelman 1997, Ogilvie Dubus 2001), wind-driven warping and precession (Schandl Meyer 1994, Quillen 2001), and spin-spin precession (Bardeen Petterson 1975, Armitage Natarajan 1999) can yield precession periods of several weeks to a few months."535 In all these mechanisms the observed optical and X-ray modulation points to precession of the disk. whereas the radio variations might originate in the jet.," In all these mechanisms the observed optical and X-ray modulation points to precession of the disk, whereas the radio variations might originate in the jet."536 The use of emission lines as a diagnosis tool for the state of binary systems has been proposed in the past (e.g.. for an investigation on supermassive black hole binarity. see Torres et al.," The use of emission lines as a diagnosis tool for the state of binary systems has been proposed in the past (e.g., for an investigation on supermassive black hole binarity, see Torres et al."537 2003. also Gaskell 2003: Zakharov et al.," 2003, also Gaskell 2003; Zakharov et al."538 2004a.b).," 2004a,b)."539 Here we show that a similar method can be used to extract information about the precession status of microquasars., Here we show that a similar method can be used to extract information about the precession status of microquasars.540 For the case of Cygnus X-1. we shall assume that the time-averaged disk inclination angle is 357. which is in agreement with the fitting of the system's Fe line (Miller et al.," For the case of Cygnus X-1, we shall assume that the time-averaged disk inclination angle is $^\circ$, which is in agreement with the fitting of the system's Fe line (Miller et al."541 2002)., 2002).542 Values around this time-averaged inclination angle were also found for other binary systems ( e.g. Her X-1. LMC X-4. SMC X-I. etc.," Values around this time-averaged inclination angle were also found for other binary systems ( e.g., Her X-1, LMC X-4, SMC X-1, etc."543 e.g.. as discussed by Larwood 1998).," e.g., as discussed by Larwood 1998)."544" We also assume two extreme cases for the amplitude of the disk precession: (1) the disk inclination angle precesses from to 39"" (very low magnitude of the precession angle): (2) the disk inclination angle precesses from 5° to 65° (large magnitude of the precession angle).", We also assume two extreme cases for the amplitude of the disk precession: (1) the disk inclination angle precesses from $^\circ$ to $^\circ$ (very low magnitude of the precession angle); (2) the disk inclination angle precesses from $^\circ$ to $^\circ$ (large magnitude of the precession angle).545 The amplitude of the precession of the inner disk should not be large if it is due to the tidal force of the secondary star and if the disk (especially the outer disk region) develops a significant warp., The amplitude of the precession of the inner disk should not be large if it is due to the tidal force of the secondary star and if the disk (especially the outer disk region) develops a significant warp.546 However. if the initial spin direction of the BH ts significantly different from the orbital angular momentum direction. the inner disk. which ts confined to the equatorial plane of the BH (if the spin is high) due to the Bardeen-Peterson effect. may precess around the total angular momentum (dominated by the orbital angular momentum) with an amplitude as large as the initial orbital inclination angle with respect to the BH equatorial plane.," However, if the initial spin direction of the BH is significantly different from the orbital angular momentum direction, the inner disk, which is confined to the equatorial plane of the BH (if the spin is high) due to the Bardeen-Peterson effect, may precess around the total angular momentum (dominated by the orbital angular momentum) with an amplitude as large as the initial orbital inclination angle with respect to the BH equatorial plane."547 If we assume that the disk is rigidly precessing around the total angular momentum (dominated by the orbital angular momentum). then the amplitude of the precession may also be around 30”.," If we assume that the disk is rigidly precessing around the total angular momentum (dominated by the orbital angular momentum), then the amplitude of the precession may also be around $^\circ$."548 Several calculations on the disk line profiles have been performed., Several calculations on the disk line profiles have been performed.549" We use a ray-tracing technique and elliptic integrals (Rauch Blandford 1994; see also Yu Lu 2000: Lu Yu 2001 and references therein) to follow the trajectories of photons from the observer. keeping track of all coordinates until the photons either intersect the accretion disk plane. disappear below the event horizon. or escape to ""infinity"" (operationally defined to be r21000GM/c7 away from the BH)."," We use a ray-tracing technique and elliptic integrals (Rauch Blandford 1994; see also Yu Lu 2000; Lu Yu 2001 and references therein) to follow the trajectories of photons from the observer, keeping track of all coordinates until the photons either intersect the accretion disk plane, disappear below the event horizon, or escape to ""infinity"" (operationally defined to be $r=1000GM/c^2$ away from the BH)."550 We then calculate the redshift factor for a photon (to the observer) emitted from a particular position on the disk., We then calculate the redshift factor for a photon (to the observer) emitted from a particular position on the disk.551 The solid angle subtended at the observer by each disk element ts also calculated., The solid angle subtended at the observer by each disk element is also calculated.552" We set the inner radius of the disk to be at the marginally stable orbit (67. for a Schwarzschild black hole or 1.237. for a Kerr black hole with spin ¢/M—0.998. where r,=GM c). and the outer radius at 1607..."," We set the inner radius of the disk to be at the marginally stable orbit $6r_{\rm g}$ for a Schwarzschild black hole or $1.23r_{\rm g}$ for a Kerr black hole with spin $a/M=0.998$, where $r_{\rm g}=GM/c^2$ ), and the outer radius at $160r_{\rm g}$."553 We assume that the surface emissivity of line photons follows a power-law. 7%. with g=2.5.," We assume that the surface emissivity of line photons follows a power-law, $r^{-q}$, with $q=2.5$."554 Both the power- emissivity law and the size of the disk in Schwarszchild units. are usual assumptions (see. e.g.. Nandra et al.," Both the power-law emissivity law and the size of the disk in Schwarszchild units, are usual assumptions (see, e.g., Nandra et al."555 1997)., 1997).556 The BH spin is assumed to be a/M=0.998., The BH spin is assumed to be $a/M=0.998$.557 In microquasar systems. both the high frequency quasi-periodic oscillation and relativistic lines suggest a high spin.," In microquasar systems, both the high frequency quasi-periodic oscillation and relativistic lines suggest a high spin."558 In any case. we proved that if We were to assume a lower spin. there is not much qualitative difference for the problem we have studied here.," In any case, we proved that if we were to assume a lower spin, there is not much qualitative difference for the problem we have studied here."559 With the above assumptions. we sum up all the photons received by the observer. which is emitted from each disk element. and obtain the profile of emergent Fe Ko lines. with different inclination," With the above assumptions, we sum up all the photons received by the observer, which is emitted from each disk element, and obtain the profile of emergent Fe $\alpha$ lines, with different inclination"560"deduce that €,=ἐν and e;=ez; taking into account the symmetry of the equations.",deduce that $C_h=C_v$ and ${\sigma}^2_h = {\sigma}^2_v$ taking into account the symmetry of the equations.561" Moreover. the temperature power spectrum P(À) can be obtained. from the.defait wavelet power spectrum wa.(dA) as follows For the Haar and Mexican wavelets we can calculate: where 47=kp|bs and D. can be obtained from Py. swapping A, and As."," Moreover, the temperature power spectrum $P(k)$ can be obtained from the wavelet power spectrum $w_{\alpha \alpha }(R,R;\vec k)$ as follows For the Haar and Mexican wavelets we can calculate: where $k^2 = k_1^2 + k_2^2$ and $\tilde{\Gamma}_v$ can be obtained from $\tilde{\Gamma}_h$, swapping $k_1$ and $k_2$."562 The variance of thedefait. wavelet coellicients for the Haar and Mexican Hat systems. assuming the standard CDAL model. is presented in Figure 1.," The variance of the wavelet coefficients for the Haar and Mexican Hat systems, assuming the standard CDM model, is presented in Figure 1."563 As one can see the acoustic peaks can be clearly noticed. being more pronounced for the Mexican Hat. basis.," As one can see the acoustic peaks can be clearly noticed, being more pronounced for the Mexican Hat basis."564 This last result is a consequence of being a more localizecl wavelet. svstem., This last result is a consequence of being a more localized wavelet system.565 For a more cletailed discussion see Sanz et al., For a more detailed discussion see Sanz et al.566 1905. 1999.," 1998, 1999."567 An orthonormal basis of L(30) dilationscan be constructed. from a wavelet co through cvaclic j and translations & 1n addition. a scaling function © can be defined associate to themother wavelet c.," An orthonormal basis of $L^2(\Re )$ can be constructed from a wavelet $\psi$ through dyadic dilations $j$ and translations $k$ In addition, a scaling function $\phi$ can be defined associated to the wavelet $\psi $."568 Such a function gives rise to the sO called multiresolution analysis., Such a function gives rise to the so called multiresolution analysis.569 multiresolution analysis of L?(8) is defined as a sequence of elosed subspaces V; of ΙΩΝ). j€Z.," A multiresolution analysis of $L^2(\Re )$ is defined as a sequence of closed subspaces $V_j$ of $L^2(\Re )$, $j\in Z$."570 Properties can be seen in Ogden (1997), Properties can be seen in Ogden (1997).571" Subspaces V; are generated by dyadic dilations anc translations of the scaling function o (this function forms an orthonormal basis of V5. fO,n6r)=olr 21)."," Subspaces $V_j$ are generated by dyadic dilations and translations of the scaling function $\phi $ (this function forms an orthonormal basis of $V_o$, $\{ \phi_{o,k}(x)=\phi(x-k)\}$ )."572" Aloreover cach Vj can be expressed as the orthogona sum V;—1,1Wya. where Mj4, ds created. from wavelets ojia."," Moreover each $V_j$ can be expressed as the orthogonal sum $V_j=V_{j-1}\oplus W_{j-1}$, where $W_{j-1}$ is created from wavelets $\psi_{j-1,k}$."573 Taking into account the properties of the sealing function. together with this last) expression. we can construct at increasing levels of resolution.," Taking into account the properties of the scaling function, together with this last expression, we can construct at increasing levels of resolution."574 These are lincar combinations of dilations and translations of a scaling function ©., These are linear combinations of dilations and translations of a scaling function $\phi $.575 The dilference between two consecutiveepprozàmealions. Lo. thedelail at the corresponding resolution level. is given by a linear combination of dilations and translations of a wavelet function c.," The difference between two consecutive, i.e. the at the corresponding resolution level, is given by a linear combination of dilations and translations of a wavelet function $\psi $."576 The analysis performed in this work assumes equal dilations in the 2 dimensions involved., The analysis performed in this work assumes equal dilations in the 2 dimensions involved.577" At a fixed level of resolution. subspaces in a 2-1) multiresolution analysis are the tensor products of the corresponding one-dimensional ones Vj,=V;acας νο 2-D basis is therefore built by the product of two sealing functions. (epprorimnalion). the. product of wavelet anc scaling functions (horizontal and vertical defails) and the product of two wavelets (diagonal defaits): Horizontal. vertical and clagonaldefeif coellicients represent the variations in these directions relative to a weighted average ata lower resolution level (given by theapprorimalion coellicients)."," At a fixed level of resolution, subspaces in a 2-D multiresolution analysis are the tensor products of the corresponding one-dimensional ones ${\bf V}_{j+1}=V_{j+1}\otimes V_{j+1}$ .The 2-D basis is therefore built by the product of two scaling functions ), the product of wavelet and scaling functions (horizontal and vertical ) and the product of two wavelets (diagonal ): Horizontal, vertical and diagonal coefficients represent the variations in these directions relative to a weighted average at a lower resolution level (given by the coefficients)."578" A discrete orthonormal basis. E,Gr:j.&). can be defined by setting /?—2/ and b—2""Kk in equations (3-5). then (LGPpΟΙOu)=Mad)Opp. where () denotes the scalar ne in £709)."," A discrete orthonormal basis, ${\Gamma}_{\alpha}(\vec{x}; j, \vec{k})$, can be defined by setting $R = 2^{-j}$ and $\vec{b} = 2^{-j}\vec{k}$ in equations (3-5), then $({\Gamma}_{\alpha}(\vec{x}; j, \vec{k}){\Gamma}_{{\alpha}^{\prime}}(\vec{x};579j^{\prime}, {\vec{k}}^{\prime})) = {\delta}_{\alpha580{\alpha}^{\prime}}{\delta}_{jj^{\prime}}{\delta}_{\vec{k}{\vec{k}}^{\prime}}$, where $()$ denotes the scalar product in $L^2(\Re ^2)$."581 Wo we define the discrete wavelet coefficients associated to anydefaif by the equation we can thus reconstruct the image with all the In particular. we get the following expression for the moment of the image that expresses how the energy of the field is. distributed locally at any scale ancldefe.," If we define the discrete wavelet coefficients associated to any by the equation (6) we can thus reconstruct the image with all the In particular, we get the following expression for the second-order moment of the image that expresses how the energy of the field is distributed locally at any scale and."582" Fora finite image. £2,5Rovere. in order to reconstruct it we must add. to equation (19) an. approximation wsGOL,CEE) with LEB)=OrRiehi) PCrRiehe) and ws(he)={απ)Ε.Ε). representing the Ποιά at the lower resolution."," For a finite image, $R_{max}\times R_{max}$, in order to reconstruct it we must add to equation (19) an approximation $w_a(\vec{k}){\Gamma}_a(\vec{x}; \vec{k})$ with ${\Gamma}_a(\vec{x}; \vec{k})\equiv \Phi (x_1; R_{max},k_1)$ $\Phi (x_2; R_{max},k_2)$ and $w_a(\vec{k}) \equiv \int583d\vec{x}\,f(\vec{x})\,{\Gamma}_a(\vec{x},\vec k)$, representing the field at the lower resolution."584" (9) represents the temperature fluctuation field then the variance is given by <GNIZTY>=(GNT/T))2NS. being AN, the number of pixels."," If $f(\vec x)$ represents the temperature fluctuation field then the variance is given by $<(\Delta T/T)^2>=((\Delta T/T)^2)/N_p$, being $N_p$ the number of pixels."585 The orthonormal basis that we are going to use are the standard. Daubechies IN. (Llaar corresponds to N= 1). that has been extensively used in the literature because of their special properties: they are defined in a compact support. have increasing with No and vanishing moments up to order ΑΝ velNN(Daubechies 1988).," The orthonormal basis that we are going to use are the standard Daubechies $N$ (Haar corresponds to $N = 1$ ), that has been extensively used in the literature because of their special properties: they are defined in a compact support, have increasing regularity with $N$ and vanishing moments up to order $N - 1$ (Daubechies 1988)."586 On the contrary. the Alexican Lat is not defined in a compact support and it is not appropriate for this multiresolution analysis.," On the contrary, the Mexican Hat wavelet is not defined in a compact support and it is not appropriate for this multiresolution analysis."587 For discrete. wavelet. analysis of the CMD we use the Matlab Wavelet ToolboxCMisiti et al., For discrete wavelet analysis of the CMB maps we use the Matlab Wavelet Toolbox (Misiti et al.588 1996)., 1996).589" ---""a""Ehis toolbox is an extensive collection of programs for denoising and compressing signals and 2-D images."," This toolbox is an extensive collection of programs for analyzing, denoising and compressing signals and 2-D images."590 Discrete Wavelet decomposition is performed as described above to, Discrete Wavelet decomposition is performed as described above to591parameters to which the BBIL background is sensitive.,parameters to which the BBH background is sensitive.592" Our results show that for M.<LOM... the background is not likely to be detected through cross-correlation by two advanced detectors even at r»~0.43Mpe""Myr.!|[."," Our results show that for $M_{c} \lesssim 10 M_{\odot}$, the background is not likely to be detected through cross-correlation by two advanced detectors even at $r_{2} \sim5930.43\,\rm{Mpc}^{-3}\rm{Myr}^{-1}$."594 Only for erealer values of Af... as have been predicted (o result. Hom ΕΟΓΑΗ svstems such as NGC300 X-1 and 1010 X-1 (Bulikοἱal.2011).. there is scope for detection.," Only for greater values of $M_{c}$, as have been predicted to result from BH-WR systems such as NGC300 X-1 and IC10 X-1 \citep{Bulik08}, there is scope for detection."595 To further assess (he detecGon. prospects for second generation detectors. we have considered the possibility of combining a worldwide network of advanced detectors to improve the cross-correlation statistic. namely the methods FC and CP. described in section 5.3.," To further assess the detection prospects for second generation detectors, we have considered the possibility of combining a worldwide network of advanced detectors to improve the cross-correlation statistic, namely the methods FC and CP described in section 5.3."596 We find that of these (wo approaches. CP can produce an improvement of up to 40% agalnst a standard eross-correlation between (wo detectors.," We find that of these two approaches, CP can produce an improvement of up to $40\%$ against a standard cross-correlation between two detectors."597 For the third generation detector. ET. the signal is accessible with a SNR of 59 and 112at the lower rate estimate ry~ using ET-B and ET-D sensitivities respectively.," For the third generation detector, ET, the signal is accessible with a SNR of 59 and 112at the lower rate estimate $r_{1} \sim 3.1 \times 10^{-2}\,\rm{Mpc}^{-3}\rm{Myr}^{-1}$ using ET-B and ET-D sensitivities respectively."598 This signal could mask the primordial background signal at below around Occ4xLO Mat ~LOO III., This signal could mask the primordial background signal at below around $\Omega_{\rm{GW}}\sim 4 \times 10^{-10}$ at $\sim 100$ Hz.599 We note (hat (he rates used in (his study. are computed assuming Milky Wavy (νρο ealaxies and the standard. formation channel — isolated. binary evolution., We note that the rates used in this study are computed assuming Milky Way type galaxies and the standard formation channel – isolated binary evolution.600 Massive binary formation in early elliptical galaxies is expected (o improve the coalescence rate (deFre-etal.2006:OShaughnessy 2010).," Massive binary formation in early elliptical galaxies is expected to improve the coalescence rate \citep{elli,os10}."601. This is parüeularly. important. [or BBIIs due to the longer delay time., This is particularly important for BBHs due to the longer delay time.602 In addition. dvnamical formation scenarios in dense stellar environments can make a significant contribution to BBIT rates.," In addition, dynamical formation scenarios in dense stellar environments can make a significant contribution to BBH rates."603 These other formation channels will not only increase the event rate of coalescing BBIIs. but also adel additional uncertainty to the average component masses of the DDII population.," These other formation channels will not only increase the event rate of coalescing BBHs, but also add additional uncertainty to the average component masses of the BBH population."604 For example. simulations by Sadowskietal.(2008) suggest that the average chirp mass in clusters is (M)~20M... much larger than the same found in the field (M)~7.M..," For example, simulations by \citet{sado} suggest that the average chirp mass in clusters is $\langle M_{\rm{c}} \rangle \sim 20 M_{\odot}$, much larger than the same found in the field $\langle M_{\rm{c}} \rangle605\sim 7 M_{\odot}$."606 This might indicate two similar backerounds peaking at quite cdillerent frequencies., This might indicate two similar backgrounds peaking at quite different frequencies.607" We have shown a minimun detectable ry for ET at around. 10/7?\Ipe""Myr.|. which may. be in the range of rate. predictions from dvnamieal formation scenarios (O'Learyetal.2007:SadowskiLauburg 2009)."," We have shown a minimum detectable $r_0$ for ET at around $10^{-3} \hspace{1mm}608\rm{Mpc}^{-3} \rm{Myr}^{-1}$, which may be in the range of rate predictions from dynamical formation scenarios \citep{oleary07,sado,miller}."609. Therefore. detection at the sensitivity of ET could enable these two potential backeround signals to be wntaneled. Cans allowing the average properties of the clilferent populations to be probed.," Therefore, detection at the sensitivity of ET could enable these two potential background signals to be untangled, thus allowing the average properties of the different populations to be probed."610 Additionally. clues to how these two populations contribute to a contusion background mav be provided by Advanced LIGO/Virgo through single detections in the shot noise (DC« 0.1) regime.," Additionally, clues to how these two populations contribute to a confusion background may be provided by Advanced LIGO/Virgo through single detections in the shot noise $DC \ll 0.1$ ) regime."611 New data analvsis techniques. such as the probability. event. horizon method (Coward&Burman2005:Lowelletal.2007) which extracts the temporal signature from a population of transient sources or the maximum likelihood statistic 2003).. could prove valuable in interrogating this regime.," New data analysis techniques, such as the probability event horizon method \citep{Coward05,Howell07} which extracts the temporal signature from a population of transient sources or the maximum likelihood statistic \citep{drasco}, , could prove valuable in interrogating this regime."612in Hawai. the Arizona Radio Observatory’s Submillimeter Telescope (ARO/SMT: S) in Arizona. and two telescopes of the Combined Array for Research in. Millimeter-wave Astronomy (CARMA: C and D. located ~60 m apart) in California.,"in Hawaii, the Arizona Radio Observatory's Submillimeter Telescope (ARO/SMT; S) in Arizona, and two telescopes of the Combined Array for Research in Millimeter-wave Astronomy (CARMA; C and D, located $\sim60$ m apart) in California."613 On Mauna Kea. the Submillimeter Array (SMA) housed the VLBI recording system and synthesized the hydrogen maser based VLBI reference used at the JCMT.," On Mauna Kea, the Submillimeter Array (SMA) housed the VLBI recording system and synthesized the hydrogen maser based VLBI reference used at the JCMT."614 Masers at all sites were checked against ultra-stable crystals; combined losses due to maser instabilities and local oscillator decoherence are estimated to be < 5%.., Masers at all sites were checked against ultra-stable crystals; combined losses due to maser instabilities and local oscillator decoherence are estimated to be $\lesssim5$ .615. Observations occurred. over three nights: 2009 April 5-7 (days 95-97)., Observations occurred over three nights: 2009 April 5–7 (days 95–97).616 Sources were observed in left circular polarization in two 480 MHz bandwidths centered at 229.089 and 229.601 GHz (low and high bands)., Sources were observed in left circular polarization in two 480 MHz bandwidths centered at 229.089 and 229.601 GHz (low and high bands).617 Data recorded at all sites was shipped to MIT Haystack Observatory in Westford. Massachusetts for processing on the Mark4 VLBI correlator.," Data recorded at all sites was shipped to MIT Haystack Observatory in Westford, Massachusetts for processing on the Mark4 VLBI correlator."618 Once correlated. data for each scan (typically 10-15 minutes) were corrected for coherence losses due to atmospheric turbulence and searched for detections using methods detailed in Doelemanetal.