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The time delay for this case is If the redshift of the lens zy were known. we could compute the Hubble parameter from the time delay using the fundamental equation connecting the time delay Ar and the parameter 7 As zy ts still unknown. we cannot use this formula to get Hy. | The time delay for this case is If the redshift of the lens $z_\mathrm{d}$ were known, we could compute the Hubble parameter from the time delay using the fundamental equation connecting the time delay $\Delta t$ and the parameter $T$ As $z_\mathrm{d}$ is still unknown, we cannot use this formula to get $H_0$. |
However. simply a canonical value for Hy allows us to predict the redshift of the lens. or better. to constrain the range of possible values for zy. | However, simply a canonical value for $H_0$ allows us to predict the redshift of the lens, or better, to constrain the range of possible values for $z_\mathrm{d}$ . |
Figure 4. shows the product of time delay and Hubble parameter as a function of zy. | Figure \ref{fig:timdelz} shows the product of time delay and Hubble parameter as a function of $z_\mathrm{d}$. |
For Ar= 0.73yr. Hy=SOkms-!Mpe7!. Q=I. and A=0. the SIST model predicts sy=0.79. and the velocity dispersion of the galaxy for this model is σι=332kms7!. | For $\Delta t=0.73\,\mathrm{yr}$ , $H_0=50\mathrm{\,km\,s^{-1}\, Mpc^{-1}}$, $\Omega=1$, and $\lambda=0$, the SIST model predicts $z_\mathrm{d}=0.79$, and the velocity dispersion of the galaxy for this model is $\sigma_v=332\mathrm{\,km\,s^{-1}}$. |
This corresponds to a mass of 9.21011M. inside of one Einstein radius. well within the range expected for a reasonably massive galaxy. | This corresponds to a mass of $9.2\,10^{11}\,M_\odot$ inside of one Einstein radius, well within the range expected for a reasonably massive galaxy. |
With an I. band magnitude of 20.9 according to R98. the mass-to-light ratio would then be of the order of 10 solar units. again quite consistent with the expectations for such a galaxy KKeeton et citekeeton98 )). | With an $I_c$ band magnitude of 20.9 according to R98, the mass-to-light ratio would then be of the order of 10 solar units, again quite consistent with the expectations for such a galaxy Keeton et \\cite{keeton98}) ). |
Recently. values for the time delay have been predicted based on the assumption that one of the two strong metal absorption line systems at z21.32 or z—1.66 can be identified with the deflector. | Recently, values for the time delay have been predicted based on the assumption that one of the two strong metal absorption line systems at $z=1.32$ or $z=1.66$ can be identified with the deflector. |
R98 give Ar—19h) yrs. Courbin et al. (1998)) | R98 give $\Delta t \simeq 1.9\,h_{50}^{-1}$ yrs, Courbin et al. \cite{courbin98}) ) |
even 3h yrs. | even $3.5\,h_{50}^{-1}$ yrs. |
Since we can reliably exclude Ar>| vyr. our results are not compatible with zy significantly larger than 1: in particular. the absorbers at 1.32 and 1.66 can be ruled out. | Since we can reliably exclude $\Delta t > 1$ yr, our results are not compatible with $z_{\mathrm{d}}$ significantly larger than 1; in particular, the absorbers at 1.32 and 1.66 can be ruled out. |
We have searched our higher resolution NTT spectra of HE 1805 LLopez et citelopez98)) for absorption lines within the redshift range permitted by reffig:timdelz.. | We have searched our higher resolution NTT spectra of HE $-$ 1805 Lopez et \\cite{lopez98}) ) for absorption lines within the redshift range permitted by \\ref{fig:timdelz}. |
An additional demand ts that the lines should be stronger in A. as this component is located closer to the deflector. | An additional demand is that the lines should be stronger in A, as this component is located closer to the deflector. |
Two absorption systems. at z—0.52 and 0.73. meet the criteria. | Two absorption systems, at $z=0.52$ and 0.73, meet the criteria. |
Of these. zy=0.52 is acceptable only for a time delay as short as ~O.4 yyrs. and is furthermore not compatible with the 7& colour estimate of R98. | Of these, $z_\mathrm{d}=0.52$ is acceptable only for a time delay as short as $\sim 0.4$ yrs, and is furthermore not compatible with the $I-K$ colour estimate of R98. |