(2001.2008).," Once correlated, data for each scan (typically 10–15 minutes) were corrected for coherence losses due to atmospheric turbulence and searched for detections using methods detailed in \citet{doeleman2001, doeleman2008}."619. Atmospheric. coherence times ranged from a few to —20 s. depending on weather conditions at each telescope.," Atmospheric coherence times ranged from a few to $\sim20$ s, depending on weather conditions at each telescope."620 The VLBI correlation coefficient for each baseline was multiplied by the geometric mean of the System Equivalent Flux Density (SEFD) of both antennas., The VLBI correlation coefficient for each baseline was multiplied by the geometric mean of the System Equivalent Flux Density (SEFD) of both antennas.621 The SEFD is a product of antenna gain (Jy/K) and the opacity-corrected system temperature. which was measured just prior to each VLBI sean using a vane calibration technique that corrects for the atmosphere.," The SEFD is a product of antenna gain (Jy/K) and the opacity-corrected system temperature, which was measured just prior to each VLBI scan using a vane calibration technique that corrects for the atmosphere."622 For the JCMT and ARO/SMT. antenna gains were determined from observations of planets at several points during the multiple day campaign. and the gains were observed to be stable.," For the JCMT and ARO/SMT, antenna gains were determined from observations of planets at several points during the multiple day campaign, and the gains were observed to be stable."623 Relative gains for the two CARMA dishes were estimated using observations taken by CARMA in interferometric array mode before each VLBI scan. and the gains were then set to a common flux scale using planet scans at the end of each night.," Relative gains for the two CARMA dishes were estimated using observations taken by CARMA in interferometric array mode before each VLBI scan, and the gains were then set to a common flux scale using planet scans at the end of each night."624" The flux densities of all VLBI targets (Sgr A*. 1924—292, M87. 3C273. 3C345. 1733-130. 3C279. 08544201) were measured with CARMA."," The flux densities of all VLBI targets (Sgr A*, $-$ 292, M87, 3C273, 3C345, $-$ 130, 3C279, $+$ 201) were measured with CARMA."625 For Ser A*. data with baselines shorter than 20 KA were discarded to filter out extended emission in the Galactic center.," For Sgr A*, data with baselines shorter than 20 $\lambda$ were discarded to filter out extended emission in the Galactic center."626 The measured flux densities of all sources increased from day 95 to day 96 and from day 96 to day 97., The measured flux densities of all sources increased from day 95 to day 96 and from day 96 to day 97.627 We attribute this systematic trend to errors in the planet calibrations made shortly after sunrise. when antenna focus. pointing offsets. and atmospheric coherence typically change.," We attribute this systematic trend to errors in the planet calibrations made shortly after sunrise, when antenna focus, pointing offsets, and atmospheric coherence typically change."628 The flux density measured for the calibrator 1924—294. observed over the same time and elevation ranges as Ser A*. was 9.95. 10.21. and 10.75 Jy on days 95. 96. and 97.," The flux density measured for the calibrator $-$ 294, observed over the same time and elevation ranges as Sgr A*, was 9.95, 10.21, and 10.75 Jy on days 95, 96, and 97."629 We normalized CARMA gains to a constant flux density of 10.25 Jy on all three days., We normalized CARMA gains to a constant flux density of 10.25 Jy on all three days.630 The resulting measured flux densities for Sgr A* are 3.03. 3.16. and 3.61 Jy on days 95. 96. and 97. respectively.," The resulting measured flux densities for Sgr A* are 3.03, 3.16, and 3.61 Jy on days 95, 96, and 97, respectively."631 We adopt these fluxes for all subsequent analysis., We adopt these fluxes for all subsequent analysis.632 As shown in the upper panels of Figures | and 2.. there are still noticeable variations in the correlated flux densities even after renormalizing the day-to-day flux scales.," As shown in the upper panels of Figures \ref{fig-1921-scans} and \ref{fig-sgra-scans}, there are still noticeable variations in the correlated flux densities even after renormalizing the day-to-day flux scales."633" These residual calibration. errors and amplitude variation can be corrected for by making three simplifying assumptions that allow us to use standard. ""self-calibration"" techniques."," These residual calibration errors and amplitude variation can be corrected for by making three simplifying assumptions that allow us to use standard “self-calibration"" techniques."634 First. the flux densities of detections m the low and high bands. which differ by only in frequency. are assumed to be equal in each sean.," First, the flux densities of detections in the low and high bands, which differ by only in frequency, are assumed to be equal in each scan."635 Second. flux densities on the SC and SD baselines are assumed to be equal.," Second, flux densities on the SC and SD baselines are assumed to be equal."636 While one could in principle require that JC and JD flux densities be equal as well. the signal-to-noise ratio (SNR) is generally much lower on the JC and JD baselines than on the shorter VLBI baselines (SC and SD). since both 1924—292 and Ser A* are more resolved on longer baselines.," While one could in principle require that JC and JD flux densities be equal as well, the signal-to-noise ratio (SNR) is generally much lower on the JC and JD baselines than on the shorter VLBI baselines (SC and SD), since both $-$ 292 and Sgr A* are more resolved on longer baselines."637 Third. CARMA antenna gains are adjusted to make the correlated flux density on the CD baseline (with a fringe spacing measured in arcseconds) equal to the total flux density measured each night by CARMA.," Third, CARMA antenna gains are adjusted to make the correlated flux density on the CD baseline (with a fringe spacing measured in arcseconds) equal to the total flux density measured each night by CARMA."638 This final constraint enforces a constant source flux density over the duration of each night of observation., This final constraint enforces a constant source flux density over the duration of each night of observation.639 While some of the observed variation in Ser A* over the course of a night may be due to intrinsic. variability. the 1924—292 data exhibit similar scatter. suggesting that calibration errors may dominate over source variability.," While some of the observed variation in Sgr A* over the course of a night may be due to intrinsic variability, the $-$ 292 data exhibit similar scatter, suggesting that calibration errors may dominate over source variability."640 Combined. these assumptions result in a closed-form solution for gain-correction coefficients for telescopes C. D. and S in each band.," Combined, these assumptions result in a closed-form solution for gain-correction coefficients for telescopes C, D, and S in each band."641 Henceforth. we will use the term “gain-corrected” to refer to flux densities that have been multiplied by these gain-correction coefficients.," Henceforth, we will use the term “gain-corrected” to refer to flux densities that have been multiplied by these gain-correction coefficients."642 We note that if the total flux density (CD) is varied. the SJ flux densities are unchanged while other flux densities vary as the square root of the factor.," We note that if the total flux density (CD) is varied, the SJ flux densities are unchanged while other flux densities vary as the square root of the factor."643 The quasar 1924—292 was easily detected on all baselines (Table 1))., The quasar $-$ 292 was easily detected on all baselines (Table \ref{table-detections}) ).644 On each scan. low-band and high-band fluxes after a-priort calibration track each other consistently (Figure 1)).," On each scan, low-band and high-band fluxes after a-priori calibration track each other consistently (Figure \ref{fig-1921-scans}) )."645 After gain correction assuming a total flux density of 10.25 Jy. the data from all three days are highly consistent with one another.," After gain correction assuming a total flux density of $10.25$ Jy, the data from all three days are highly consistent with one another."646 The SC and SD baselines show consistent variation in the correlated flux density that is repeated each day., The SC and SD baselines show consistent variation in the correlated flux density that is repeated each day.647 The long-baseline detections (SJ. JC. and JD) also show day-to-day repeatable behavior. indicating detection of stable source structure presumably associated with a jet (Shen1997).," The long-baseline detections (SJ, JC, and JD) also show day-to-day repeatable behavior, indicating detection of stable source structure presumably associated with a jet \citep{shen1997}."648. The consistency of these data demonstrates the validity of the gain-correction technique., The consistency of these data demonstrates the validity of the gain-correction technique.649 Based on the statistics of the data on scans of 1924-292. systematic errors are estimated to be ~S%..," Based on the statistics of the data on scans of $-$ 292, systematic errors are estimated to be $\sim5$."650 We report the first 1.3 mm VLBI detections of Ser A* on Hawatn-California baselines with correlated flux densities for several scans of =400 mJy on the JC and JD baselines during day 96 (Figure 2))., We report the first 1.3 mm VLBI detections of Sgr A* on Hawaii-California baselines with correlated flux densities for several scans of $\gtrsim400$ mJy on the JC and JD baselines during day 96 (Figure \ref{fig-sgra-scans}) ).651 Nondetections on the JC and JD baselines on day 95 are attributable to the higher opacity at the JCMT on that day., Nondetections on the JC and JD baselines on day 95 are attributable to the higher opacity at the JCMT on that day.652 The robust detections on the long (Hawatt-Arizona and Hawarn-California) baselines confirm the detection of event horizon scale structure reported in Doelemanetal. (2008)., The robust detections on the long (Hawaii-Arizona and Hawaii-California) baselines confirm the detection of event horizon scale structure reported in \citet{doeleman2008}.653 Because Ser Á* was detected on baselines between all three sites. we are able to measure closure phase: the sum of interferometric phase around a closed triangle of baselines.," Because Sgr A* was detected on baselines between all three sites, we are able to measure closure phase: the sum of interferometric phase around a closed triangle of baselines."654 This quantity is relatively immune to calibration errors and in general provides important constraints on source structure., This quantity is relatively immune to calibration errors and in general provides important constraints on source structure.655 On the CARMA-ARO/SMT-JCMT triangle. the phase closures on Ser A* for day 96 (5 independent measurements) were computed using 10-second coherent integrations. which were averaged over full 10-minute VLBI scans to increase SNR (Rogersetal.1995).," On the CARMA-ARO/SMT-JCMT triangle, the phase closures on Sgr A* for day 96 (5 independent measurements) were computed using 10-second coherent integrations, which were averaged over full 10-minute VLBI scans to increase SNR \citep{rogers1995}."656". Because of the relatively low SNR on the long baselines to the JCMT. it is only possible to say that the closure phases are consistent with a value of zero with a variation of +40""."," Because of the relatively low SNR on the long baselines to the JCMT, it is only possible to say that the closure phases are consistent with a value of zero with a variation of $\pm40^\circ$ ."657calibrate a much tighter relation.,calibrate a much tighter relation.658 Allen Fabian (1998) also noticed that the relation for the hottest clusters tends to flatten to the self.similar scaling prediction. possibly suggesting that the elfect of extra heating becomes negligible for such systems.," Allen Fabian (1998) also noticed that the relation for the hottest clusters tends to flatten to the self–similar scaling prediction, possibly suggesting that the effect of extra heating becomes negligible for such systems."659 Figure 11. shows the effect of extra heating on the relation of nearby clusters., Figure \ref{fi:lt} shows the effect of extra heating on the relation of nearby clusters.660 The GII runs are clearly at variance with respect to data over the whole sampled range of temperatures., The GH runs are clearly at variance with respect to data over the whole sampled range of temperatures.661 Heating with the SN-1 recipe provides sone stecpening of the relation at the group scale. although not enough to reach agreement with cata points.," Heating with the SN-1 recipe provides some steepening of the relation at the group scale, although not enough to reach agreement with data points."662 A larger suppression of Lx is achieved. with the S-50 ancl S-100 heating schemes and. for the LHickson group. with the SN-4 run.," A larger suppression of $L_X$ is achieved with the S-50 and S-100 heating schemes and, for the Hickson group, with the SN-4 run."663" Quite interestingly. the SN-4 heating scheme requires the same heating energy. 4,c1.4 keV/part as the 8-50. entropy oor. but. provides a significantly smaller luminosity. às à consequence of the lower gas density in the central region of the Hickson group (see also Fig. SJ)."," Quite interestingly, the SN-4 heating scheme requires the same heating energy, $E_h\simeq 1.4$ keV/part as the S-50 entropy floor, but provides a significantly smaller luminosity, as a consequence of the lower gas density in the central region of the Hickson group (see also Fig. \ref{fi:fbar}) )."664 Therefore. a better ellicieney is reached. in this case by gradually dumping energy within the virialized regions of the ICM. rather than imposing an impulsive precollapse heating on the whole turnaround region.," Therefore, a better efficiency is reached in this case by gradually dumping energy within the virialized regions of the ICM, rather than imposing an impulsive pre–collapse heating on the whole turn–around region."665 In à similar wav. Ligure 12 shows a similar comparison with observations for distant. 0.52zZ1.3. clusters.," In a similar way, Figure \ref{fi:lt_hz} shows a similar comparison with observations for distant, $0.5\mincir z \mincir6661.3$, clusters."667 Independent analyses have confirmed that data on relation of distant. clusters are consistent with a lack of evolution (e.g. Mushotzky Scharf 1997. Donahue ct al.," Independent analyses have confirmed that data on relation of distant clusters are consistent with a lack of evolution (e.g. Mushotzky Scharf 1997, Donahue et al."668 1999. Della Ceca et al.," 1999, Della Ceca et al."669 2000. Borgani οἱ al.," 2000, Borgani et al."670 2001b. Stanford et al.," 2001b, Stanford et al."671 2002. Ποιάσον et al.," 2002, Holden et al."672 2002)., 2002).673 Since no data are available on 7S1 keV groups in the above z range. we do not include in this comparison results for the Hickson runs.," Since no data are available on $T\mincir 1$ keV groups in the above $z$ –range, we do not include in this comparison results for the Hickson runs."674 Although temperature determinations for distant clusters are prone to larger crrorbars. the results are quite in line with what shown in Fig. H1:," Although temperature determinations for distant clusters are prone to larger errorbars, the results are quite in line with what shown in Fig. \ref{fi:lt}:"675" the relation of distant. clusters requires preheating of the ICM with £,z1 keV/part.", the relation of distant clusters requires pre–heating of the ICM with $E_h\magcir 1$ keV/part.676" the probability that a planetary mass object in Upper Sco conservatively,would fall within oof any of the stellar members we observed is only 0.002.","conservatively, the probability that a planetary mass object in Upper Sco would fall within of any of the stellar members we observed is only 0.002."677 We can now factor the common proper motion constraint into the analysis., We can now factor the common proper motion constraint into the analysis.678" Using the proper motion dispersion of ~8 mas ΥΓ! in RA and DEC reported by (Bouy&Martin2009) for the low-mass members of Upper Sco, the probability that two unrelated Sco would share a common proper motion within Upper4-5 mas yr objectsper axis, as we have observed, is 0.13."," Using the proper motion dispersion of $\sim$ 8 mas $^{-1}$ in RA and DEC reported by \citep{bouy09} for the low-mass members of Upper Sco, the probability that two unrelated Upper Sco objects would share a common proper motion within 4-5 mas $^{-1}$ per axis, as we have observed, is 0.13."679" Thus taken together, !the proximity and common proper motion of the primary and companion indicate a probability of 2.6x10“ of chance "," Thus taken together, the proximity and common proper motion of the primary and companion indicate a probability of $2.6\times10^{-4}$ of chance alignment."680"So given this small probability, despite the lack of alignment.orbital motion detection,very we treat the candidate companion as a truly bound companion for the remainder of this paper."," So given this very small probability, despite the lack of orbital motion detection, we treat the candidate companion as a truly bound companion for the remainder of this paper."681 The new J-band spectrum of the companion is shown in Fig., The new $J$ -band spectrum of the companion is shown in Fig.682" 3 along with the spectrum of a field L3 dwarf, the spectrum of a young LO brown dwarf member of Upper Sco, and model from the DUSTY (Chabrier and DRIFT spectraPHOENIX (Witteetal.2009;Helling atmosphere models for low and high surface gravity."," \ref{fig:jspec} along with the spectrum of a field L3 dwarf, the spectrum of a young L0 brown dwarf member of Upper Sco, and model spectra from the DUSTY \citep{chabrier00} and DRIFT PHOENIX \citep{witte09,helling08} atmosphere models for low and high surface gravity."683" The new J-band spectrum shows typical features of late-M or dwarfs, absorption H2O beyond ~1.33 early-L um, the K I namelydoublet at important1.24-1.25 um, byand absorption by FeH at 1.24 «um; the S/N is too small to identify other individual features but the general shape of the continuum is qualitatively as expected through the band."," The new $J$ -band spectrum shows typical features of late-M or early-L dwarfs, namely important absorption by $_2$ O beyond $\sim$ 1.33 $\mu$ m, the K I doublet at 1.24-1.25 $\mu$ m, and absorption by FeH at 1.24 $\mu$ m; the S/N is too small to identify other individual features but the general shape of the continuum is qualitatively as expected through the band."684" As seen from the reasonable agreement with the model spectrum of Ίεῃ= K, the new spectrum is consistent with the previous estimate of the effective temperature of the companion."," As seen from the reasonable agreement with the model spectrum of $T_{\rm eff}=1800$ K, the new spectrum is consistent with the previous estimate of the effective temperature of the companion."685 Figure 4 shows the merged JHK spectrum of aalong with synthetic spectra from the DUSTY and DRIFT PHOENIX atmosphere models for different temperatures and surface gravities., Figure \ref{fig:jhkspec} shows the merged $JHK$ spectrum of along with synthetic spectra from the DUSTY and DRIFT PHOENIX atmosphere models for different temperatures and surface gravities.686" From this figure, it is clear that the companion has low surface gravity: the slope of the continuum through the H and K bands are much better fit by low gravity spectra for both sets of models."," From this figure, it is clear that the companion has low surface gravity: the slope of the continuum through the $H$ and $K$ bands are much better fit by low gravity spectra for both sets of models."687 The DRIFT PHOENIX models provide a better fit of the overall spectral shape., The DRIFT PHOENIX models provide a better fit of the overall spectral shape.688" In particular, the red side of the H band, which is poorly fit by the low-gravity DUSTY models owing to uncertainties in the model opacities used, is well fit the by the DRIFT PHOENIX models."," In particular, the red side of the $H$ band, which is poorly fit by the low-gravity DUSTY models owing to uncertainties in the model opacities used, is well fit the by the DRIFT PHOENIX models."689" For the latter models, the steepness of the slope on either side of the H band even provides some constraint on the effective temperature, favoring 1700-1800 K. Although less apparent from the figure, the K band is also better reproduced by the DRIFT PHOENIX models, the DUSTY models spectra falling off slightly too rapidly at the blue side."," For the latter models, the steepness of the slope on either side of the $H$ band even provides some constraint on the effective temperature, favoring 1700–1800 K. Although less apparent from the figure, the $K$ band is also better reproduced by the DRIFT PHOENIX models, the DUSTY models spectra falling off slightly too rapidly at the blue side."690" The shape of the K band spectrum,according to the DRIFT PHOENIX models, also favors a temperature of 1800 K. The companion was detected in both the NB3.05 and L' images at the level of —5o and -3o, respectively; see Fig. 5.."," The shape of the $K$ band spectrum,according to the DRIFT PHOENIX models, also favors a temperature of 1800 K. The companion was detected in both the NB3.05 and $L^\prime$ images at the level of $\sim$ $\sigma$ and $\sim$ $\sigma$, respectively; see Fig. \ref{fig:longlbd}."691 The flux of the companion and primary were determined from photometry in an aperture of diameter 6 pixels., The flux of the companion and primary were determined from photometry in an aperture of diameter 6 pixels.692 The uncertainty on the companion flux was estimated from the dispersion of the noise in 21 such apertures spread azimuthally around circle of radius ccentered on the a star., The uncertainty on the companion flux was estimated from the dispersion of the noise in 21 such apertures spread azimuthally around a circle of radius centered on the primary star.693 We obtained a contrast of 6.5+0.2 mag in NB3.05 primaryand 6.1--0.3 mag in L’., We obtained a contrast of $6.8\pm0.2$ mag in NB3.05 and $6.1\pm0.3$ mag in $L^\prime$ .694" Unfortunately, we cannot derive the companion's flux in a straightforward manner as we did not observe"," Unfortunately, we cannot derive the companion's flux in a straightforward manner as we did not observe"695and S<3 pixels for surface photometry.,and $\times$ 3 pixels for surface photometry.696 This leads to a final error of close το 100 οpixel|.," This leads to a final error of close to 400 $\rm e^{-} 697pixel^{-1}$."698 Exrors for cach bin are caliulated based ou the uuuber of nou-niasked. pixels iu that biu. ratioed to the error expected for all pixels in that bin having data.," Errors for each bin are calulated based on the number of non-masked pixels in that bin, ratioed to the error expected for all pixels in that bin having data."699 As photon noise iu the sky is the dominant source of error in our data. we give the expected error por bin for both the smallest bin we use for R-profiles <3 pixels) and the largest bin we use for :-profiles «50 pixels).," As photon noise in the sky is the dominant source of error in our data, we give the expected error per bin for both the smallest bin we use for $R$ -profiles $\times$ 3 pixels) and the largest bin we use for $z$ -profiles $\times$ 50 pixels)."700 The error for the faintest part of NGC 1565 is close to 183 6pixel1. or 63 οaresce7.," The error for the faintest part of NGC 4565 is close to 183 $\rm e^{-} pixel^{-1}$, or 63 $\rm701e^{-} arcsec^{-2}$."702 That is. the relative eror of measured fix at 28.77 mag 7 is LOO%.. leading to an error bar of 0.75 mag 2 7.," That is, the relative error of measured flux at 28.77 mag $^{-2}$ is , leading to an error bar of 0.75 mag $^{-2}$ ."703 Thisqol also corresponds to au error ofuaa 0.25 mae 27 at a surface] brightuess: offaye 27.5 mag ., This also corresponds to an error of 0.25 mag $^{-2}$ at a surface brightness of 27.5 mag $^{-2}$.704 Iu fact. the error is a little higher than this. because there exist masked regions in the measured boxes.," In fact, the error is a little higher than this, because there exist masked regions in the measured boxes."705 The main sources of error are from large-scale variation of fat-field. «ky fitting and residuals frou star subtraction.," The main sources of error are from large-scale variation of flat-field, sky fitting and residuals from star subtraction."706 As others have done (cf, As others have done (cf.707 NJ). we use a contour map to determine the position angle of the major axis.," NJ), we use a contour map to determine the position angle of the major axis."708 Then the ska-subtracted image is rotated to that angle to put the major axis of the object galaxy alone the x-axis direction., Then the sky-subtracted image is rotated to that angle to put the major axis of the object galaxy along the x-axis direction.709 At the same time. all circular masks but the three masks used for the object ealaxy were transformed to the new coordinate syste and imposed ou the rotated image (Figure L).," At the same time, all circular masks but the three masks used for the object galaxy were transformed to the new coordinate system and imposed on the rotated image (Figure 4)."710 For purposes of analysis. we measure the liunosity profiles of NGC 1565 in two orthogonal directions.," For purposes of analysis, we measure the luminosity profiles of NGC 4565 in two orthogonal directions."711" One direction is parallel to the galaxy minor axis (the ""z direction). the other is parallel to the major axis (the ""R direction)."," One direction is parallel to the galaxy minor axis (the $z$ ” direction), the other is parallel to the major axis (the $R$ ” direction)."712 We sample the + direction in discrete leneths (parallel to the major axis) of 35 κοιν (1 arcuuin) on both sides of the major axis., We sample the $z$ direction in discrete lengths (parallel to the major axis) of 35 pixels $\sim$ 1 arcmin) on both sides of the major axis.713" We employ. bius of varving width perpeudicular to the uajor axis (i.c., aloug the + direction): from 1 pixel when 2 = 0 (i6. on the major axis) to 50 pixels for the areest 2 distances (~ 77)."," We employ bins of varying width perpendicular to the major axis (i.e., along the $z$ direction): from 1 pixel when $z$ = 0 (i.e., on the major axis) to 50 pixels for the largest $z$ distances $\sim 7'$ )."714 This methodology vields bin sizes that varv from &1 pixels to 450 pixels., This methodology yields bin sizes that vary from $\times$ 1 pixels to $\times$ 50 pixels.715 Onlv munasked pixels ave used. auc the flux cited is the median value for that bin.," Only unmasked pixels are used, and the flux cited is the median value for that bin."716 The measured 2 and & xofiles ave shown in Fieure 5., The measured $z$ and $R$ profiles are shown in Figure 5.717" Here we adopt a distance of 115 Mpc. with 1""=0.0703 kpe."," Here we adopt a distance of 14.5 Mpc, with $1'' = 0.0703$ kpc."718 We sce that the four z-profiles in each plot G.e.. all four quadrants of the galaxy) agree reasonably well down to surface brightucss of 28 mae . or alevel of of sky) within a radius of 6 arcimin.," We see that the four $z$ -profiles in each plot (i.e., all four quadrants of the galaxy) agree reasonably well down to surface brightness of 28 mag $^{-2}$, or alevel of of sky) within a radius of 6 arcmin."719 Greaterthanthat distance. the well-known warp in the disk of this ealaxv (SE to NW) (cf. Saucisi L976:," Greaterthanthat distance, the well-known warp in the disk of this galaxy (SE to NW) (cf. \cite{S76}; ;"720Ayr. instead of our adopted LOO Myr. probably reduces our final mass estimates by. a factor of (wo.,"Myr, instead of our adopted 100 Myr, probably reduces our final mass estimates by a factor of two."721 Dynamical interactions wilh Neptune and passing stus can also remove substantial amounts of material (e.g..Holman&Wisdom1993:LevisonStern1995:al.2000).," Dynamical interactions with Neptune and passing stars can also remove substantial amounts of material \citep[e.g.,][]{hol93,lev95,dun95,mal96,lev97,mor97, ida00}."722. These studies suggest that a combination of collisional grinding aud clvnamical interactions wilh Neptune or a passing star can reduce a minimum mass solar nebula to (he mass observed today in the Ixuiper Bell., These studies suggest that a combination of collisional grinding and dynamical interactions with Neptune or a passing star can reduce a minimum mass solar nebula to the mass observed today in the Kuiper Belt.723 We plan to describe additional tests of these possibilities in future publications., We plan to describe additional tests of these possibilities in future publications.724 Finally. our calculations provide additional evidence that observations of INuiper Bell objects probe the formation and early evolution of Neptune and other icv planets in the outer solar svstem.," Finally, our calculations provide additional evidence that observations of Kuiper Belt objects probe the formation and early evolution of Neptune and other icy planets in the outer solar system."725 Better limits on the sizes of the largest IXDOs probe the timescale [ου Neptuneformation!., Better limits on the sizes of the largest KBOs probe the timescale for Neptune.726. These observations also constrain the bulk strength of IKDOs during the formation epoch., These observations also constrain the bulk strength of KBOs during the formation epoch.727 The detection of small IKDOs. r22 0.110 km. by occultations or by direct imaging (e.g..OW£L: vields complementary constraints.," The detection of small KBOs, $r \approx$ 0.1–10 km, by occultations \citep[e.g. {\it TAOS}; or by direct imaging \citep[e.g., {\it OWL}; yields complementary constraints."728 As the observations improve. the theoretical challenge is to combine collisional (this paper: Goldreich.Lithwick.&Sari (2004))) and dynamical (e.g.Malhotra.1995:Gomes2003:Levison&Morbidelli:Quillen.Trilling.&Blackman2004) calculations to derive robust predictions for the formation and evolution of Uranus. Neptune. and smaller iev planets at heliocentric distances 2 15 AU.," As the observations improve, the theoretical challenge is to combine collisional (this paper; \cite{gol04}) ) and dynamical \citep[e.g.][]{mal95,gom03,lev03,qui04} calculations to derive robust predictions for the formation and evolution of Uranus, Neptune, and smaller icy planets at heliocentric distances $\gtrsim$ 15 AU."729 Together. the caleulations and (he observations promise detailed tests oftheories of planet formation.," Together, the calculations and the observations promise detailed tests oftheories of planet formation."730 σον We acknowledge a generous allotment. ~ 3000 cpu clavs from February 2003 through March 2004. of computer (ime at the supercomputing center at the Jet Propulsion Laboratory through funding from the NASA Olfiees of Mission to Planet Earth. Aeronauties. and Space Science.," 6ex We acknowledge a generous allotment, $\sim$ 3000 cpu days from February 2003 through March 2004, of computer time at the supercomputing center at the Jet Propulsion Laboratory through funding from the NASA Offices of Mission to Planet Earth, Aeronautics, and Space Science."731 Advice ancl comments from M. Geller and S. A. Stern improved our presentation., Advice and comments from M. Geller and S. A. Stern improved our presentation.732 We thank P. Michel ancl A. Morbidelli lor extensive discussions that improved our treatment of collisional disruption., We thank P. Michel and A. Morbidelli for extensive discussions that improved our treatment of collisional disruption.733 We also acknowledge discussions with P. Goldreich and M. Holman., We also acknowledge discussions with P. Goldreich and M. Holman.734 The supported part of this project through grant, The supported part of this project through grant NAG5-13278.735"the variations in the arca we detect are so strong that, possibly. à non-linear analysis of the variations 1s required, hence, the classical models are not suitable to explain these observations.","the variations in the area we detect are so strong that, possibly, a non-linear analysis of the variations is required, hence, the classical models are not suitable to explain these observations."736" If not being flux tube oscillation modes, the pattern we observe might be the forcing due to the evolution of the granules."," If not being flux tube oscillation modes, the pattern we observe might be the forcing due to the evolution of the granules."737" Since the magnetic fields on the quiet Sun have mainly strengths lower than the equipartition field in the photosphere (~300—500G:seee.g.Lin1995:Khomenkoetal.2003:MartínezGonzález2008:OrozcoSuárez 2007).. the field lines are continuously buffeted by granular flows, being squashed or released everywhere and hence the magnetic fields are constantly being amplified or weakened."," Since the magnetic fields on the quiet Sun have mainly strengths lower than the equipartition field in the photosphere \citep[$\sim738300-500$ G; see e.g.][]{lin_95, khomenko_03, marian_08, david_07}, the field lines are continuously buffeted by granular flows, being squashed or released everywhere and hence the magnetic fields are constantly being amplified or weakened."739" However, the present observations do not allow us to reject cither scenario."," However, the present observations do not allow us to reject either scenario."740" Now, an interesting question arises: do these waves propagate up through the solar atmosphere?"," Now, an interesting question arises: do these waves propagate up through the solar atmosphere?"741" We predict that, in case these waves propagate across the solar atmosphere, the very same phenomena reported in this letter should be observed in the filter-polarimeters onboard the Hinode satellite."," We predict that, in case these waves propagate across the solar atmosphere, the very same phenomena reported in this letter should be observed in the filter-polarimeters onboard the Hinode satellite."742 The different instruments onboard the Hinode satellite provide valuable simultaneous data tracing the solar atmosphere (seee.Martínez 2009).," The different instruments onboard the Hinode satellite provide valuable simultaneous data tracing the solar atmosphere \citep[see e.743g.][]{marian_09}."744. This data may be interesting to future work devoted to a detailed study of the propagation of these waves from the photosphere to the chromosphere., This data may be interesting to future work devoted to a detailed study of the propagation of these waves from the photosphere to the chromosphere.745" Wave propagation is an efficient means of carrying energy between different atmospheric heights and of dissipating it efficiently. mainly, through the formation of shocks."," Wave propagation is an efficient means of carrying energy between different atmospheric heights and of dissipating it efficiently, mainly, through the formation of shocks."746" Therefore, we should put additional efforts into unveiling the role of this newly detected magnetic field oscillation in heating atmospheric layers."," Therefore, we should put additional efforts into unveiling the role of this newly detected magnetic field oscillation in heating atmospheric layers."747analvsis.,analysis.748 Foleheraiter ancl co-workers (1997) already provided indications on the source N-rav shape: they found that either a power law with a photon index of L8 or. alternatively. a thermal model with a KT of about 2 keV was appropriate to fit the 0.52 keV low cnerev X-ray (ROSAT and ABCA) cata.," Folgheraiter and co-workers (1997) already provided indications on the source X-ray shape: they found that either a power law with a photon index of 1.8 or, alternatively, a thermal model with a kT of about 2 keV was appropriate to fit the 0.5–2 keV low energy X-ray (ROSAT and ASCA) data."749 Both models required absorption in excess o the Galactic value which in the source direction is 9.93 107. em? (Dickey Lockman. 1990).," Both models required absorption in excess to the Galactic value which in the source direction is 9.93 $\times$ $^{21}$ $^{-2}$ (Dickey Lockman, 1990)."750 Our broad. band 5-110 keV. spectrum is poorly fitted with a simple power aw absorbed by the Galactic absorption (472—307 /260) rut the addition of extra absorption. probably intrinsic to he source improves the fit significantly: (at a confidence evel c 99.99% ancl provides the best description οἱ he source spectrum)) (4722255/259).," Our broad band 0.5-110 keV spectrum is poorly fitted with a simple power law absorbed by the Galactic absorption $\chi^{2}$ =307/260) but the addition of extra absorption, probably intrinsic to the source improves the fit significantly (at a confidence level $>$ ) and provides the best description of the source spectrum $\chi^{2}$ =255/259)."751" ""Phe amount of extra column density is Ng. —4 107 cm7 while the value of οποίο index is P=1.56: the eross calibration is found to be 1.65023 indicating possible variability between the pointed XMM observation and the IBIS average measurement.", The amount of extra column density is $_{H}$ $\sim$ 4 $\times$ $^{21}$ $^{-2}$ while the value of photon index is $\Gamma$ =1.56; the cross calibration is found to be $^{+0.28}_{-0.22}$ indicating possible variability between the pointed XMM observation and the IBIS average measurement.752" The combined «ΧΑΛΙΛΗΝΓΙΟΛΙ, unfolded spectrum. fitted with this mocde is shown in figure 10 and. described. in table 3.", The combined XMM/INTEGRAL unfolded spectrum fitted with this model is shown in figure 10 and described in table 3.753 The spectral. parameters are quite in agreement with what found by Halpern from the NMM data analysis alone but not fully compatible with the spectral parameters reported. by Foleheraiter ct al. (, The spectral parameters are quite in agreement with what found by Halpern from the XMM data analysis alone but not fully compatible with the spectral parameters reported by Folgheraiter et al. (7541997). although we ect a similar flux in the 0.5-2 keV energy band (~2 £ 7? ο].,1997) although we get a similar flux in the 0.5-2 keV energy band $\sim$ 2 $\times$ $^{-12}$ $^{-2}$ $^{-1}$ ).755" On the other hand. it is worth noting that a thermal mocel does not fit our broad band We conclude that LGA 18538-0102. as already. argued bv Llalpern CGotthell (2010). is unlikely a compact object in the supernova remnant. (92.109 but. could. be a backeround ACN that is coincicentally aligned with the supernova,"," On the other hand, it is worth noting that a thermal model does not fit our broad band We conclude that IGR J18538-0102, as already argued by Halpern Gotthelf (2010), is unlikely a compact object in the supernova remnant G32.1-09 but could be a background AGN that is coincidentally aligned with the supernova."756 In this work we have cross-correlated the list of the still unidentified hard N-ray emitters [listed in the 4th. LBIS survey with the archive of all pointings finding a set of 6 objects with archivalLI data., In this work we have cross-correlated the list of the still unidentified hard X-ray emitters listed in the 4th IBIS survey with the archive of all pointings finding a set of 6 objects with archival data.757 First. we studied the EPIC images in order to [find in the LBIS error circle the X-ray counterpart(s).," First, we studied the EPIC images in order to find in the IBIS error circle the X-ray counterpart(s)."758 In the case where an associated source has been found. the data have then been used together the spectra to study the broad. band slope and investigate the possible nature of the source.," In the case where an associated source has been found, the data have then been used together the spectra to study the broad band slope and investigate the possible nature of the source."759 In table 4 à summary of our proposed identifications is In a couple of cases no obvious X-ray counterpart has been found. from the observations. like IGI J1173331.2406 and LOR J17445-2747.," In table 4 a summary of our proposed identifications is In a couple of cases no obvious X-ray counterpart has been found from the observations, like IGR J173331–2406 and IGR J17445-2747."760 In the first case. no X-ray source has been detected.," In the first case, no X-ray source has been detected."761 This is in perfect agreement with the LBIS survey data where this source has been found to be transient., This is in perfect agreement with the IBIS survey data where this source has been found to be transient.762 Extrapolating to the low energies (0.5-10 keV) the spectrum seen by LBIS during the source outburst and comparing it with the NM. upper limit. we found a dynamical range of the order of 3000.," Extrapolating to the low energies (0.5-10 keV) the spectrum seen by IBIS during the source outburst and comparing it with the XMM upper limit, we found a dynamical range of the order of 3000."763 Such a high. value strongly suggests that LGR: J17331.2406 could. be. either a transient. black hole in the Galactic bulge or a SEXT although this latter interpretation can be ruled out clue to source location olf the Galactic plane (~ 5r. degrees) as well as its significantly longer. outburst duration. compared. to classical SENXTs., Such a high value strongly suggests that IGR J17331–2406 could be either a transient black hole in the Galactic bulge or a SFXT although this latter interpretation can be ruled out due to source location off the Galactic plane $\sim$ 5 degrees) as well as its significantly longer outburst duration compared to classical SFXTs.764 Vhe other case where the NMM observation: does not provide a secure X-ray counterpart is that of LOR J17445-2747., The other case where the XMM observation does not provide a secure X-ray counterpart is that of IGR J17445-2747.765 From the imaging analysis we found a faint NAIA source at the border of the IBIS error circle which has also been detected by both ονΧΙΙ and. Chandra., From the imaging analysis we found a faint XMM source at the border of the IBIS error circle which has also been detected by both Swift-XRT and Chandra.766 On the other hand. from archival searches we found. an NAIA slew source well inside. the high energy positional uncertainty which has been seen only once by NMM and therefore is again in perfect agreement with the high energy survey data which classified this source extremely variable: we therefore associate LGR J17445-214T 1o NAIAISLI J174429.4-274600 In the remaining four cases we have found a convincing X-rav counterpart in the IBIS error circle for which it has eni possible to search for counterparts in other wavelength xnds and also perform. the spectral data. analysis. in he 0.5110 keV band.," On the other hand, from archival searches we found an XMM slew source well inside the high energy positional uncertainty which has been seen only once by XMM and therefore is again in perfect agreement with the high energy survey data which classified this source extremely variable; we therefore associate IGR J17445-2747 to XMMSL1 J174429.4-274609 In the remaining four cases we have found a convincing X-ray counterpart in the IBIS error circle for which it has been possible to search for counterparts in other wavelength bands and also perform the spectral data analysis in the 0.5–110 keV band."767 The spectral parameters obtained ogether with the possible Ht/optical/radio counterpart ound allowec us to investigate on the nature of each source., The spectral parameters obtained together with the possible IR/optical/radio counterpart found allowed us to investigate on the nature of each source.768 We conclude that LGR. J15859-5750 is an AGN of intermediate tvpe for which we were able to estimate he amount of the complex. absorption as well as to give constraints on the reflection ancl t1e high. energy. eut-olT., We conclude that IGR J15359-5750 is an AGN of intermediate type for which we were able to estimate the amount of the complex absorption as well as to give constraints on the reflection and the high energy cut-off.769 Lor the two ASCA sources AX J1739.3-2923 and ΑΝ J1740.2-2003. we suggest à stronely absorbed. Galactic nature and for both we argue that trev are likely persistent LIAIND systems., For the two ASCA sources AX J1739.3-2923 and AX J1740.2-2903 we suggest a strongly absorbed Galactic nature and for both we argue that they are likely persistent HMXB systems.770 More uncertain is the case of LGR. JIS53s-N02 which is spatially coincident with a hot spot. in he supernova remnant (29.109 detected: previously by LOSATL and ASCA., More uncertain is the case of IGR J18538-0102 which is spatially coincident with a hot spot in the supernova remnant G32.1-0.9 detected previously by ROSAT and ASCA.771 From the broad band spectral analysis »rformed in this work we can conclude that this object is unrelated: compact object. which happen to coincide with he supernova remnant. probably a background AGN that is coincidentally aligned even if no radio counterpart has ovn found in the more precise NMM error This research has made use of cata obtained from. the SIMDAD database operated at CDS. Strasbourg. France: the Ligh Enerey Astrophysics Science. Archive Research Center (IUEASARC). provided by NASA's Goddard Space Εισαι Center NASA/IPAC Extragalactic Database (NED).," From the broad band spectral analysis performed in this work we can conclude that this object is unrelated compact object which happen to coincide with the supernova remnant, probably a background AGN that is coincidentally aligned even if no radio counterpart has been found in the more precise XMM error This research has made use of data obtained from the SIMBAD database operated at CDS, Strasbourg, France; the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center NASA/IPAC Extragalactic Database (NED)."772 We thank the anonymous referee for the very. detailed. and careful review of this paper., We thank the anonymous referee for the very detailed and careful review of this paper.773 The authors acknowledge the ASI financial support via ASLINAV erant L/008/07/0., The authors acknowledge the ASI financial support via ASI–INAF grant I/008/07/0.774410% while Larsenοἱal.(2011) claim up to heterogeneity in the initial abundance of 7 A] in the inner solar svstem).,$\pm$ while \citet{lar11} claim up to heterogeneity in the initial abundance of $^{26}$ Al in the inner solar system).775 Ho we assume instead that the material from. which Iris formed had the lowest (7 AL/7 Al); in chondrule-containing parent bodies (from (2011))). the ordinary chondrite parent body. ο ΑΙ y=l.63x 10°. then Iris crystallized ab least 1.8 Myr alter CAIs.," If we assume instead that the material from which Iris formed had the lowest $^{26}$ $^{27}$ $_0$ in chondrule-containing parent bodies (from \citet{lar11}) ), the ordinary chondrite parent body, $^{26}$ $^{27}$ $_0$ $\times$ $^{-5}$, then Iris crystallized at least 1.8 Myr after CAIs."776 The formation time of Iris compared to ehondrules from other meteorites. as well as a CAI-like Stardust fragment. is shown in Figure 4..," The formation time of Iris compared to chondrules from other meteorites, as well as a CAI-like Stardust fragment, is shown in Figure \ref{almg}."777 The probability density curve for Iris is derived from the Monte Carlo simulations discussed above. whereas the curves lor other objects are normalized suns of reported measurements of AD). assuming Gaussian- errors.," The probability density curve for Iris is derived from the Monte Carlo simulations discussed above, whereas the curves for other objects are normalized sums of reported measurements of $^{26}$ $^{27}$ $_0$, assuming Gaussian-distributed errors."778 Probability density associated with negative CAD/7* AI) corresponds to ill-clefined Gime since CALI formation. so these densities. as well as (those for 77 half-lives of Al. are not shown. (," Probability density associated with negative $^{26}$ $^{27}$ $_0$ corresponds to ill-defined time since CAI formation, so these densities, as well as those for $>$ 7 half-lives of $^{26}$ Al, are not shown. ("779Consequently. the area under the curves for objects with allowed negalive or very small (ΑΙ Αμ is less than for objects that formed earlier.),"Consequently, the area under the curves for objects with allowed negative or very small $^{26}$ $^{27}$ $_0$ is less than for objects that formed earlier.)"780 Since CAIs are believed to have formed when (he Sun was a class 0 or class I protostar. lis formed late in the evolution of the solu nebula. at a time when ~95% of the scattered disk is thought to have eleared (Iersant.Gautheir.&IIwé2001).," Since CAIs are believed to have formed when the Sun was a class 0 or class I protostar, Iris formed late in the evolution of the solar nebula, at a time when $\sim$ of the scattered disk is thought to have cleared \citep{her01}."781". The residual disk material mav have coated Jupiter-lamily comets with a ""late veneer” enriched in inner solar system malerial (Oglioreetal.2010).. ancl this may explain sienifiecant. differences between the Stardust sample. which sampled Wild 2 coma material ejected by jets that entrained near- dust (Bellon2010).. and chondiitie porous interplanetary dust. particles. which probably sample the bulk of Ixuiper Belt comets (Nesvornyetal.2010)."," The residual disk material may have coated Jupiter-family comets with a “late veneer” enriched in inner solar system material \citep{ogl10}, and this may explain significant differences between the Stardust sample, which sampled Wild 2 coma material ejected by jets that entrained near-surface dust \citep{bel10}, and chondritic porous interplanetary dust particles, which probably sample the bulk of Kuiper Belt comets \citep{nes10}."782. These analvses are [or a single object in the Stardust collection., These analyses are for a single object in the Stardust collection.783 However. Iris is not unique or even particularly unusual in the suite of particles returned. [rom comet Wild 2.," However, Iris is not unique or even particularly unusual in the suite of particles returned from comet Wild 2."784" Nakamuraetal.(2008) identified four chondrule-like objects in the Stardust samples which are more ""O-enriched than Iris (Figure 2)) and olivines that are less Fe-rich (Forouj. Foos. Foo)."," \citet{nak08} identified four chondrule-like objects in the Stardust samples which are more $^{16}$ O-enriched than Iris (Figure \ref{oiso}) ) and olivines that are less Fe-rich $_{79\text{--}80}$, $_{95}$, $_{91}$ )."785 At least one chondrule fragment. was also identified during the Stardust preliminary examination (Zolenskvetal.2006)., At least one chondrule fragment was also identified during the Stardust preliminary examination \citep{zol06}.786. All of these objects show igneous textures similar to Iris. though Iris appears to have formed in a more oxidizing environment.," All of these objects show igneous textures similar to Iris, though Iris appears to have formed in a more oxidizing environment."787 Recent measurements bv Joswiaketal.(2011) show two fragments of Fe-rich olivine (Fogssz. Fossa). that also have O isotopic composition close to Iris.," Recent measurements by \citet{jos11} show two fragments of Fe-rich olivine $_{62\text{--}67}$, $_{58\text{--}61}$ ), that also have O isotopic composition close to Iris."788 Chondrule-like objects from Stardust show a broad range of isotopic aud mineralogical compositions: a subset of these objects could be geneticallv related to Iris., Chondrule-like objects from Stardust show a broad range of isotopic and mineralogical compositions; a subset of these objects could be genetically related to Iris.789"The received photou density »""(e"") iu the jet comoving faune can be then approximately written as where we use e=(2D)?e42 (there are two Doppler shiftswp due to nurror effects).",The received photon density $\npp(\epspp)$ in the jet comoving frame can be then approximately written as where we use $\epspp=(2\Gam)^2\epsp$ (there are two Doppler shifts due to mirror effects).790 The couvenieut form of cross section of photon-photou collision is (Coppi Blandford 1990) where à is the usual ó-fuuctiou., The convenient form of cross section of photon-photon collision is (Coppi Blandford 1990) where $\delta$ is the usual $\delta$ -function.791 This approximation is ouly valid for case of isotropic radiation field., This approximation is only valid for case of isotropic radiation field.792 The Rsv colmponent is seen bv the blob within the solid anele AQzc2z(lcosP1)x=x/I?., The Rsy component is seen by the blob within the solid angle $\Delta \Omega \approx 2\pi(1-\cos\Gam^{-1})\approx \pi/\Gam^2$.793 Although the cross section of photon-plioton interaction holds. the interacting possibility among plotous reduces by a factor of AQ/lz=1/GD)? due to the beaming effects. which effectively reduces the opacity.," Although the cross section of photon-photon interaction holds, the interacting possibility among photons reduces by a factor of $\Delta \Omega/4\pi=1/(2\Gam)^2$ due to the beaming effects, which effectively reduces the opacity."794 Thus the pair production optical depth for photon with euergv €» reads here 79.(e.) is We will show the validity of the above approximation in the next subsection., Thus the pair production optical depth for photon with energy $\epsg$ reads here $\tgg^0(\epsg)$ is We will show the validity of the above approximation in the next subsection.795" Supposing that RSC operates eficiently iu οταν loud blazars. we cau eet fi. from the observations From equation (11) we lave πμ... From equation (11) we kuow that the observed 7/4 represents the reflection ratio aud Doppler factor of jet notion as long as the Compton catastrophe does not occi,"," Supposing that RSC operates efficiently in $\gamma$ -ray loud blazars, we can get $\lrsc$ from the observations From equation (11) we have and From equation (11) we know that the observed $\lrsc$ represents the reflection ratio and Doppler factor of jet motion as long as the Compton catastrophe does not occur."796 Tf we set fiemlans we got τνD2=(k01 for D10.," If we set $\lrsc\approx \lssc$, we get $\tblr\approx \Gam^{-2}=0.01$ for $\Gam=10$."797 This value is the lowest one in the model of Sikora. Boechuan Rees (1991) who suggest τν—0.1~0.01.," This value is the lowest one in the model of Sikora, Begelman Rees (1994) who suggest $\tblr=0.1\sim 0.01$."798" Iu act we can roughly adopt 7,,, as the covering factor which is usually taken to be 0.1 in fitting the broad cussion line x photoionization moclel.", In fact we can roughly adopt $\tblr$ as the covering factor which is usually taken to be 0.1 in fitting the broad emission line by photoionization model.799 Iuserting D aud Np [|eqs(1) and (60) intoτὸ. (Eq., Inserting $B$ and $N_T$ [eqs(1) and (6)] into$\tgg^0$ (Eq.800" 10). and letting e;=€,)./P aud 5= “-DAt,,,.. we have the pair xoduction optical depth for €; iu the observers frame where A,=DontSOnhie(DELEh-)~ ΕΞτοςτο4% for a—2.1)."," 10), and letting $\epsg=\eps_{\rm obs}/\cd$ and $s=c\cd \dt$ , we have the pair production optical depth for $\eps_{\rm obs}$ in the observer's frame where $K_{\alpha}=\frac{(3-\al)\st c}{80\pi h \nu_0^2}801 \left(\frac{h}{m_ec^2}\right)^{\al-1 \over 2}$ $K_{\alpha}=7.9\times 10^{-18}$ for $\alpha=2.4$ )."802" There are five observational parameters: 14. Msc. a, Afus and fc: aud the uukuown Doppler factor D."," There are five observational parameters: $\nu_{\rm s}$ , $\nu_{\rm rsc}$, $\al$, $\dt$ and $\lrsc$; and the unknown Doppler factor $\cd$."803" For the typical value of pirzuneters; à=2.1 i,—10«10:TIz. and Me=LO.109 Πε. Δι=1 day, and D=10. we have where Diy=D/10."," For the typical value of parameters, $\al=2.4$, $\nu_{\rm s}=4.0\times 10^{14}$ Hz, and $\nu_{\rm rsc}=1.0\times 10^{25}$ Hz, $\dt=1$ day, and $\cd=10$, we have where $\cd_{10}=\cd/10$."804 Fieure 1 shows the opacity due to pair production of photous with very high euergv chcountering with the reflected svuchrotron plotous., Figure 1 shows the opacity due to pair production of photons with very high energy encountering with the reflected synchrotron photons.805 The equation (15) tells us the constraints on VILE from jet: (1) inaller fie. Le. stronger reflection. will leads to the absorption of TeV plotons.," The equation (15) tells us the constraints on VHE from jet: (1) smaller $\lrsc$, i.e. stronger reflection, will leads to the absorption of TeV photons."806 This parameter represents the energv density reflected by the BLR cloud including the bulk relativistic motion., This parameter represents the energy density reflected by the BLR cloud including the bulk relativistic motion.807 From this estimation we know that TeV photon will be absorbed by the reflected svuchrotron plotous provided that fp.<1.9. (, From this estimation we know that TeV photon will be absorbed by the reflected synchrotron photons provided that $\lrsc<1.9$. (808"2) T. Is sensitive to n, and mie. (",2) $\tgg$ is sensitive to $\nu_{\rm s}$ and $\nu_{\rm rsc}$. (8093) τ.- Is proportional to PD! in contrast to the usual down-linüt (sce Mattox et al 1993. and Doudi Cdiselliui 1995). providing the wpper μπιτ Doppler factor of bulk motion from 7...<1. This is a new coustraint. which is expressed bv the observational quantities.,"3) $\tgg$ is proportional to $\cd^4$, in contrast to the usual down-limit (see Mattox et al 1993, and Dondi Ghisellini 1995), providing the upper limit Doppler factor of bulk motion from $\tgg\leq 1$, This is a new constraint, which is expressed by the observational quantities."810 It. leuds us a simple iud efficient way to select TeV candidates from kuown blazars iu teria of their known characteristics., It lends us a simple and efficient way to select TeV candidates from known blazars in term of their known characteristics.811 The received photous reflected by BLR iu comoving fune is amisotropic. therefore. the pair opacity should be carefully treated.," The received photons reflected by BLR in comoving frame is anisotropic, therefore, the pair opacity should be carefully treated."812 We lave made iportaut o»proxinatious that the BLR is thought to be a plane nürror and treated the photou-photon iuteractiou in au o»proxinate wav., We have made important approximations that the BLR is thought to be a plane mirror and treated the photon-photon interaction in an approximate way.813 Now let us show the validity of this o»proxination., Now let us show the validity of this approximation.814 We adopt the geometry shown iu Fig lc of Clüsellin Macau (1996)., We adopt the geometry shown in Fig 1c of Ghisellin Madau (1996).815 They. show that the energy density of reflected svuchrotron photon strongly depeuds ou the location of cmittine blob., They show that the energy density of reflected synchrotron photon strongly depends on the location of emitting blob.816 We should duit that the axiual sviuiuetrv holds iu the reflected svuchrotrou cluission., We should admit that the aximal symmetry holds in the reflected synchrotron emission.817" We approximate the Thonison scattering event by isotropic scattering with cross section o, aud neglect recoil which is a very good approximation when ες 1."," We approximate the Thomson scattering event by isotropic scattering with cross section $\st$ and neglect recoil, which is a very good approximation when $\eps_s \ll 1$ ."818 The angular distribution ofreflected svuchrotron cussion is given λεω.fiero)Πο](μιολες (no is aconstaut). the function fiery) determines the angular distribution of reflected svuchrotron photons (κοπή Madau 1996)," The angular distribution ofreflected synchrotron emission is given by $n_{\rm ph}(\eps_s, \mu, r_0)=n_0 f(\mu,r_0)\eps_s^{-q}$ $n_0$ is aconstant), the function $f(\mu, r_0)$ determines the angular distribution of reflected synchrotron photons (Ghisellini Madau 1996)"819This work was partially supported by CAPES (CoordenacGkzmarkmainDBodyEnd1752mainDodyStart1753a00 de Aperleigooamento cle Pessoal de Nivvel Superior).,This work was partially supported by CAPES (Coordena\c{c}\\tikzmark{mainBodyEnd1752}\~\tikzmark{mainBodyStart1753}aoo de Aperfeiçooamento de Pessoal de vel Superior).820Comparison of [Cu/Felsz» to [(Cu/Fe]sio5 indicates that the DID did not in fact affect the Cu feature and ils removal by (his simple means has not introduced any appreciable fitting error: (he spectrum fits for this line are as good as 40.05 dex.,Comparison of $_{5782}$ to $_{5105}$ indicates that the DIB did not in fact affect the Cu feature and its removal by this simple means has not introduced any appreciable fitting error; the spectrum fits for this line are as good as $\pm$ 0.05 dex.821 In every case bul (wo (stars L2208 and L4201). the abunclances from the 5782 and 5105 lines agree to 0.1 dex.," In every case but two (stars L2208 and L4201), the abundances from the 5782 and 5105 lines agree to 0.1 dex."822 Though the 5105 line was available for all MA stars. it was not possible in every case Lo determine an abundance from it.," 	Though the 5105 line was available for all M4 stars, it was not possible in every case to determine an abundance from it."823 In stars cooler than 4225 Ix. (with the exception of L2406) the spectrum was too crowded by strong Megll lines to achieve a reliable fit of the sviithesis to the observed spectrum., In stars cooler than 4225 K (with the exception of L2406) the spectrum was too crowded by strong MgH lines to achieve a reliable fit of the synthesis to the observed spectrum.824 M15 is the most metal poor cluster in Chis sample., 	M15 is the most metal poor cluster in this sample.825 The overall metallicity is so low that the 5782 feature is too weak {ο synthesize even in the cooler stars: all Chat could be derived [rom it were unenlishtening upper limits., The overall metallicity is so low that the 5782 feature is too weak to synthesize even in the cooler stars; all that could be derived from it were unenlightening upper limits.826 We have therefore synthesized only the 5105 line in M15 stars., We have therefore synthesized only the 5105 line in M15 stars.827 Given the usually g00d agreement between the two lines in other clusters. we are confident that the derived abundance [rom this line acciuratelv reflects the Cu content of a particular star.," Given the usually good agreement between the two lines in other clusters, we are confident that the derived abundance from this line accurately reflects the Cu content of a particular star."828 However. even the stronger 5105 line is still quite weak in the M15 spectra. and individual abundances are sUll uncertain.," However, even the stronger 5105 line is still quite weak in the M15 spectra, and individual abundances are still uncertain."829 We put larger errors on MI5 abundances. and our average abundance for this clusterhas a high o.," We put larger errors on M15 abundances, and our average abundance for this clusterhas a high $\sigma$."830 The most metal rich cluster in the sample. M1. posed a different sort of problem for our analvsis.," 	The most metal rich cluster in the sample, M71, posed a different sort of problem for our analysis."831 The spectrum becomes so crowded with lines Chat it is very difficult to determine the level of the continuum., The spectrum becomes so crowded with lines that it is very difficult to determine the level of the continuum.832 Onlv six stars [rom Snedenetal.(1994). vielded credible results., Only six stars from \citet{Sneden1994} yielded credible results.833 In the coolest stars. we found that |Cu/Fe]| correlated with Ἐν with the," In the coolest stars, we found that [Cu/Fe] correlated with $_{eff}$ , with the"834systems with edge-on class Il. and one not-edge-on class II object.,"systems with edge-on class II, and one not-edge-on class II object."835 Towards the class 0-I objects. L1527. IRC-L1041-2. and IRASO4302. we have detected abundant H»O. CO». and CO ice in the envelope.," Towards the class 0-I objects, L1527, IRC-L1041-2, and IRAS04302, we have detected abundant $_2$ O, $_2$, and CO ice in the envelope."836 The column density ratio of CO» to HO ice is 2]—28%.. which coincides with the ratio observed bySST towards YSOs with various inclinations.," The column density ratio of $_2$ to $_2$ O ice is $21-28$, which coincides with the ratio observed by towards YSOs with various inclinations."837 The weak absorption at ~4.1 jm can be fitted by HDO τος; the HDO/H:O ratio ranges from 2 to 22%., The weak absorption at $\sim 4.1$ $\mu$ m can be fitted by HDO ice; the $_2$ O ratio ranges from 2 to 22.838. The absorption in the vicinity of the CO band (4.76 um) is double-peaked and fitted by combining CO ice. OCN'. and CO gas.," The absorption in the vicinity of the CO band (4.76 $\mu$ m) is double-peaked and fitted by combining CO ice, $^-$, and CO gas."839 The large column density of CO ice suggests that the envelope is still very dense and cold. while OCN™ and CO gas features would originate in the region close to the protostar.," The large column density of CO ice suggests that the envelope is still very dense and cold, while $^-$ and CO gas features would originate in the region close to the protostar."840 The column density of OCN7 is as high as 2—6 relative to H3O. which is much higher than previous observations.," The column density of $^-$ is as high as $2-6$ relative to $_2$ O, which is much higher than previous observations."841 Our lines of sight (high inclinations from the rotation axis) may preferentially trace the regions with high UV irradiation. such as the surface of a forming disk and/or torus envelope.," Our lines of sight (high inclinations from the rotation axis) may preferentially trace the regions with high UV irradiation, such as the surface of a forming disk and/or torus envelope."842" The spectrum of IRASO4302 includes the 3.5 gm absorption band. but the feature does not match either CH:OH or CH,."," The spectrum of IRAS04302 includes the 3.5 $\mu$ m absorption band, but the feature does not match either $_3$ OH or $_4$."843 An OCS absorption band is tentatively detected towards IRC-L1041-2., An OCS absorption band is tentatively detected towards IRC-L1041-2.844 Towards the edge-on class II objects. ASR41 and 2MASS J1628137-243139. we have detected the Π.Ο 2005). 2007))," Towards the edge-on class II objects, ASR41 and 2MASS J1628137-243139, we have detected the $_2$ \cite{crbr05}) \cite{terada07})"845 Towards the edge-on class II objects. ASR41 and 2MASS J1628137-243139. we have detected the Π.Ο 2005). 2007)).," Towards the edge-on class II objects, ASR41 and 2MASS J1628137-243139, we have detected the $_2$ \cite{crbr05}) \cite{terada07})"846is arelation between aad Hu some galaxies.,is a relation between and in some galaxies.847 However. the yplane has been increasingly populated with less certain cestimates that have potentially been included. on the asstuption that r; is spatially resolved. ioc. that they ollow a previously estimated rrelatiou defined by higher quality cestimates.," However, the plane has been increasingly populated with less certain estimates that have potentially been included on the assumption that $r_i$ is spatially resolved, i.e., that they follow a previously estimated relation defined by higher quality estimates."848 Iu these cases; as the simulations prescuted vere show. anebserved irelation will avise simply as a result of the +; selection effect. even if lis randomly distributed within ealaxics.," In these cases, as the simulations presented here show, an relation will arise simply as a result of the $r_i$ selection effect, even if is randomly distributed within galaxies."849 Does a population of underauassive SMDIIs exist. aud have they been detected?," Does a population of under-massive SMBHs exist, and have they been detected?"850 If the irelation is au upper lait. then there should be galaxies that host low mass SMDITIs. as suggested by simulations (Vittorinietal.2005:Volouteri2007)..," If the relation is an upper limit, then there should be galaxies that host low mass SMBHs, as suggested by simulations \citep{2005MNRAS.363.1376V,2007ApJ...663L...5V}."851 Indeed. both the simulations preseuted here. and the observatious plotted in Fieure 23. show that uuderanassive SMDIIs cau be. and have been. detected.," Indeed, both the simulations presented here, and the observations plotted in Figure \ref{fig:3}, show that under-massive SMBHs can be, and have been, detected."852 Some notable cases are that of NGC 1135 (Coccatoetal.2006).. a sample of barred ealaxies (Cvaham2008a) and uarrow-line Sevtert 1 ealaxies (Mathur&Grupe2005)..," Some notable cases are that of NGC 4435 \citep{2006MNRAS.366.1050C}, a sample of barred galaxies \citep{2008ApJ...680..143G} and narrow-line Seyfert 1 galaxies \citep{2005ApJ...633..688M}."853 Tn fact. the evidence to suggest the presence of uuderauassive SMDIIS is not matched by auy evidence for a siguificaut population of over-Inassive SMDIIS leftward of theobserved 1rclation.," In fact, the evidence to suggest the presence of under-massive SMBHs is not matched by any evidence for a significant population of over-massive SMBHs leftward of the relation."854 It is iuportaut to note some intricacies with the two dominant techniques for measuring ((stellar and eas dynamics)., It is important to note some intricacies with the two dominant techniques for measuring (stellar and gas dynamics).855 Iu the case of stellar cdyvuauuies. there are systematics to the models that may allow a large range of in a eiven bulee (Valhuiotal.2001)..," In the case of stellar dynamics, there are systematics to the models that may allow a large range of in a given bulge \citep{2004ApJ...602...66V}."856 Tn the case of eas dvnandes. it is unclear what the inclination of the clear eas disk may be (e.g.Marconietal.2003)..," In the case of gas dynamics, it is unclear what the inclination of the nuclear gas disk may be \citep[e.g.,][]{2003ApJ...586..868M}."857 Both uethods allow the potential for many of the current cestimates to iu fact be upper lanits. ic. the true yplane mav have a large distribution of uuderauassive SMBUs.," Both methods allow the potential for many of the current estimates to in fact be upper limits, i.e., the true plane may have a large distribution of under-massive SMBHs."858 Therefore. underauassive SMDIIS may have j'en observed. their inass over-cstimated. and their inpact over-looked.," Therefore, under-massive SMBHs may have been observed, their mass over-estimated, and their impact over-looked."859 All SMDBII models allow stringent upper limits to be ulaced on citep|e.g..|[|2002ÀpJ...567..2:278.2009A pJ...692..856D..," All SMBH models allow stringent upper limits to be placed on \\citep[e.g.,][]{2002ApJ...567..237S,2009ApJ...692..856B}."860 Ilowever. these uupper huits will also be depenudeut on the available spatial resolution.," However, these upper limits will also be dependent on the available spatial resolution."861 Αν kineniatical data will lave two velocity points spatially separated on a scale of R., Any kinematical data will have two velocity points spatially separated on a scale of $\Re$.862 An upper linut to lis estimated by iucluding au increasing dark mass wutil the derived model becomes iucousisteut with the data.ie. a higher upper luit to Mill be estimated using a lower R.," An upper limit to is estimated by including an increasing dark mass until the derived model becomes inconsistent with the data,i.e., a higher upper limit to will be estimated using a lower $\Re$."863" There are still important coustraints that can be added to the pplane from estimates of ""upper lits. however. as upper lits that fall below theobserved rvolation provide the same evideuce for underauassive SMBs as would a tightly coustrained low massM,."," There are still important constraints that can be added to the plane from estimates of upper limits, however, as upper limits that fall below the relation provide the same evidence for under-massive SMBHs as would a tightly constrained low mass."864. At present. most uupper lanits are based on data clerived from gas dynamics.," At present, most upper limits are based on data derived from gas dynamics."865" Couscequently. these limits generally fall above theobserved ielation due to uninown amounts of Lue broadening frou, non-gravitational processes. anc uncertainties iu the inclination if the nuclear gas disk."," Consequently, these limits generally fall above the relation due to unknown amounts of line broadening from non-gravitational processes, and uncertainties in the inclination if the nuclear gas disk."866 Ifthe irelation represcuts au upper lit iu the pplaue. then what is this hnüt?," If the relation represents an upper limit in the plane, then what is this limit?"867" In 77. an upper lait of a,=&.7.5,5.0 was found based on the distribution ofobserved SMDITIS leftward of theobserved irclation."," In \ref{mands} an upper limit of $\alpha_u=8.7, \beta_u=5.0$ was found based on the distribution of SMBHs leftward of the relation."868 This is likely a good approximation to the Huit as there are uo reports of a steeper relation., This is likely a good approximation to the limit as there are no reports of a steeper relation.869 ILowever. this estinate does not include the poteutial overauassivo SMDIIS from the upper lanits calculated w Beiflorictal.(2009)..," However, this estimate does not include the potential over-massive SMBHs from the upper limits calculated by \cite{2009ApJ...692..856B}."870" Tuclucdine these limits to the upper limit sample gives values of a,=8.8.3,3.9 too3,,."," Including these limits to the upper limit sample gives values of $\alpha_u=8.8, \beta_u=3.9$ to."871". As expected. due to the addition of SAIBIT nuits at lowerM,.. this lait is more shallow with a higher zero-point."," As expected, due to the addition of SMBH limits at lower, this limit is more shallow with a higher zero-point."872 Iucludiug hese linüts at the lower eond of the ane addresses. i part. a limitation of the sample used here.," Including these limits at the lower end of the plane addresses, in part, a limitation of the sample used here."873 As already noted. the ccatalog used here is likely incomplete due το the difficulty of iieasuriug Hin faint galaxies at ereater distances.," As already noted, the catalog used here is likely incomplete due to the difficulty of measuring in faint galaxies at greater distances."874 In addition. the cceatalog likely coutains iuhoimogenuuous nmeasurenienuts that may not translate from bulee to bulec.," In addition, the catalog likely contains inhomogenuous measurements that may not translate from bulge to bulge."875 What are the consequences to galaxy evolution models if there is oulv a irclation?, What are the consequences to galaxy evolution models if there is only a relation?876 First. galaxies will no longer be required to obey the rrelation. and could host a SMDII with anv j)below0.," First, galaxies will no longer be required to obey the relation, and could host a SMBH with any below."877"),4.. Models that 1uclude feedback from he SMDII to the galaxy will then need to be carefully reconsidered.", Models that include feedback from the SMBH to the galaxy will then need to be carefully reconsidered.878 While the SAIBIT will undoubtedly have sole iufiueuce on a portion of the host ealaxy. it would iof need to affect large scale properties: evolution of the SMDBII would be a result of host galaxy evolution.," While the SMBH will undoubtedly have some influence on a portion of the host galaxy, it would not need to affect large scale properties; evolution of the SMBH would be a result of host galaxy evolution."879 Aw upper limit iu the yplane would also represeu otιο pinnacle of SMDIT evolution as a function of0... iu which galaxies evolve up to the lanit.," An upper limit in the plane would also represent the pinnacle of SMBH evolution as a function of, in which galaxies evolve up to the limit."880 A signature of such a scenario could be a cosmic variation in € (the scatter would iucrease with redshift) aud anobserved rrelation that docs uot exceed05)., A signature of such a scenario could be a cosmic variation in $\epsilon$ (the scatter would increase with redshift) and an relation that does not exceed.881 Tf the distribution of lis random within bulges. then when compared with the localobserved relation. cestimates from ligher redshift could fall to the left or the right.," If the distribution of is random within bulges, then when compared with the local relation, estimates from higher redshift could fall to the left or the right."882" Treuetal.(2007). find a population of z=0.36 Sevtert l1 ealaxics that lie above the localobserved rrelation by Aloga= Alogl/,=0.5 L butthispopulationstilllicsbelowthe( ]inüt estimated. here."," \cite{2007ApJ...667..117T} find a population of z=0.36 Seyfert 1 galaxies that lie above the local relation by $\Delta\log\sigma=0.13, \Delta\log$ $=0.54$ but this population still lies below the limit estimated here."883 Finally. if SMDIISs can reside auvwhere below the," Finally, if SMBHs can reside anywhere below the"884 pdB/By + 2x Dy dpedv| ο iP. 2py0D / Dy+ 2x Dy dpdeyo f pin Dy. where (he approximate expressions retain only linear terms in perturbed quantities.," p_0 B / B_0 + 2 B_0 d d f m )^2, 2 p_0 B / B_0 + 2 B_0 d d f m B_0, where the approximate expressions retain only linear terms in perturbed quantities."885 Linearizing the expression lor the relaxed Maxwellian in equation (3)) about. fy. the BGI collision operator is given by ) — vof c vfux (ry m ," Linearizing the expression for the relaxed Maxwellian in equation \ref{eq:BGK}) ) about $f_0$ , the drift-kinetic BGK collision operator is given by ) = f + f_0 u ) - -."886The cdiift-kinetic equation including the DGIx operator can be linearized to obtain the following equation lor 9f Of= αμ.” X. η.A −⊲mw)(ΜΗ, The drift-kinetic equation including the BGK operator can be linearized to obtain the following equation for $\delta f$ f= - )f_0 (-i B )+887sinall portion of the spectrum of JOLL757 A is not shown because it falls between the atmospheric windows where the telhivic correction was very poor.,small portion of the spectrum of J041757 A is not shown because it falls between the atmospheric windows where the telluric correction was very poor.888 The detection of JO11757 D was too weak for a useful spectrum., The detection of J041757 B was too weak for a useful spectrum.889 Using IR spectroscopy. Quauzetal.(2010). classified CATIA Tau 1 as à vouug brown dwiuf with a spectral type of L2+0.5.," Using IR spectroscopy, \citet{qua10} classified CAHA Tau 1 as a young brown dwarf with a spectral type of $\pm$ 0.5."890 If Ποτοῦ A is a ember of Taurus. Barradoetal.(20090)/ estimated that it should have a temperature of 15501750 I& based on a comparison of its photometry to the fluxes predicted by theoretical evolutionary models. which also correspouds to an L spectral type (Dahnetal.2002).," If J041757 A is a member of Taurus, \citet{bar09} estimated that it should have a temperature of 1550–1750 K based on a comparison of its photometry to the fluxes predicted by theoretical evolutionary models, which also corresponds to an L spectral type \citep{dah02}."891. To assess the accuracy of these classifications. we beein bv comparing our spectra of CATIA Tau 1 and JOll?57 A iu Fieure 1 o a spectrum of oue of the coolest known menibers of Taurus. KPNO 1(M9.5:Driceiioetal.2002).. which has been reddened to roughly match the spectral slopes of the two candidates.," To assess the accuracy of these classifications, we begin by comparing our spectra of CAHA Tau 1 and J041757 A in Figure \ref{fig:spec} to a spectrum of one of the coolest known members of Taurus, KPNO 4 \citep[M9.5;][]{bri02}, which has been reddened to roughly match the spectral slopes of the two candidates."892 The most prominent features m the spectrum of IKRPNO. Ll are the deep H2O absorption bands., The most prominent features in the spectrum of KPNO 4 are the deep $_2$ O absorption bands.893 CAILA Tau 1 and JO11757 A should show Πο bands that are as strong or stronecr as those in KPNO 1 if they are L-type members of Taurus. but this is nof the case.," CAHA Tau 1 and J041757 A should show $_2$ O bands that are as strong or stronger as those in KPNO 4 if they are L-type members of Taurus, but this is not the case."894 Instead. CATA Tau 1 exhibits weak Πο absorption that is indicative of a spectral type of M5.M6 if it is a dwarf and M3ML if it is a voungstar’.," Instead, CAHA Tau 1 exhibits weak $_2$ O absorption that is indicative of a spectral type of M5–M6 if it is a dwarf and M3–M4 if it is a young."895. The absence of detectable Ποο absorption in the spectra of JOILT5T A places constraints of (dwaif) and ΠΟ (voune) on the spectral type., The absence of detectable $_2$ O absorption in the spectrum of J041757 A places constraints of $\lesssim$ M2 (dwarf) and $\lesssim$ M0 (young) on the spectral type.896 The M2near-IR absorption features frou the plotospleres of vouug stars can be diluted by contiuuuu veiling from circtustellar dust cluission. but this is nof a possible explanation for the absence of strong IIO absorption for CAITÀA Tau I aud JOI1T57 À since they do not exhibit IR excess cission (Section 3.2.0)).," The near-IR absorption features from the photospheres of young stars can be diluted by continuum veiling from circumstellar dust emission, but this is not a possible explanation for the absence of strong $_2$ O absorption for CAHA Tau 1 and J041757 A since they do not exhibit IR excess emission (Section \ref{sec:mid}) )."897 Both candidates are iuuch too faint to be members of Taurus with spectral types of M3.ALL aud ZMAO., Both candidates are much too faint to be members of Taurus with spectral types of M3–M4 and $\lesssim$ M0.898 Thus. we classify them as background stars rather than substellar ποος of Taurus.," Thus, we classify them as background stars rather than substellar members of Taurus."899 Iu addition to spectroscopy. we have used the available photometry to examine whether the candidates from Quizetal.(2010) and Barracoetal.(2009) ave likely to be voung brown dwarfs.," In addition to spectroscopy, we have used the available photometry to examine whether the candidates from \citet{qua10} and \citet{bar09} are likely to be young brown dwarfs."900 We have retrieved photometry in the five optical bands of SDSS (ugriz:Fukueitaotal.1906) from the Sixth Data Release of the survey (Acdelmau-MeCarthyetal.2008). for CAITA Tau 15 aud ΙΟτο A (the D compoucut was not detected by SDSS)., We have retrieved photometry in the five optical bands of SDSS \citep[$ugriz$;][]{fuk96} from the Sixth Data Release of the survey \citep{ade08} for CAHA Tau 1--5 and J041757 A (the B component was not detected by SDSS).901 The calibration of these images is described by Padiuauabhnauetal.(2008)., The calibration of these images is described by \citet{pad08}.902".. We selected the data measured with an aperture radius of 1.715"". Barra", We selected the data measured with an aperture radius of $1.745\arcsec$.903doctal.(2009) ineasured / and + photometry for JOLLT57 A and D from archival ππασος from the Canacda-Frauce- Telescope (CFUT)., \citet{bar09} measured $i$ and $z$ photometry for J041757 A and B from archival images from the Canada-France-Hawaii Telescope (CFHT).904 The data for J011757 A from Darradoetal.(2009) agree withthose frou SDSS. which sugeests that the two photometric svstems are simular.," The data for J041757 A from \citet{bar09} agree with those from SDSS, which suggests that the two photometric systems are similar."905 Therefore. we have adopted the / aud : photometry frou Barradoctal.(2009) for οτον D. We have compiled photometry at J. 77. and A frou the Two-Microu All-Skyv Survey (2\TASS:Shautskie2006) for CAITA Tau 1. 2. Lo and 5. from (2010) for CATIA Tau 3. aud from Dirradoetal. for JOLL757 A and D. All of these sources also appear within archival images at 3.6. 15. 5.8. 8.0. aud 2124 that were obtained by theTelescope.," Therefore, we have adopted the $i$ and $z$ photometry from \citet{bar09}906 for J041757 B. We have compiled photometry at $J$, $H$, and $K_s$ from the Two-Micron All-Sky Survey \citep[2MASS;][]{skr06} for CAHA Tau 1, 2, 4, and 5, from \citet{qua10} for CAHA Tau 3, and from \citet{bar09} for J041757 A and B. All of these sources also appear within archival images at 3.6, 4.5, 5.8, 8.0, and 24 that were obtained by the."907" We have ieasured photometry frou, these images using the methods that were applied to the kuowu nembers of Taurus by Lulunanetal.(2010)..", We have measured photometry from these images using the methods that were applied to the known members of Taurus by \citet{luh10tau}.908 JO11757 D )econies increasingly dominant over JOLL757 À at ongcr wavelengths. as shown in Fieure 2..," J041757 B becomes increasingly dominant over J041757 A at longer wavelengths, as shown in Figure \ref{fig:sub}."909 To measure photometry at 3.6 and 1.5 for 0Ητοῦ A. we subtracted a scaled point spread ποοι (PSF) at the location of J011757 D. (Mareugoetal.2006).," To measure photometry at 3.6 and 4.5 for J041757 A, we subtracted a scaled point spread function (PSF) at the location of J041757 B \citep{mar06}."910. The A component was uot detected in the PSF-subtracted images at 5.8 and &.0sau., The A component was not detected in the PSF-subtracted images at 5.8 and 8.0.911 The spatial resolution of the image at 21 jis too low for resolving J011757 A aud D. We have assigned all of the 21 Hux to JOST D since it is much redder than ΠΕτο A at 3.68.0pau., The spatial resolution of the image at 24 is too low for resolving J041757 A and B. We have assigned all of the 24 flux to J041757 B since it is much redder than J041757 A at 3.6–8.0.912 We have adopted the average ueasuremieut ina eiven band if an object was observed at inultiple epochs bwSpifzer., We have adopted the average measurement in a given band if an object was observed at multiple epochs by.913 We did not measure photometry from the second| epoch of images at 3.6 Tor J01l757 A aud D because they were coutaminatedX cosnuie rays., We did not measure photometry from the second epoch of images at 3.6 for J041757 A and B because they were contaminatedby cosmic rays.914 Our measurements ofSpitzer plotometry or CATIA Tau 1:5 aud JOII757 A aud Bare preseuted iu Table 1.., Our measurements of photometry for CAHA Tau 1–5 and J041757 A and B are presented in Table \ref{tab:phot}.915 To determine if the candidates from Quangctal.(2010) and Darradoetal.(2009) have the appropriate optical colors aud magnitudes for low-mass members of Taurus we plot them on a diagram of / versus /i in Figure 3. with all known late-tvpe members of Taurus (>AI6) that were detected by SDSS.," To determine if the candidates from \citet{qua10} and \citet{bar09} have the appropriate optical colors and magnitudes for low-mass members of Taurus, we plot them on a diagram of $i$ versus $i-z$ in Figure \ref{fig:col}916 with all known late-type members of Taurus $>$ M6) that were detected by SDSS."917 We include im that diagram all other point sources in the SDSS nuages that have photometric uncertainties less than 0.1 mae., We include in that diagram all other point sources in the SDSS images that have photometric uncertainties less than 0.1 mag.918 All of the candidates appear below the sequence of known members. which iudicates that they are probably field stars or galaxies.," All of the candidates appear below the sequence of known members, which indicates that they are probably field stars or galaxies."919 CATIA Tau 2. Land 5 were detected in the survey by Luliuau(2001) and were identified as probable uommembers for the same reason.," CAHA Tau 2, 4, and 5 were detected in the survey by \citet{luh04tau} and were identified as probable nonmembers for the same reason."920 One additional candidate. CATIA Tau 3. was euconipassed by the images from Liulunan(2001)... but its sigual-to-noise ratio was too low for useful photometry.," One additional candidate, CAHA Tau 3, was encompassed by the images from \citet{luh04tau}, but its signal-to-noise ratio was too low for useful photometry."921 Young stars that are occulted by eireuustellar disks and seeu in scattered liebt can appear anomalously faint for their colors. but JOUTS7 D is the only caudidate that shows possible evidence of a disk im its mid-IR photometry (Section 3.2.0)).," Young stars that are occulted by circumstellar disks and seen in scattered light can appear anomalously faint for their colors, but J041757 B is the only candidate that shows possible evidence of a disk in its mid-IR photometry (Section \ref{sec:mid}) )."922 A diagrain of /A. versus JZT is useful for distinguishing between late-tvpe objects aud reddened stars at earlier types (Luliman 2000). , A diagram of $i-K_s$ versus $J-H$ is useful for distinguishing between late-type objects and reddened stars at earlier types \citep{luh00tau}. .923We show a diagram of this Kind in Fieure 3 for the candidates from: Quangctal.(2010) and Biuradoetal. (2009). the known late-type members of Taurus.aud all other sources with errors less than 0.1 mae in the SDSS aud 2MASS images of Taurus.," We show a diagram of this kind in Figure \ref{fig:col} for the candidates from \citet{qua10} and \citet{bar09}, , the known late-type members of Taurus,and all other sources with errors less than 0.1 mag in the SDSS and 2MASS images of Taurus."924 (ΑΠΔ Tau 2 is the only candidate that has the appropriate colors for a voung object later than M6., CAHA Tau 2 is the only candidate that has the appropriate colors for a young object later than M6.925 Given its position iu / versus / :," Given its position in $i$ versus $i-z$ ,"926 Given its position iu / versus / :.," Given its position in $i$ versus $i-z$ ,"927recent study of the ovewall (infra-red to X-ray) spectrum of hhas been published byv Janiuk ((2001). considering in particular the strong emission in the UV and soft X-ray bands and proposing its origin in à warm optically thick ‘skin’ on the aceretion disc.,"recent study of the overall (infra-red to X-ray) spectrum of has been published by Janiuk (2001), considering in particular the strong emission in the UV and soft X-ray bands and proposing its origin in a warm optically thick `skin' on the accretion disc."928 This work also included an analysis of an extended: oobservation in LOOT. suggesting a cold rellection factor Ro = Ofer. where ο is the solid. angle subtended by the reflecting matter. of order unity.," This work also included an analysis of an extended observation in 1997, suggesting a cold reflection factor R = $\Omega$ $\pi$ , where $\Omega$ is the solid angle subtended by the reflecting matter, of order unity."929 wavas observed by oon 2001 June 15 vieling a useful exposure of 60 ksec., was observed by on 2001 June 15 yielding a useful exposure of $\sim$ 60 ksec.930 In this paper we use data from the EPIC pn camera (Strüdder al.2001). which has he best sensitivity of any instrument llown to date in the 10 keV spectral band. the combined EPIC MOS cameras (Lurner 22001). and the Reflection Crating SpectrometersROS (den Herder 22001).," In this paper we use data from the EPIC pn camera (Strüdder 2001), which has the best sensitivity of any instrument flown to date in the $\sim$ 6-10 keV spectral band, the combined EPIC MOS cameras (Turner 2001), and the Reflection Grating Spectrometer/RGS (den Herder 2001)."931 Reference to the Optical Monitor (Mason 22001) confirmed the strong optical ancl UV. emission was close to the tvpical level in143., Reference to the Optical Monitor (Mason 2001) confirmed the strong optical and UV emission was close to the typical level in.932.. AM X-ray data were first. screened. with the NAIA SAS v5.3 software and events corresponding to patterns 0-4. (single ancl double pixel events) were selected for the pn data and patterns 0-12 for MOSI and ALOS2. the latter then being combined.," All X-ray data were first screened with the XMM SAS v5.3 software and events corresponding to patterns 0-4 (single and double pixel events) were selected for the pn data and patterns 0-12 for MOS1 and MOS2, the latter then being combined."933 A low οσον cut of 200 eV. was applied to all X-ray data and known hot or bad. pixels were removed., A low energy cut of 200 eV was applied to all X-ray data and known hot or bad pixels were removed.934 We extracted source counts within a circular region of rpadius defined around the centroid position οἱ143.. with the background. being taken from a similar region. olfse from but close to the source.," We extracted source counts within a circular region of radius defined around the centroid position of, with the background being taken from a similar region, offset from but close to the source."935 The 2-10 keV. X-ray pn light curve is reproduced as figure 1 and shows ~80 percent Lux changes over 6 ksec. similar o those seen in the delata.," The 0.2-10 keV X-ray pn light curve is reproduced as figure 1 and shows $\sim$ 30 percent flux changes over $\sim$ 6 ksec, similar to those seen in the data."936 Individual spectra were binned to a minimum of 20 counts per bin. to facilitate use of the X7 minimalisation echnique in spectral fitting.," Individual spectra were binned to a minimum of 20 counts per bin, to facilitate use of the $\chi^2$ minimalisation technique in spectral fitting."937 Itesponse functions for spectral itting to the RGS data were generated from the SAS v5.3., Response functions for spectral fitting to the RGS data were generated from the SAS v5.3.938 Spectral fitting was based on the XAspec package (Arnaud 1996) and used a grid of ionised absorber mocels calculated with the NSTAR code (Ixallman 11996)., Spectral fitting was based on the Xspec package (Arnaud 1996) and used a grid of ionised absorber models calculated with the XSTAR code (Kallman 1996).939 All spectral fits include absorption due to the line-D. . ∪⇂−⊳∖↓⋏∙≟↓∐≺∣⋜↧↓⋯⇍⇂⊔∼≼∼∪↓⊔⊔↓⊔∪⇂⇀∖⊓∶−≽⋅↖∖⋅↱≻↓∪↾≼∼⊔↓⊳∟↓⋅↓⋅∪↓⋅⊳∖, All spectral fits include absorption due to the line-of-sight Galactic column of $N_{H}=2.85\times10^{20}\rm{cm}^{-2}$.940⋅⇁⋅σι2 ∙⊲ ⋜⊔⋅⋖⋅⊏↥⊔∪↿⋖⋅∠⇂⋜∐↿⇂↥∢⋅≤⋗∪⊲∕⋰∣↙≼⇍∪⊔∐∠⇂∢⋅⊔≼⇍∢⊾↓⋖⊾∖⇁∢⊾↓↿∖∆∖⇉∶⇉⋅−⇂∎∪↓⋅∪⊔⋖⋅ interesting parameter)., Errors are quoted at the confidence level $\Delta \chi^{2}=2.7$ for one interesting parameter).941 X-ray spectra of AGN at 210 keV are well fitted. to first order. with a power law of photon index E in the range ~1.6-2 for most radio quiet AGN. with a fraction (eg NLS1) jwing somewhat steeper indices.," X-ray spectra of AGN at 2–10 keV are well fitted, to first order, with a power law of photon index $\Gamma$ in the range $\sim$ 1.6-2 for most radio quiet AGN, with a fraction (eg NLS1) having somewhat steeper indices."942" The widelv held: view is hat this ‘hare’ X-ray continuum in Sevlert galaxies arises w Comptonisation of thermal emission from the accretion disc in a ‘hot’ corona (eg Haardt and. Alaraschi 1991). and »oduces. additional spectral features. by ""reflection [rom dense matter in the disc (eg Pounds 11990. Fabian 22000)."," The widely held view is that this `hard' X-ray continuum in Seyfert galaxies arises by Comptonisation of thermal emission from the accretion disc in a `hot' corona (eg Haardt and Maraschi 1991), and produces additional spectral features by `reflection' from dense matter in the disc (eg Pounds 1990, Fabian 2000)."943 We began our analysis of bby confirming there were no obvious spectral changes with source [ux and then proceeded to fit the ppn and MOS data integrated. over the full 00 Ksec observation., We began our analysis of by confirming there were no obvious spectral changes with source flux and then proceeded to fit the pn and MOS data integrated over the full $\sim$ 60 ksec observation.944 A simple power law fit over the L10 keV band yielded a photon index of P—1.79 (pn) and E—1.71 (MOS). with a broad. excess in the dataumodel ratio between 37 keV. and evidence of absorption at higher energies in both data sets (figure 2).," A simple power law fit over the 1–10 keV band yielded a photon index of $\Gamma$$\sim$ 1.79 (pn) and $\Gamma$$\sim$ 1.71 (MOS), with a broad excess in the data:model ratio between 3–7 keV, and evidence of absorption at higher energies in both data sets (figure 2)."945 The fit was statistically unacceptable with an overall x2 /dof of 1541/1176., The fit was statistically unacceptable with an overall $\chi^{2}$ /dof of 1541/1176.946" When extrapolated to 0.3 keV. the 1.10 keV fits to both pn and MOS data revealed a strong ""soft excess’ (figure 3)."," When extrapolated to 0.3 keV, the 1–10 keV fits to both pn and MOS data revealed a strong `soft excess' (figure 3)."947 To improve the 110 keV fit we added further. spectra components to match the most obvious features in the data., To improve the 1–10 keV fit we added further spectral components to match the most obvious features in the data.948 The indication of an extreme broad emission line suggestec rellection from the inner accretion disc. conventionally modelled with a λος line in Nspec (Laor. 1991).," The indication of an extreme broad emission line suggested reflection from the inner accretion disc, conventionally modelled with a LAOR line in Xspec (Laor 1991)."949" The addition of a LAO. linc. with inclination initially Lixec at 30° and 42,,,7100/2, ( where Re=CMfC is the eravitational radius for mass AZ). resulted in a significan statistical improvement (C dotof 1304/1172). but with an unrealistically large. EW of ~l4 keV (pn) and ον]. keV (MOS)."," The addition of a LAOR line, with inclination initially fixed at $\deg$ and $R_{out}$ $R_{g}$ ( where $R_{\rm g} = GM/c^2$ is the gravitational radius for mass $M$ ), resulted in a significant statistical improvement $\chi^{2}$ /dof of 1304/1172), but with an unrealistically large EW of $\sim$ 1.4 keV (pn) and $\sim$ 1.1 keV (MOS)."950 To better fit the broad. line profile we added. a eaussian line with energv tied to that ofthe LAOR. line. (, To better fit the broad line profile we added a gaussian line with energy tied to that ofthe LAOR line. (951 Physically such a gaussian line could. represent emission from larger radii on the disc)., Physically such a gaussian line could represent emission from larger radii on the disc).952 This addition gave a further, This addition gave a further953"where a((T,,v) is the Gaunt factor assumed to be 1, a correct value for the range of astrophysical quantities involved in our calculations; v and r, are the frequency measured in MHz and the free-free optical depth, respectively, and T, is the electron temperature in K of the intervening ionized gas.","where $T_{e}$ $\nu$ ) is the Gaunt factor assumed to be 1, a correct value for the range of astrophysical quantities involved in our calculations; $\nu$ and $\tau_{\nu}$ are the frequency measured in MHz and the free-free optical depth, respectively, and $\mathrm{T_{e}}$ is the electron temperature in K of the intervening ionized gas."954" By measuring the relative strengths of the [FelI] lines observed in the near and mid infrared emission, ? conclude that the emitting region behind the J-type shocks as observed in the J and H bands of the 2MASS has a temperature of 12000 K. Although not quantified, the authors recognize a large uncertainty associated with this magnitude as a consequence of different beam size and possibly different filling factors in their measurements."," By measuring the relative strengths of the [FeII] lines observed in the near and mid infrared emission, \citet{rho01}955 conclude that the emitting region behind the J-type shocks as observed in the J and H bands of the 2MASS has a temperature of 12000 K. Although not quantified, the authors recognize a large uncertainty associated with this magnitude as a consequence of different beam size and possibly different filling factors in their measurements."956 If we assume that Τε is in a reasonable range between 8000-12000 K (which includes the temperature as estimated from the IR observations) and use the optical depth derived from our radio study particularly for this region where the thermal absorption is stronger (r74— 0.3) we obtain an EM between approximately 2.8x10? and 5.0x10? cm~® pc for the eastern rim., If we assume that $\mathrm{T_{e}}$ is in a reasonable range between 8000-12000 K (which includes the temperature as estimated from the IR observations) and use the optical depth derived from our radio study particularly for this region where the thermal absorption is stronger $\tau_{74}\sim0.3$ ) we obtain an EM between approximately $2.8\times10^{3}$ and $5.0\times10^{3}$ $^{-6}$ pc for the eastern rim.957" By combining this emission measure with the postshock electron density, we can roughly calculate the thickness of the molecular gas layer that has been dissociated and ionized by the SNR shock front."," By combining this emission measure with the postshock electron density, we can roughly calculate the thickness of the molecular gas layer that has been dissociated and ionized by the SNR shock front."958" If we assume an electron density of n,~500 cm? as estimated by ? and ? on the basis of forbidden [FelI] lines, we conclude that the dissociation and ionization processes took place ina thin screen of about 3.4 to 6.0 x10!6 cm (—0.01-0.02 pc)."," If we assume an electron density of $n_{e}\sim\,500$ $^{-3}$ as estimated by \citet{fes80} and \citet{rea00} on the basis of forbidden [FeII] lines, we conclude that the dissociation and ionization processes took place in a thin screen of about 3.4 to 6.0 $\times10^{16}$ cm $\sim$ 0.01-0.02 pc)."959" This is a small path compared with the transverse dimensions over which thermal absorption is observed, but is a lower limit if the ionized gas is clumped."," This is a small path compared with the transverse dimensions over which thermal absorption is observed, but is a lower limit if the ionized gas is clumped."960"potential, where no component of angular momentum is conserved and we see an interesting box orbit as a consequence.","potential, where no component of angular momentum is conserved and we see an interesting box orbit as a consequence."961" Frequent, oblique passages through the disk would presumably increase the potential for encounters with massive structures such as stellar clusters or giant molecular clouds and may be partly or wholly responsible for the high velocity dispersion observed in the Hydra I and the EBS stream."," Frequent, oblique passages through the disk would presumably increase the potential for encounters with massive structures such as stellar clusters or giant molecular clouds and may be partly or wholly responsible for the high velocity dispersion observed in the Hydra I and the EBS stream."962" The EBS stream adds to the growing list of halo streams that can be mapped over a sufficient extent that, with suitable follow-up observations, they could be used as probes of the Galactic potential."," The EBS stream adds to the growing list of halo streams that can be mapped over a sufficient extent that, with suitable follow-up observations, they could be used as probes of the Galactic potential."963 A preliminary orbit estimate shows that the EBS is unrelated to either the Anticenter or Monoceros streams., A preliminary orbit estimate shows that the EBS is unrelated to either the Anticenter or Monoceros streams.964 The somewhat intermediate breadth of the stream together with its relatively high velocity dispersion suggests the possibility that the progenitor could have been more massive than the globular clusters thought to be responsible for the half dozen very cold streams discovered in the SDSS footprint to date., The somewhat intermediate breadth of the stream together with its relatively high velocity dispersion suggests the possibility that the progenitor could have been more massive than the globular clusters thought to be responsible for the half dozen very cold streams discovered in the SDSS footprint to date.965" However, if the progenitor had been a dark matter dominated dwarf galaxy, it would be difficult to understand how it could have held onto it’s dark matter envelope for any length of time in such a confined and eccentric orbit."," However, if the progenitor had been a dark matter dominated dwarf galaxy, it would be difficult to understand how it could have held onto it's dark matter envelope for any length of time in such a confined and eccentric orbit."966" On the other hand, this very orbit may have subjected both the progenitor and the stream to significant heating through encounters with massive structures in the disk."," On the other hand, this very orbit may have subjected both the progenitor and the stream to significant heating through encounters with massive structures in the disk."967" If Hydra I is indeed the progenitor of the EBS, then it is only the second probably unbound progenitor to be associated with a tidal stream."," If Hydra I is indeed the progenitor of the EBS, then it is only the second probably unbound progenitor to be associated with a tidal stream."968 A more detailed examination of the structure and stellar kinematics in this remnant may shed new light on the end stage of tidal disruption., A more detailed examination of the structure and stellar kinematics in this remnant may shed new light on the end stage of tidal disruption.969" Though contamination by field stars is high, Hydra I may be particularly attractive in this respect as it is four times closer to us than Bootes III(Grillmair2009)."," Though contamination by field stars is high, Hydra I may be particularly attractive in this respect as it is four times closer to us than Bootes III\citep{grill2009}."970. Refinement of the orbit will require radial velocity and proper motion measurements of carefully selected stars along the length of the stream., Refinement of the orbit will require radial velocity and proper motion measurements of carefully selected stars along the length of the stream.971" Given the very low surface density of stream stars and very high field star contamination, this will necessarily be an ongoing task."," Given the very low surface density of stream stars and very high field star contamination, this will necessarily be an ongoing task."972" In this respect, the EBS may be particularly well situated for follow-up by the upcoming spectroscopic LAMOST survey."," In this respect, the EBS may be particularly well situated for follow-up by the upcoming spectroscopic LAMOST survey."973 Gaia and LSST proper motion measurements may also help us to refine the orbit and perhaps trace the stream over a much longer arc., Gaia and LSST proper motion measurements may also help us to refine the orbit and perhaps trace the stream over a much longer arc.974 The author is grateful to an anonymous referee for constructive and insightful comments., The author is grateful to an anonymous referee for constructive and insightful comments.975 Thanks also go to Kevin Schlaufman for providing the positions of ECHOS member stars., Thanks also go to Kevin Schlaufman for providing the positions of ECHOS member stars.976" Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. Sloan.."," Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. ."977 4.9. the value found by Helsdon Ponman: however. the intercepts for the two samples differ at greater than the 20 level.,"$\sim$ 4.9, the value found by Helsdon Ponman; however, the intercepts for the two samples differ at greater than the $\sigma$ level."978 In addition we used a 1-D KS test to compare the temperature and luminosity distributions of sample | and sample 2., In addition we used a 1-D KS test to compare the temperature and luminosity distributions of sample 1 and sample 2.979 We find iat the luminosity distributions of the samples are consistent with their being drawn from a single parent population. whereas 1e temperature distributions are different at the ~ 90 per cent Contidence level.," We find that the luminosity distributions of the samples are consistent with their being drawn from a single parent population, whereas the temperature distributions are different at the $\sim$ 90 per cent confidence level."980 Therefore. we find a small. but significant difference in ve |uminosity-temperature relation for groups containing radio galaxies. with higher temperatures found at a given luminosity.," Therefore, we find a small, but significant difference in the luminosity-temperature relation for groups containing radio galaxies, with higher temperatures found at a given luminosity."981 There are two possible interpretations for this result: either the radio galaxies are heating their environments. or they are reducing the luminosity of the groups.," There are two possible interpretations for this result: either the radio galaxies are heating their environments, or they are reducing the luminosity of the groups."982 To test whether the second scenario could be true. we assumed that all of the material through which the radio source passes while expanding has been affected by the radio source and no longer emits in X-rays (e.g. it may have been lifted out to a distance where the subsequent decrease in density produces this effect).," To test whether the second scenario could be true, we assumed that all of the material through which the radio source passes while expanding has been affected by the radio source and no longer emits in X-rays (e.g. it may have been lifted out to a distance where the subsequent decrease in density produces this effect)."983 Modelling the expanding radio source as a cone. and comparing the square of number density integrated over the volume through which the radio source will have passed with the same integral for the entire group. we find that only 7 per cent of the luminosity of 3C 66B could have been removed in this way.," Modelling the expanding radio source as a cone, and comparing the square of number density integrated over the volume through which the radio source will have passed with the same integral for the entire group, we find that only 7 per cent of the luminosity of 3C 66B could have been removed in this way."984 Using the original group luminosity. a temperature of 0.92+0.21 keV s predicted from our best-fitting relation for radio-quiet groups.," Using the original group luminosity, a temperature of $\pm0.21$ keV is predicted from our best-fitting relation for radio-quiet groups."985 The effect will be at a similar level in other sources., The effect will be at a similar level in other sources.986 Therefore we conclude that the radio galaxy could not have produced such a decrease in luminosity., Therefore we conclude that the radio galaxy could not have produced such a decrease in luminosity.987 For this reason. we interpret these results as providing indirect evidence for radio-source heating of group environments.," For this reason, we interpret these results as providing indirect evidence for radio-source heating of group environments."988 This result shows that groups which contain detected radio sources are systematically hotter than those which do not. providing the first evidence that radio-source heating is occurring at a detectable level in the majority of such groups.," This result shows that groups which contain detected radio sources are systematically hotter than those which do not, providing the first evidence that radio-source heating is occurring at a detectable level in the majority of such groups."989 It is apparent from Fig., It is apparent from Fig.990 12. that 3C 66B is much hotter than predicted by either of the two relations slotted., \ref{lt} that 3C 66B is much hotter than predicted by either of the two relations plotted.991 There are three contributing factors which could explain 3C 66B's exceptional behaviour., There are three contributing factors which could explain 3C 66B's exceptional behaviour.992 Firstly. it is more powerful than any of the sources in the radio-loud sample. and so would be expected ο transfer more energy to the group gas.," Firstly, it is more powerful than any of the sources in the radio-loud sample, and so would be expected to transfer more energy to the group gas."993 As described above. it is also likely to be comparatively old for an FR-I radio galaxy. so will dave been putting energy into its environment for a longer period of time.," As described above, it is also likely to be comparatively old for an FR-I radio galaxy, so will have been putting energy into its environment for a longer period of time."994 Finally. the environment of this source is less massive han the environments of other large. powerful sources. such as 3C 3|.," Finally, the environment of this source is less massive than the environments of other large, powerful sources, such as 3C 31."995 It seems plausible that these three factors have combined to make 3C 66B particularly efficient at raising the temperature of its environment., It seems plausible that these three factors have combined to make 3C 66B particularly efficient at raising the temperature of its environment.996 Our images of 3C 66B and 3C 449 provide direct evidence that their environments are having a major effect on the evolution of the radio sources., Our images of 3C 66B and 3C 449 provide direct evidence that their environments are having a major effect on the evolution of the radio sources.997 In both cases large rounded lobes are associated with large amounts of X-ray-emitting gas. whereas narrower lobes are seen where there is no surrounding material.," In both cases large rounded lobes are associated with large amounts of X-ray-emitting gas, whereas narrower lobes are seen where there is no surrounding material."998 In the case of 3C 66B the presence of a blob of gas at the end of the eastern jet and bounded lobe is suggestive of an obstacle having a strong impact on the lobe morphology., In the case of 3C 66B the presence of a blob of gas at the end of the eastern jet and bounded lobe is suggestive of an obstacle having a strong impact on the lobe morphology.999 We have revisited the luminosity-temperature relation for, We have revisited the luminosity-temperature relation for1000in frequency shifts at selected. values of ας duringA4N2J andΑΛ.,in frequency shifts at selected values of $|m|/\ell$ during and.1001 We again notice that the lrequencies at all latitudes during24 are lower than (hose during2., We again notice that the frequencies at all latitudes during are lower than those during.1002 Further. in view of the above discussion. il is not surprising to obtai a single epoch of mininmnm atALV2J for all three values of |m{6," Further, in view of the above discussion, it is not surprising to obtain a single epoch of minimum at for all three values of $|m|/\ell$."1003 On the contrary. the frequency. shilts hint towards a double minima at ALIN for η = 0.5. and a single minimum [for |m|/( = 0.7 and 0.9.," On the contrary, the frequency shifts hint towards a double minima at for $|m|/\ell$ = 0.5, and a single minimum for $|m|/\ell$ = 0.7 and 0.9."1004 Although most of well-known surface activity indices do not indicate the minimum in late 2007. as the downward trend in their values continued until (he end of 2008. there are observations where early signs of the beginning of the new cycle were possibly seen.," Although most of well-known surface activity indices do not indicate the minimum in late 2007, as the downward trend in their values continued until the end of 2008, there are observations where early signs of the beginning of the new cycle were possibly seen."1005 The appearance of a sunspot in Active Region 10981 [or three consecutive davs during 2008 Jan 4. Gal high latitude (80° N) with new evcle polarities hinted towards the rise of evele 24 in early 2008 (Phillips2008a).., The appearance of a sunspot in Active Region 10981 for three consecutive days during 2008 Jan 4 – 6 at high latitude $^{\mathrm{o}}$ N) with new cycle polarities hinted towards the rise of cycle 24 in early 2008 \citep{newcycle}.1006 ILowever. more sunspots fulfilling the criteria of evele 24 were not visible for several months alter 2008 January.," However, more sunspots fulfilling the criteria of cycle 24 were not visible for several months after 2008 January."1007 The emergence of three big sunspots al low latitudes will previous evcle polarities a few months later (magnetic polarity in accordance with evele 23) suggested that the minimum after cycle 23 had not vel been reached (Phillips2003b).., The emergence of three big sunspots at low latitudes with previous cycle polarities a few months later (magnetic polarity in accordance with cycle 23) suggested that the minimum after cycle 23 had not yet been reached \citep{oldcycle}.1008 These observations are not. unusual as sunspots from both eveles are ταον seen during the minimum before approaching the bottom level of the activity., These observations are not unusual as sunspots from both cycles are randomly seen during the minimum before approaching the bottom level of the activity.1009 The (wo strong dips seen in oscillation Irequencies al certain latitudes can be understood in terms of localized changes in the activitv level., The two strong dips seen in oscillation frequencies at certain latitudes can be understood in terms of localized changes in the activity level.1010 The mean variation in sunspot number and radio [ux during the two minima discussed here is shown in Figure 5., The mean variation in sunspot number and radio flux during the two minima discussed here is shown in Figure 5.1011 A close examination of the right panels of Figure 5 reveals that there was indeed a slight rise in activity al (he beginning of 2008 but the trend did not continue., A close examination of the right panels of Figure 5 reveals that there was indeed a slight rise in activity at the beginning of 2008 but the trend did not continue.1012 The two dips seen in oscillation frequencies mav be interpreted as the manilestation of the competition between the magnetic fields from both the solar eveles., The two dips seen in oscillation frequencies may be interpreted as the manifestation of the competition between the magnetic fields from both the solar cycles.1013 We also note periodic variations in ὃν thatare addressed in Section 4., We also note periodic variations in $\delta\nu$ thatare addressed in Section 4.1014"This ensures that The observed multiplicity frequency fap,=Notuttipte/M is. after this selection. 35+6% (Poisson errors). wheretotal Notutiple 18 the number of binary or multiple systems (38) and N44; 18 the number of observed systems (108).","This ensures that The observed multiplicity frequency $f_\mathrm{obs}=N_\mathrm{Multiple}/N_\mathrm{Total}$ is, after this selection, $35\pm6\%$ (Poisson errors), where $N_\mathrm{Multiple}$ is the number of binary or multiple systems (38) and $N_\mathrm{Total}$ is the number of observed systems (108)."1015 Figure 5 shows the observed multiplicity fraction for each primary spectral type., Figure 5 shows the observed multiplicity fraction for each primary spectral type.1016 The multiple systems included in the following analysis can be found in Table 2. and the number of single:binary:triple:quadruple systems in Table 4.," The multiple systems included in the following analysis can be found in Table 2, and the number of single:binary:triple:quadruple systems in Table 4."1017 To compute the actual multiplicity frequency. we need to consider two effects: (1) at small separations. we detect more equal brightness binaries than systems with large component brightness differences. and (11) a brightness-limited sample is biased in favour of (previously unresolved) binaries or multiple systems compared to single stars.," To compute the actual multiplicity frequency, we need to consider two effects: (i) at small separations, we detect more equal brightness binaries than systems with large component brightness differences, and (ii) a brightness-limited sample is biased in favour of (previously unresolved) binaries or multiple systems compared to single stars."1018 Assuming that the flux ratio distribution is independent of the separation in the observed range (which can be transformed into a flat mass ratio distribution). we estimate the number of multiple systems of close separations that we miss using the following method.," Assuming that the flux ratio distribution is independent of the separation in the observed range (which can be transformed into a flat mass ratio distribution), we estimate the number of multiple systems of close separations that we miss using the following method."1019 We divide the number of binaries in Fig., We divide the number of binaries in Fig.1020 3 of observed Az' as a function of angular separation p into four different regions of interest., 3 of observed $\Delta z^\prime$ as a function of angular separation $\rho$ into four different regions of interest.1021" Assuming that our sample is complete to Ar’<5.5 between angular separation and complete to Az’€2.5 for closer separations. the ratioof companions in the region p=0.5”-33"". ADS225-535 and p=0.5""—PLZ 37, Az=0-2.5 is the same as the ratio of companions in p.=0.1—0.57, Az=2.5—5.5 and p50.1720.57, Az=0—2.5."," Assuming that our sample is complete to $\Delta z^\prime\la5.5$ between angular separation and complete to $\Delta z^\prime\la2.5$ for closer separations, the ratioof companions in the region $\rho=0.5\arcsec-3\arcsec$, $\Delta z^\prime=2.5-5.5$ and $\rho=0.5\arcsec-3\arcsec$ , $\Delta z^\prime=0-2.5$ is the same as the ratio of companions in $\rho=0.1\arcsec-0.5\arcsec$, $\Delta z^\prime=2.5-5.5$ and $\rho=0.1\arcsec-0.5\arcsec$, $\Delta z^\prime=0-2.5$."1022 This would result in the survey missing two binary companions in the close separation - high flux ratio region. hence the total multiple fraction should be increased to 37+6%.," This would result in the survey missing two binary companions in the close separation - high flux ratio region, hence the total multiple fraction should be increased to $37\pm6\%$."1023 We compute the multiplicity fraction for a volume-limited sample. f. following the method and Eq. (," We compute the multiplicity fraction for a volume-limited sample, $f^\prime$ , following the method and Eq. ("1024+) of ? whereobs δε.=0.37obs is the fraction of observed binaries after sensitivity correction.,"4) of \citet{Burgasser2003}1025 where $f^\prime_\mathrm{obs}=0.37$ is the fraction of observed binaries after sensitivity correction."1026 ? consider a values in the range 2.8.) corresponding to only equal brightness systems. to 1.9. which corresponds to a flat flux ratio distribution.," \citet{Burgasser2003} consider $\alpha$ values in the range 2.8, corresponding to only equal brightness systems, to 1.9, which corresponds to a flat flux ratio distribution."1027 The distribution of z-band brightness ratios (see Table 2) in our sample is more peaked towards unequal systems (on a linear brightness ratio scale). resulting ina=1.73.," The distribution of $z^\prime$ -band brightness ratios (see Table 2) in our sample is more peaked towards unequal systems (on a linear brightness ratio scale), resulting in $\alpha = 1.73$."1028 According to Eq. (, According to Eq. (10294) of ?.. this then yields a multiplicity fraction for a volume-limited sample of f!=2546%.,"4) of \citet{Burgasser2003}, this then yields a multiplicity fraction for a volume-limited sample of $f^\prime=25\pm6\%$."1030" However. the ? sample is based on a correlation of M dwarf candidates selected from the 400 million sources in the 2MASS point source catalogue (PSC.angularresolution2"",?) with the 1500000 sources in the ROSAT AII Sky Survey (RASS.angularresolution~30.?).. thus the brightness limit is imposed by the X-ray luminosity of the sources."," However, the \citet{Riaz2006} sample is based on a correlation of M dwarf candidates selected from the 400 million sources in the 2MASS point source catalogue \citep[PSC, angular resolution $\sim2\arcsec$,][]{Cutri2003} with the 000 sources in the ROSAT All Sky Survey \citep[RASS, angular resolution $\sim30\arcsec$, ][]{Voges1999}, thus the brightness limit is imposed by the X-ray luminosity of the sources."1031 Hence. we need to correct for the excess of multiple systems as two or more stellar components emit more X-rays than the corresponding primary component would do if it were single.," Hence, we need to correct for the excess of multiple systems as two or more stellar components emit more X-rays than the corresponding primary component would do if it were single."1032 We can do this straightforwardly by simply examining all our a posteriori known multiple systems and determining which ones would not have beer included in the sample if the primary had been single., We can do this straightforwardly by simply examining all our a posteriori known multiple systems and determining which ones would not have been included in the sample if the primary had been single.1033" X-ray counts and errors are available from ROSAT (?). for each of the 44 multiple systems (except for one system. J20500010-1154092., which is counted as a non-detection here)."," X-ray counts and errors are available from ROSAT \citep{Voges1999} for each of the 44 multiple systems (except for one system, J20500010-1154092, which is counted as a non-detection here)."1034 Given that the components in any given system should be coeval. it is assumed that the X-ray brightness depends only on the stellar luminosity.," Given that the components in any given system should be coeval, it is assumed that the X-ray brightness depends only on the stellar luminosity."1035 According to ον. Lx/Lpo is roughly constant as function of spectral type. hence to a reasonable approximation the X-ray count rate can be assumed to be directly proportional to the brightness fraction in. z-band in linear units.," According to \citet{Riaz2006}, $L_{\rm X} / L_{\rm bol}$ is roughly constant as function of spectral type, hence to a reasonable approximation the X-ray count rate can be assumed to be directly proportional to the brightness fraction in $z^\prime$ -band in linear units."1036 Thus. we use the known Az’ for each system in combination with the unresolved X-ray count rate to estimate the rate for the primary component alone.," Thus, we use the known $\Delta z^\prime$ for each system in combination with the unresolved X-ray count rate to estimate the rate for the primary component alone."1037 If the new value results in S/N«3.3. the multiple system in question is counted as having been positively selected for and is excluded for the purpose of calculating the multiple fractio for a volume-limited sample. where S/N=3.3 Is the relevant criterion for detection according to the tables of ?..," If the new value results in $S/N < 3.3$, the multiple system in question is counted as having been positively selected for and is excluded for the purpose of calculating the multiple fraction for a volume-limited sample, where $S/N = 3.3$ is the relevant criterion for detection according to the tables of \citet{Voges1999}."1038 In total. 7 systems are identified as contaminants in this way.," In total, 7 systems are identified as contaminants in this way."1039 Hence. applying corrections for the X-ray flux limit as described above. it follows that the multiplicity fraction f is given by f=(38—7)/(1087)1.05332+6%.," Hence, applying corrections for the X-ray flux limit as described above, it follows that the multiplicity fraction $f$ is given by $f = (38-7) / (108-7)*1.053 = 32\pm6$."1040. While both multiplicity fractions f and f’ agree within the uncertainties. in the following we assume a multiplicity fraction f=32+6%. as the brightness limit is primarily imposed by the X-ray luminosity.," While both multiplicity fractions $f$ and $f^\prime$ agree within the uncertainties, in the following we assume a multiplicity fraction $f=32\pm6\%$, as the brightness limit is primarily imposed by the X-ray luminosity."1041 We note that some overabundance of short-period binaries (P<20 days) might be present in the X-ray selected sample. but this cannot be quantified until future radial velocity observations have been performed.," We note that some overabundance of short-period binaries $<$ 20 days) might be present in the X-ray selected sample, but this cannot be quantified until future radial velocity observations have been performed."1042" We also note that this fraction might still include a small contamination by non-physical (""optical"") binaries. as second-epoch observations for some of the systems are still pending. although we reiterate that the fraction of binaries that are merely optical must be very small (see Fig."," We also note that this fraction might still include a small contamination by non-physical (“optical”) binaries, as second-epoch observations for some of the systems are still pending, although we reiterate that the fraction of binaries that are merely optical must be very small (see Fig."1043 4)., 4).1044 The individual component photometric spectral types from Sect., The individual component photometric spectral types from Sect.1045 3.1 are transformed to approximate masses using the mass estimates of ? for young (~500 MMyr) stars., 3.1 are transformed to approximate masses using the mass estimates of \citet{KrausHillenbrand2007} for young $\sim500$ Myr) stars.1046 We interpolate linearly to obtain masses for subclasses of 0.5 and calculate the mass-ratios. g= ΜΜ.," We interpolate linearly to obtain masses for subclasses of 0.5 and calculate the mass-ratios, $q=M_2/M_1$ ."1047 The binarieswhere the secondary star is suspected to be an L dwarf are not included in the mass-ratio distribution because of the high uncertainties in mass., The binarieswhere the secondary star is suspected to be an L dwarf are not included in the mass-ratio distribution because of the high uncertainties in mass.1048We also exclude components at separations greater than 6” from the,We also exclude components at separations greater than $6\arcsec$ from the1049equilibrium: required. for the N-ray mass. modelling will therefore not apply.,equilibrium required for the X-ray mass modelling will therefore not apply.1050 The A-ray images for the other clusters included in the present sample do not exhibit any dramatic substructure that would clearly invalidate such assumptions., The X-ray images for the other clusters included in the present sample do not exhibit any dramatic substructure that would clearly invalidate such assumptions.1051 We note. however. the presence of an A-ray luminous subcluster. approximately 2.6 aremin (850 kpe) to the northwest of Abell 2744 (ACIS). visible in the LIRL data.," We note, however, the presence of an X-ray luminous subcluster, approximately 2.6 arcmin (850 kpc) to the northwest of Abell 2744 (AC118), visible in the HRI data."1052 This subeluster is also identified in the weak lensing analysis of Small (L997)., This subcluster is also identified in the weak lensing analysis of Smail (1997).1053 The details of the ASCA and ROSAT observations are summarized in Tables 1 and 2. respectively.," The details of the ASCA and ROSAT observations are summarized in Tables 1 and 2, respectively."1054 The basic X-ray properties of the target clusters are summarized in Table 3., The basic X-ray properties of the target clusters are summarized in Table 3.1055 The lensing clusters studied in this paper are crawn from a larger sample of X-ray luminous svstems cliscussecl by Allen CI997. in preparation).," The lensing clusters studied in this paper are drawn from a larger sample of X-ray luminous systems discussed by Allen (1997, in preparation)."1056 A more detailed description of, A more detailed description of1057like to be able to recoucile our scheme with the observed abuudances of simple iiolecular ious aud their deuterated counterparts.,like to be able to reconcile our scheme with the observed abundances of simple molecular ions and their deuterated counterparts.1058 The observed range of values for 77 nuplies a value of S of 500035000 (equ. [1]., The observed range of values for $\bar{R}$ implies a value of $\cal S$ of 5000–35000 (eqn. \ref{DCOP}] ]).1059 Tn order to calculate the expected value of S in LISIN from equation (3)). we need to know the electron. fraction. ἐς. aud »kjc(mng). the total removal rate of ToD! throughli reactions with heavy species.," In order to calculate the expected value of $\cal S$ in L134N from equation \ref{calS}) ), we need to know the electron fraction, $x_e$, and $\sum_j k_j x(m_j)$, the total removal rate of $_2$ $^+$ through reactions with heavy species."1060" We can calculate these values approximately frou the the steady-state IL} concentration, which is given by and the charge conservation equation: Note that the rate coefficients iun equation (13)) are the samme as in equation (3)). suco wo assune that ID! reacts at the same rate as IL}. except for electron recolubination. where we use the value for oULL) of LAS<10""(P/3001I&)999 measured by Suudstrónmui (1991)."," We can calculate these values approximately from the the steady-state $_3^+$ concentration, which is given by and the charge conservation equation: Note that the rate coefficients in equation \ref{h3plus}) ) are the same as in equation \ref{calS}) ), since we assume that $_2$ $^+$ reacts at the same rate as $_3^+$, except for electron recombination, where we use the value for $\alpha_e({\rm H_3^+})$ of $1.15\times10^{-7}(T/300\,{\rm K})^{-0.65}$ measured by Sundströmm (1994)."1061 TCO! and NoII! have been observed in L131N. aud their respective abuudauces are 1.2«10 “and τς1019 (Seide 1980: Womack 1992a: Dickeus 2000).," $^+$ and $_2$ $^+$ have been observed in L134N, and their respective abundances are $1.2\times10^{-8}$ and $7\times10^{-10}$ (Swade 1989; Womack 1992a; Dickens 2000)."1062" Adopting plivsical paramcters of T= LOW and 1.)=2010! ? (Dickens 2000). we thus have three equations (3|. |13]]. and |L1]]) in three unknowns νο, (IL) ame Εμ]."," Adopting physical parameters of $T=10$ K and $n({\rm H_2}) =10632\times10^4$ $^{-3}$ (Dickens 2000), we thus have three equations \ref{calS}] ], \ref{h3plus}] ], and \ref{econs}] ]) in three unknowns $x_e$, $x({\rm H_3^+})$, and $\sum_j k_j x(m_j)$ )."1064 Solving these equations for different values of S allows us to coustrain the chemical state ofLISIN., Solving these equations for different values of $\cal S$ allows us to constrain the chemical state of.1065. Also. because the rate cocfhicicuts for reactions of I. aud IbD! with heavy molecules are z2.10P ems howe can calculate the total abundance of heavy molecules frou oux derived value of »kein).," Also, because the rate coefficients for reactions of $_3^+$ and $_2$ $^+$ with heavy molecules are $\approx 2\times10^{-9}$ $^3$ $^{-1}$, we can calculate the total abundance of heavy molecules from our derived value of $\sum_j k_j x(m_j)$."1066" For S=5000. we caleulate x,=Lbs107. (ILI)=1.6«10. ὃν and EE=16«10 Ll consistent with little depletion of CO. No. and ο from the gas phase."," For ${\cal S} = 5000$, we calculate $x_e = 1.4\times10^{-8}$, $x({\rm1067H_3^+}) = 1.6\times10^{-9}$ , and $\sum_j x(m_j) = 1.6\times10^{-4}$ consistent with little depletion of CO, $_2$, and O from the gas phase."1068 Ou the other haud. for S=35000. we derive L9«10 Sey) =6«107. and SSG)=L9«10 . auplving siguificaut depletion.," On the other hand, for ${\cal S} = 35000$, we derive $x_e =10691.9\times10^{-8}$ , $x({\rm H_3^+}) = 6\times10^{-9}$, and $\sum_j1070x(m_j) = 1.9\times10^{-5}$ , implying significant depletion."1071 For the intermediate value of Sz10! interred from the deuterated auunonia fractionation. we find that partial depletion (~50% )) of heavy molecules is required to account for the observed deuterim enhancements.," For the intermediate value of ${\cal S} \approx 10^4$ inferred from the deuterated ammonia fractionation, we find that partial depletion $\sim 50$ ) of heavy molecules is required to account for the observed deuterium enhancements."1072 A similar couclision has Όσοι reached by Roberts Milhuw (2000)., A similar conclusion has been reached by Roberts Millar (2000).1073 Finally. as our calculated ionization levels lead to eood agrecment with the observed aabundanee (63). we conclude that the observed abundances aud fractionations in LIStN are wellanatched by steady-state tou-imolecule Chemistry.," Finally, as our calculated ionization levels lead to good agreement with the observed abundance $\S\ref{secgasamm}$ ), we conclude that the observed abundances and fractionations in L134N are well-matched by steady-state ion-molecule chemistry."1074 Despite reservations concerning the plivsical conditions in LISIN. some as vet unidentified mechanisu may be retimming mmautle-formed molecules to the gas there.," Despite reservations concerning the physical conditions in L134N, some as yet unidentified mechanism may be returning mantle-formed molecules to the gas there."1075 The uantle abundances of ammonia isotoponiers computed miuericalh bv Brown Mill (1989) (see their table 2) effectively rule out a erain surface origin when scaled to he amunonia abundanceiuEN., The mantle abundances of ammonia isotopomers computed numerically by Brown Millar (1989) (see their table 2) effectively rule out a grain surface origin when scaled to the ammonia abundancein.1076. However. their surface reaction scheme permits lareer D/ITI ratios than those xeseuted. since the fractionation is proportional to the eas pliase atomic D/II ratio. R(D). which may be higher hau the value asstmed iu thei calculations.," However, their surface reaction scheme permits larger D/H ratios than those presented, since the fractionation is proportional to the gas phase atomic D/H ratio, $R$ (D), which may be higher than the value assumed in their calculations."1077 Following he scheme of Brown Millar. we cau derive values for he surface fractionation ratios: Thus.if RED)z 0.05. then it is also possible to explain the observed abundances by surface formation of annona.," Following the scheme of Brown Millar, we can derive values for the surface fractionation ratios: Thus,if $R({\rm D}) \approx 0.05$ , then it is also possible to explain the observed abundances by surface formation of ammonia."1078"cut-off located at the peak of the integrand, relatively more will be removed of mass m at the first dip than of other masses.","cut-off located at the peak of the integrand, relatively more will be removed of mass $m$ at the first dip than of other masses."1079" We also note that the additive peaks of the minimum (cut-off) mass, shown with red solid curves, are not correlated with the location of the dip in the distribution (marked with a black solid tick mark), but shift as a function of the collision velocity."," We also note that the additive peaks of the minimum (cut-off) mass, shown with red solid curves, are not correlated with the location of the dip in the distribution (marked with a black solid tick mark), but shift as a function of the collision velocity."1080" At higher collisional velocity, where waves are stronger, the largest number of cut-off particles are actually produced by the particles in the dip, which would provide a negative feedback according to the traditional picture, canceling the waves."," At higher collisional velocity, where waves are stronger, the largest number of cut-off particles are actually produced by the particles in the dip, which would provide a negative feedback according to the traditional picture, canceling the waves."1081 Our analysis shows that positive feedback is not the dominant effect in the production of the waves., Our analysis shows that positive feedback is not the dominant effect in the production of the waves.1082" The location of the peak of the removal term (Term I in Paper I) is the determining factor in the formation of the waves, which can be given by solving where m gives the location of the first dip and M is given so that X(u,M)=m."," The location of the peak of the removal term (Term I in Paper I) is the determining factor in the formation of the waves, which can be given by solving where $m$ gives the location of the first dip and $M$ is given so that $X(\mu,M)\equiv m$."1083" Unfortunately, an analytic solution can not be given, as the derivative is transcendent, but is easily solvable numerically."," Unfortunately, an analytic solution can not be given, as the derivative is transcendent, but is easily solvable numerically."1084" The variable that determines the solution will be X, which depends on the collisional velocity, the tensile strength law, and the value of min."," The variable that determines the solution will be $X$, which depends on the collisional velocity, the tensile strength law, and the value of $m_{\rm min}$ ."1085" For a given system, where Mmin and the tensile strength law do not change as a function of radial location, the single variable determining the wavy structure is the collisional velocity."," For a given system, where $m_{\rm min}$ and the tensile strength law do not change as a function of radial location, the single variable determining the wavy structure is the collisional velocity."1086 The minimum mass will change as a function stellar types and some material/velocity dependence of the tensile strength law can be expected between systems., The minimum mass will change as a function stellar types and some material/velocity dependence of the tensile strength law can be expected between systems.1087" In Section 2,, we have shown that variations in the proxies for the collisional velocity (such as disk radius) can in fact result in wavy size distributions, even within a narrow debris ring."," In Section \ref{models}, we have shown that variations in the proxies for the collisional velocity (such as disk radius) can in fact result in wavy size distributions, even within a narrow debris ring."1088" Extended debris disks will be even more likely to have higher collisional velocities, as the particles with higher 8 values less than get placed on high eccentricity orbits."," Extended debris disks will be even more likely to have higher collisional velocities, as the particles with higher $\beta$ values (but less than 0.5) get placed on high eccentricity orbits."1089 (butThese small particles0.5) from the inner rings will collide with the particles in the external rings with increased velocities due to the non-zero collisional angles (Thébault&Augereau2007)., These small particles from the inner rings will collide with the particles in the external rings with increased velocities due to the non-zero collisional angles \citep{thebault07}.1090". To study the effects of variations only in the collisional velocity, we set the collisional velocity directly within our code to specific values, not changing any other parameters."," To study the effects of variations only in the collisional velocity, we set the collisional velocity directly within our code to specific values, not changing any other parameters."1091 We present the results from these runs in Figure 9.., We present the results from these runs in Figure \ref{fig:v}.1092 The figure shows that waves start to appear at collisional velocityvalues of 3kms! and above., The figure shows that waves start to appear at collisional velocityvalues of $3~{\rm km~s}^{-1}$ and above.109310σ deviation from the mean.,$10\sigma$ deviation from the mean.1094 The inconsistency with the milder decline found in hydrodynamical simulations ?) was also noted by GO9.," The inconsistency with the milder decline found in hydrodynamical simulations \citep[e.g.,][]{roncarelli} was also noted by G09."1095eqreffirehose)) and mirror-mode instabilities eqrefmirrormode)) in a manner similar to that (Equationseen in observations of the solar wind (Hellingeretal.2006;Baleetal.2009) and in earlier low- current sheet simulations (Drakeetal.,") and mirror-mode instabilities ) in a manner similar to that seen in observations of the solar wind \citep{Hellinger06, Bale09}1096 and in earlier $\beta$ current sheet simulations \citep{Drake10}."1097" reffiredist shows 2010)..the data for our system in the space of where a= P,/P,.", \\ref{firedist} shows the data for our system in the space of $\alpha$ $\beta_\parallel$ ) where $\alpha = P_\perp/P_\parallel$ .1098" This plot is generated by (α,β)calculating the anisotropy o and the β for each grid point.", This plot is generated by calculating the anisotropy $\alpha$ and the $\beta_{\parallel}$ for each grid point.1099" The plot is a two-dimensional histogram of grid points in space, where is calculated based on The ("," The plot is a two-dimensional histogram of grid points in $\alpha$ $\beta_{\parallel}$ ) space, where $\beta_{\parallel}$ is calculated based on $P_\parallel$."1100"o,8j)parallel and perpendicularBj pressures are calculatedP4. by taking the diagonal components of the pressure tensor after rotating into the frame of the local magnetic field, such that the two perpendicular components are equal."," The parallel and perpendicular pressures are calculated by taking the diagonal components of the pressure tensor after rotating into the frame of the local magnetic field, such that the two perpendicular components are equal."1101" We look at the distribution at t—80,120, and "," We look at the distribution at $t = 80, 120,$ and $160\Omega_{\text{ci}}^{-1}$."1102"At early times the anisotropies have not yet fully 1609,,'.developed and the plasma still occupies a small region in (a,6)) space.", At early times the anisotropies have not yet fully developed and the plasma still occupies a small region in $\alpha$ $\beta_{\parallel}$ ) space.1103" By t=1200! the anisotropy has reached the two stability boundaries, and continues to be confined between these two boundaries at t= even as the average ( increases."," By $t=120\Omega_{\text{ci}}^{-1}$ the anisotropy has reached the two stability boundaries, and continues to be confined between these two boundaries at $t=160\Omega_{\text{ci}}^{-1}$, even as the average $\beta$ increases."1104" The anisotropy 1600;,',reaches the stability boundaries at a time after the short wavelength Weibel modes have dissipated.", The anisotropy reaches the stability boundaries at a time after the short wavelength Weibel modes have dissipated.1105" Since at this point there are no longer large regions with essentially zero magnetic fields, the firehose and mirror-mode instabilities are what determine the boundaries of the temperature anisotropies."," Since at this point there are no longer large regions with essentially zero magnetic fields, the firehose and mirror-mode instabilities are what determine the boundaries of the temperature anisotropies."1106 There are no clear signatures of the classical mirror-mode instability at this time., There are no clear signatures of the classical mirror-mode instability at this time.1107" The firehose and mirror-mode instabilities may be hard to distinguish among the turbulent interacting magnetic islands, or the islands may just stop generating anisotropy as they approach the instability boundaries."," The firehose and mirror-mode instabilities may be hard to distinguish among the turbulent interacting magnetic islands, or the islands may just stop generating anisotropy as they approach the instability boundaries."1108" The islands maintain an elongated form for the simulation shown in clear until t=1200;', the latest time simulated refjzbeta((c)for 6=4.8."," The islands maintain an elongated form for the simulation shown in \\ref{jzbeta}( (c) clear until $t=120\Omega_{\text{ci}}^{-1}$, the latest time simulated for $\beta=4.8$."1109 This is shown in refjzanisotropy((a) showing the out-of-plane current for t=, This is shown in \\ref{jzanisotropy}( (a) showing the out-of-plane current for $t=120\Omega_{\text{ci}}^{-1}$.1110" Since the edges of the islands are pushing against the 120051.firehose instability, the tension force in the magnetic fields is eliminated."," Since the edges of the islands are pushing against the firehose instability, the tension force in the magnetic fields is eliminated."1111 This can be seen in refjzanisotropy((b) which shows the regions that are unstable to the firehose instability., This can be seen in \\ref{jzanisotropy}( (b) which shows the regions that are unstable to the firehose instability.1112" The magnetic islands that reach a significant amplitude are much more elongated at high 8, than at low 8..", The magnetic islands that reach a significant amplitude are much more elongated at high $\beta_e$ than at low $\beta_e$.1113 These elongated islands should be found even for moderate values of θε at realistic mass ratios., These elongated islands should be found even for moderate values of $\beta_e$ at realistic mass ratios.1114" Island elongation is caused by the suppression of the shorter wavelength tearing modes by pressure anisotropies (Pj> P,) that develop due to the Fermi acceleration of electrons.", Island elongation is caused by the suppression of the shorter wavelength tearing modes by pressure anisotropies $P_\parallel > P_\perp$ ) that develop due to the Fermi acceleration of electrons.1115 Later in time the plasma develops pressure anisotropies of both ions and electrons that are limited by the firehose and Weibel instabilities., Later in time the plasma develops pressure anisotropies of both ions and electrons that are limited by the firehose and Weibel instabilities.1116 A Weibel mode develops that kinks the magnetic field lines., A Weibel mode develops that kinks the magnetic field lines.1117" In the regime with a real mass ratio we would expect even longer islands to form, where multiple wavelengths of the firehose instability could develop."," In the regime with a real mass ratio we would expect even longer islands to form, where multiple wavelengths of the firehose instability could develop."1118" At late time the fraction of points unstable to the firehose instability saturates, and the anisotropy is confined between the mirror-mode and firehose instability boundaries."," At late time the fraction of points unstable to the firehose instability saturates, and the anisotropy is confined between the mirror-mode and firehose instability boundaries."1119 The long islands persist due to the low requirement of anisotropy to reach the marginal firehose condition at high 8., The long islands persist due to the low requirement of anisotropy to reach the marginal firehose condition at high $\beta$.1120 For even small anisotropies the tension in the magnetic fields is removed., For even small anisotropies the tension in the magnetic fields is removed.1121" When encountering magnetic islands in the heliosheath, we predict the formation of similar extended, sausage-shaped islands rather than the more round islands found in low-3 simulations (Drakeet 2010)."," When encountering magnetic islands in the heliosheath, we predict the formation of similar extended, sausage-shaped islands rather than the more round islands found in $\beta$ simulations \citep{Drake10}."1122". The cores of these islands should also be at the marginal firehose condition, so the magnetic tension that drives them to become round vanishes."," The cores of these islands should also be at the marginal firehose condition, so the magnetic tension that drives them to become round vanishes."1123" We would thus expect these sausage shapes to persist long after the islands have ceased growing, and thus could be found even in regions where reconnection is no longer occurring."," We would thus expect these sausage shapes to persist long after the islands have ceased growing, and thus could be found even in regions where reconnection is no longer occurring."1124 These elongated islandsexhibit signatures that can be seen in data., These elongated islandsexhibit signatures that can be seen in data.1125" In particular, measures all three components of the magnetic field."," In particular, measures all three components of the magnetic field."1126" Of particular interest for the explorations of islands that grow in the ecliptic plane is the angle αλ= tan~!(Br/Br), where Br "," Of particular interest for the explorations of islands that grow in the ecliptic plane is the angle $\lambda =\tan^{-1}\left(B_T/B_R\right)$ , where $B_T$ "1127lluxes from. Bergeron.ctal.(2001) ancl several similar measurements (AleCook&Sion1999): variability appears possible in this star.,fluxes from \citet{ber01} and several similar measurements \citep{mcc99}; variability appears possible in this star.1128.. NLI'T 43806 is [listed among nearby white dwarts with a photometric distance of 15 pe (Llolberectal.2008:WKawka&Vennes 2006).. based on an estimated = mag (Salim&Could.2003).," NLTT 43806 is listed among nearby white dwarfs with a photometric distance of 15 pc \citep{hol08,kaw06}, based on an estimated $V=15.9$ mag \citep{sal03}."1129. Phe SDSS photometry implies a distance greater than 20 pe. with g=17.0 mag (V=16.5 mag) and d—24 pe.," The SDSS photometry implies a distance greater than 20 pc, with $g=17.0$ mag $V\approx16.8$ mag) and $d=24$ pc."1130.. Vhis white dwarf is neither a binary nor binary suspect., This white dwarf is neither a binary nor binary suspect.1131 Cireenetal.(2000). incorrectIy identified this extreme ultraviolet source with anearby. unrelated: infrared source (Farihietal.2006).," \citet{gre00} incorrectly identified this extreme ultraviolet source with anearby, unrelated near-infrared source \citep{far06}."1132... GD 231 is a double. degenerate: (Morales-etal.2005). and may displav mild. near-infrared excess due to its unseen companion. but the larger 2ALASS excess is not confirmed.," GD 231 is a double degenerate \citep{mor05} and may display mild near-infrared excess due to its unseen companion, but the larger 2MASS excess is not confirmed."1133 Figure A4O— demonstrates. that he entire spectral energy. distribution. can be decently matched by a 16500 KODA model. but. this may simply reflect a good approximation of the composite light rather han an accurate effective temperature of either Component.," Figure \ref{fig40} demonstrates that the entire spectral energy distribution can be decently matched by a 16500 K DA model, but this may simply reflect a good approximation of the composite light rather than an accurate effective temperature of either component."1134 Assuming the 18500 Ix. spectroscopic temperature derived » Bergeronetal.(1992). is correct. Figure ΑΕ predicts an excess at JLAN. that is consistent with a 6000 Ix. DC companion.," Assuming the 18500 K spectroscopic temperature derived by \citet{ber92} is correct, Figure \ref{fig41} predicts an excess at $JHK$ that is consistent with a 6000 K DC companion."1135. Vhis star was tentatively classified as a magnetic DA. but has since been correctly reclassified as DB (Jordan2001).," This star was tentatively classified as a magnetic DA, but has since been correctly reclassified as DB \citep{jor01}."1136. Phe apparent 2\LASS excess at this white dwarl is not confirmed: the 13000 Ix fit to its spectral energy distribution shown in Figure X43. is the first time an elfective temperature has been assessed for this DB star. ., The apparent 2MASS excess at this white dwarf is not confirmed; the 13000 K fit to its spectral energy distribution shown in Figure \ref{fig43} is the first time an effective temperature has been assessed for this DB star. .1137. Vhe C-band. photometry for this DZ star appears influenced by its strong Ca LL ancl Ix. absorption. and. possibly other elements (Sionctal.1990).," The $U$ -band photometry for this DZ star appears influenced by its strong Ca H and K absorption, and possibly other elements \citep{sio90}."1138... GD 402 is a suspected DA|DC system based on the fact that its optical colors (and. the shape of its optical spectrum) predict a significantly higher effective temperature than do its. relatively weak Balmer lines (Bergeronctal.1990)., GD 402 is a suspected DA+DC system based on the fact that its optical colors (and the shape of its optical spectrum) predict a significantly higher effective temperature than do its relatively weak Balmer lines \citep{ber90}.1139.. Although the expanded: spectral energy distribution | including the WYER near-infrared data can be nearly. reproduced by a single 7000 Ix. component as shown in Figure οι the photometry can also be well-modeled with two white dwarf components of approximately SOOO Ix and 5000 Ix. (Figure X47)).," Although the expanded spectral energy distribution – including the IRTF near-infrared data – can be nearly reproduced by a single 7000 K component as shown in Figure \ref{fig46}, the photometry can also be well-modeled with two white dwarf components of approximately 8000 K and 5000 K (Figure \ref{fig47}) )."1140 This magnetic white dwarf has a spectral energv distribution that cannot be [fitted by a single temperature (non-magnetic) white dwarf. model., This magnetic white dwarf has a spectral energy distribution that cannot be fitted by a single temperature (non-magnetic) white dwarf model.1141 Figure Ads fits the combined ultraviolet ancl optical fluxes. to vielel a temperature near 13000. WK. while Figure ALO fits the combined optical ancl near-infrarecl colors with a temperature around 10500. Ix. It is unclear. whether this clilliculty is related to the magnetic nature of the star. or if there is a real Jiffy photometric excess (relative to magnetic nmioclels). implying the possibility of binarity. .," Figure \ref{fig48} fits the combined ultraviolet and optical fluxes to yield a temperature near 13000 K, while Figure \ref{fig49} fits the combined optical and near-infrared colors with a temperature around 10500 K. It is unclear whether this difficulty is related to the magnetic nature of the star, or if there is a real $JHK$ photometric excess (relative to non-magnetic models), implying the possibility of binarity. ."1142. Vhis white dwarl may have a small A-band excess. but more data are needed to confirm or rule out this possibility: the V-band Dux appears too bright for the mocel shown in Figure A50.. .," This white dwarf may have a small $K$ -band excess, but more data are needed to confirm or rule out this possibility; the $V$ -band flux appears too bright for the model shown in Figure \ref{fig50}. ."1143. 6213-07 is by far the best near-infrared excess candidate based on its 2A\LASS data. which appear reliable at all wavelengths.," G273-97 is by far the best near-infrared excess candidate based on its 2MASS data, which appear reliable at all wavelengths."1144 Llowever. the ΗΤΙ observations demonstrate that the 2ALASS catalog contains significant errors even al S/N 10..," However, the IRTF observations demonstrate that the 2MASS catalog contains significant errors even at S/N $>10$."1145. Both Vossetal.(2007) and. Beauchampetal.(1999) give. dup=24500 Ww assuning no hvdrogen for this DBZ star.," Both \citet{vos07} and \citet{bea99} give $T_{\rm eff}\approx114624500$ K – assuming no hydrogen – for this DBZ star."1147 However. both authors eive alternative effective. temperatures near 22500 Ix. for a nominal hydrogen abundance.," However, both authors give alternative effective temperatures near 22500 K for a nominal hydrogen abundance."1148 The higher temperature overpredicts the fluxes for this star. and the fit shown in Figure A52. emplovs a temperature. of 21500 Ix to mateh all the photometry: possibly indicating some hvdrogen is present. ancl closer to the 19000 Ix. value eiven bv Koesteretal.(2005a).," The higher temperature overpredicts the fluxes for this star, and the fit shown in Figure \ref{fig52} employs a temperature of 21500 K to match all the photometry; possibly indicating some hydrogen is present and closer to the 19000 K value given by \citet{koe05a}."1149. This white dwarf is another exemplary case of a 2MLASS excess not being corroborated by targeted. JLLdy photometry: the lack of infrared excess is also confirmed byIRAC observations (Farihietal.2009)., This white dwarf is another exemplary case of a 2MASS excess not being corroborated by targeted $JHK$ photometry; the lack of infrared excess is also confirmed by IRAC observations \citep{far09}.1150. The white dwarf Uluxes in the 2ALASS catalog. were the xime motivation for obtaining follow up data. hence it is relevant to ask how well they predicted. the LYLE Ην xhotometry. ancl the presence of any near-infrared excess.," The white dwarf fluxes in the 2MASS catalog were the prime motivation for obtaining follow up data, hence it is relevant to ask how well they predicted the IRTF $JHK$ photometry, and the presence of any near-infrared excess."1151 Figure 1. compares the LTE and 2\LASS fluxes (in Vega magnitudes) for all 39 Table 20 white dwarl targets with thi sets of photomoetry: transformations between filter sets were ignored as they are generally within a few percent (Carpenter2001)., Figure \ref{fig53} compares the IRTF and 2MASS fluxes (in Vega magnitudes) for all 39 Table \ref{tbl2} white dwarf targets with both sets of photometry; transformations between filter sets were ignored as they are generally within a few percent \citep{car01}.1152. The 2ALASS 1060 minimum detection limit for the whole skv is (CJ.H.IN.)=(15.8.15.1.14.3) mae (Skrutskieetal. 2006).. and there is decent accord for measurements brighter than this limit.," The 2MASS $10\sigma$ minimum detection limit for the whole sky is $(J,H,K_s)=(15.8,15.1,115314.3)$ mag \citep{skr06}, and there is decent accord for measurements brighter than this limit."1154 The generally clisagrecable behavior of the PALASS data below the 10σ limit in all three filters is not surprising. vet is most pronounced in the A band.," The generally disagreeable behavior of the 2MASS data below the $\sigma$ limit in all three filters is not surprising, yet is most pronounced in the $K$ band."1155 Somewhat unexpectedly. the J-band shows several discordant measures at the 12a level at relatively bright stars.," Somewhat unexpectedly, the $J$ -band shows several discordant measures at the $1-2\sigma$ level at relatively bright stars."1156 ln [act. of the co-observec white dwarfs at each bandpass. the //-band 2ALASS data agree most. frequently. with the LYE observations over all brightnesses.," In fact, of the co-observed white dwarfs at each bandpass, the $H$ -band 2MASS data agree most frequently with the IRTF observations over all brightnesses."1157 At the La level. the 2NLASS and LIEF photometry agree for 29 of 37 stars )) al 44. 25 of 38 stars (66%)) at J. and 1H of 29 stars (48%)) ab dy.," At the $1\sigma$ level, the 2MASS and IRTF photometry agree for 29 of 37 stars ) at $H$, 25 of 38 stars ) at $J$, and 14 of 29 stars ) at $K$."1158 An infrared excess is revealed by the relative [ux levels of three or more photometric Duxes. at leasttwo of which should. be consistent with photospheric emission ancl at least one of which is significantly higher than expected. for the photosphere alone.," An infrared excess is revealed by the relative flux levels of three or more photometric fluxes, at leasttwo of which should be consistent with photospheric emission and at least one of which is significantly higher than expected for the photosphere alone."1159 Usingthis practical definition. the PALASS photometry suggest an ff and/or A .-bandexcess relative to 2ALASS J or ultraviolet/optical photometry [ου 27 white dwarls in Table 2..," Usingthis practical definition, the 2MASS photometry suggest an $H$ and/or $K_s$ -bandexcess – relative to 2MASS $J$ or ultraviolet/optical photometry – for 27 white dwarfs in Table \ref{tbl2}. ."1160 Phe potential excess I[uxes are, The potential excess fluxes are1161for each observed svstem for a pulsar population moclel.,for each observed system for a pulsar population model.1162" Then. using Baves’ theorem. we ealeulate P(N4,)) from the likelihood P(1: Ny.) and eventually calculate PCR )) using a change of variables."," Then, using Bayes' theorem, we calculate $P$ ) from the likelihood $P$ ) and eventually calculate $P$ ) using a change of variables."1163 We repeat the whole procedure for all three observed coalescing binaries. and combine the (three individual PDFs to obtain a total PDF of Galactic coalescence rate of NS-WD binaries. ?(R4.4)).," We repeat the whole procedure for all three observed coalescing binaries, and combine the three individual PDFs to obtain a total PDF of Galactic coalescence rate of NS-WD binaries, $P$ )."1164 In paper I. we showed that a normalized PDF of the coalescence rate for an individual pulsar binary svstem can be written as follows: where C is a coellicient determined by properties of the 7! pulsar: llere. the beaming correction [actor fi is (he inverse of the traction of da sr covered bv the pulsar radiation beam during each rotation.," In paper I, we showed that a normalized PDF of the coalescence rate for an individual pulsar binary system can be written as follows: where $C_{\rm i}$ is a coefficient determined by properties of the $i^{\rm th}$ pulsar: Here, the beaming correction factor $f_{\rm b}$ is the inverse of the fraction of $4 \pi$ sr covered by the pulsar radiation beam during each rotation."1165" In (hie case of the (wo DNS svstenis. PSRs D1913—16 and B15344+12. Ixalogeraοἱal.(2001) adopted. f,~6 based on pulse profile and polarization measurements of two pulsars."," In the case of the two DNS systems, PSRs B1913+16 and B1534+12, \citet{k01} adopted $f_b\sim6$ based on pulse profile and polarization measurements of two pulsars."1166 The lack of such observations for the current sample of binaries means (hat it is difficult to estimate reliable values of {ων, The lack of such observations for the current sample of binaries means that it is difficult to estimate reliable values of $f_b$.1167" Therefore. in this paper. we do not correct for pulsar beaming (i.e. fj,= 1)."," Therefore, in this paper, we do not correct for pulsar beaming (i.e. $f_{\rm b}=$ 1)."1168 As a result. all our values should be considered as lower limits.," As a result, all our values should be considered as lower limits."1169 In paper I. we calculated PCRGJ) considering (wo observed DNSs systems (labeled by (hesubscripts 1 and 2).," In paper I, we calculated $P$ ) considering two observed DNSs systems (labeled by thesubscripts 1 and 2)."1170" We delined the total rate A...=R4+Re and showed that where C,<Cs.", We defined the total rate ${\cal R}_{\rm +} \equiv {\cal R}_{\rm 1} + {\cal R}_{\rm 2}$ and showed that where $C_{\rm 1} < C_{\rm 2}$.1171" In Appendix A.. we show that this can be extended for the eiurent case ol interest where we have three binary svstems such that Ro=Ry,+Rs RA."," In Appendix \ref{app:3systems}, we show that this can be extended for the current case of interest where we have three binary systems such that ${\cal R}_{\rm +} 1172\equiv {\cal R}_{\rm 1} + {\cal R}_{\rm 2} + {\cal R}_{\rm 3}$ ."1173 This leads to, This leads to1174 8891 is a bright. non-interacting spiral galaxy (SA(s)b: De Vaucouleurs et 11976).," 891 is a bright, non-interacting spiral galaxy (SA(s)b: De Vaucouleurs et 1976)."1175" It is very nearly edge-on aa"". PA=23°: Sofue & Nakai 1993)."," It is very nearly edge-on $i > 88^{\circ}$ , $PA = 23^{\circ}$; Sofue $\&$ Nakai 1993)."1176" NGC 891 is one of the major members of the 11023 group and its distance is estimated to be MMpe for fy=T5laus+Ape1 making for a scale of 22""/kpe or ppc/""."," NGC 891 is one of the major members of the 1023 group and its distance is estimated to be Mpc for $H_{\rm 0}=75\kms\,{\rm Mpc}^{-1}$, making for a scale of $''$ /kpc or $''$."1177 Many authors have remarked on the apparent similarity between NGC 891 and the Milky Way., Many authors have remarked on the apparent similarity between NGC 891 and the Milky Way.1178 The interstellar medium in the disk of NGC 891 has been the subject of several studies. notably radio continuum (Allen et al.," The interstellar medium in the disk of NGC 891 has been the subject of several studies, notably radio continuum (Allen et al."1179 1978; Sukumar & Allen 1991). HI (Saneist & Allen 1979: Rupen 1991). dust (Howk & Savage 1997); CO (Garcfaa-Burillo et al.," 1978; Sukumar $\&$ Allen 1991), HI (Sancisi $\&$ Allen 1979; Rupen 1991), dust (Howk $\&$ Savage 1997); CO (Garcíaa-Burillo et al."1180 1992: Scoville et al., 1992; Scoville et al.1181 1993: Sofue & Nakai 1993; Garcfaa-Burillo & Guéllin. 1995; Sakamoto et al., 1993; Sofue $\&$ Nakai 1993; Garcíaa-Burillo $\&$ Guéllin 1995; Sakamoto et al.1182 1997) and CI (Geri & Phillips 1997)., 1997) and CI (Gerin $\&$ Phillips 1997).1183 Far-infrared dust emission was observed by IRAS (see Wainscoat et al., Far-infrared dust emission was observed by IRAS (see Wainscoat et al.1184 1987: Rice et al., 1987; Rice et al.1185 1988). and at A = 1.3 mm by Guéllin et al.," 1988), and at $\lambda$ = 1.3 mm by Guéllin et al."1186 1993., 1993.1187 In this paper we present further observations of the submillimeter dust emission from NGC 891 with. the new SCUBA submillimeter continuum array detector., In this paper we present further observations of the submillimeter dust emission from NGC 891 with the new SCUBA submillimeter continuum array detector.1188 The SCUBA 850 and 450 jim images were obtained in 1997 September on the JCMT'., The SCUBA 850 and 450 $\mu$ m images were obtained in 1997 September on the JCMT.1189. SCUBA employs two arrays of cooled bolometers. each covering a field of about 2/3.," SCUBA employs two arrays of cooled bolometers, each covering a field of about $\mind 2.3$."1190 The respective filters used have central frequencies of 347 GHz and 677 GHz respectively: both filters have a bandwidth of 30 GHz., The respective filters used have central frequencies of 347 GHz and 677 GHz respectively; both filters have a bandwidth of 30 GHz.1191" We observed three fields on NGC 891 (center. northeast and southwest) in socalled ""jiggle-mode' in order to cover the whole galaxy."," We observed three fields on NGC 891 (center, northeast and southwest) in socalled `jiggle-mode' in order to cover the whole galaxy."1192 Chopping distance was 2’ perpendicular to the major axis of the galaxy., Chopping distance was $'$ perpendicular to the major axis of the galaxy.1193 Total integration time for the three fields was 128 minutes., Total integration time for the three fields was 128 minutes.1194 Reduction was performed in the standard manner., Reduction was performed in the standard manner.1195 Photometric calibration was achieved by skydip analysis and mapping of the standard star CRL 618., Photometric calibration was achieved by skydip analysis and mapping of the standard star CRL 618.1196 More complete details of the instrument as well as observing and reduction methods can be found in Holland et al. (, More complete details of the instrument as well as observing and reduction methods can be found in Holland et al. (11971998) and Jenness et al. (,1998) and Jenness et al. (11981998). as well as on the world-wide web (www.jach.hawarn.edu),"1998), as well as on the world-wide web (www.jach.hawaii.edu)."1199 The resulting images are shown in Figure |., The resulting images are shown in Figure 1.1200 Especially in the 450;/m image. residual noise is seen at the SCUBA field edges: this should be discounted.," Especially in the $\mu$ m image, residual noise is seen at the SCUBA field edges; this should be discounted."

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