This leaves the systemat z—0.73 as candidate: however. the lens could also be an elliptical galaxy for which absorption would be a poor indicator. | This leaves the systemat $z=0.73$ as candidate; however, the lens could also be an elliptical galaxy for which absorption would be a poor indicator. |
The very red colours measured by R98 support such a notion. | The very red colours measured by R98 support such a notion. |
relationship is necessary for understanding black hole growth and evolution as well as the interplay between black holes and their host galaxies. | relationship is necessary for understanding black hole growth and evolution as well as the interplay between black holes and their host galaxies. |
We have presented an updated version of the AGN Λμη-- relationship using the database of homogeneously Logsanalyzed reverberation masses from Petersonetal.(2004) and Grieretal. (2008: 22130+099) and the two-dimensional surface brightness decompositions of the AGN host galaxies described by Bentzetal.(2008).. | We have presented an updated version of the AGN $M_{\rm BH} - L_{\rm
bulge}$ relationship using the database of homogeneously analyzed reverberation masses from \citet{peterson04} and \citeauthor{grier08}
(2008; 2130+099) and the two-dimensional surface brightness decompositions of the AGN host galaxies described by \citet{bentz08b}. |
We find a strong correlation about the relationship for the 26 AGNs included here. with à best-fit powerlaw slope of0. | We find a strong correlation about the relationship for the 26 AGNs included here, with a best-fit powerlaw slope of. |
09. This is somewhat shallower than the best-fit slope for quiescent galaxies (az1.0). even though the AGN black hole masses have been scaled to bring the AGN and quiescent galaxy Mgy—o. relationships into agreement. | This is somewhat shallower than the best-fit slope for quiescent galaxies $\alpha \approx 1.0$ ), even though the AGN black hole masses have been scaled to bring the AGN and quiescent galaxy $M_{\rm BH} -
\sigma_{\star}$ relationships into agreement. |
There appear to be many systematics in both the AGN and quiescent galaxy samples that must be investigated in order to more completely understand this important relationship. | There appear to be many systematics in both the AGN and quiescent galaxy samples that must be investigated in order to more completely understand this important relationship. |
Our future plans include investigating the biases in the AG sample and extending the range of the relationship for AGNs. | Our future plans include investigating the biases in the AGN sample and extending the range of the relationship for AGNs. |
We have anHST Cycle 17 program to image the NGC objects that were excluded from this particular work with the Wide Field Camera 3 through the F547M filter. | We have an Cycle 17 program to image the NGC objects that were excluded from this particular work with the Wide Field Camera 3 through the F547M filter. |
These observations will provide us with the intermediate FOV images necessary for accurate decompositions of those galaxies. enabling us to include them at the low-mass end of the Mpy—Logs; relationship for AGNs. | These observations will provide us with the intermediate FOV images necessary for accurate decompositions of those galaxies, enabling us to include them at the low-mass end of the $M_{\rm BH} -
L_{\rm bulge}$ relationship for AGNs. |
Recent reverberation-mappinga experiments that were carried out at MDM Observatorst (spring 2007) and Lick Observatory (spring 2008) focusifa on AGNs with black hole masses in the range |«10°5«10M.. (Denney et iin preparation. Bentz et iin preparation) show promise in further extending the range and coverage of the Mig—Louis relationship for AGNs at the mass end. | Recent reverberation-mapping experiments that were carried out at MDM Observatory (spring 2007) and Lick Observatory (spring 2008) focusing on AGNs with black hole masses in the range $1 \times 10^6 - 5 \times 10^7 M_{\odot}$ (Denney et in preparation, Bentz et in preparation) show promise in further extending the range and coverage of the $M_{\rm BH} - L_{\rm bulge}$ relationship for AGNs at the low-mass end. |
We would like to thank Alessandro Marconi and Tod Lauer for helpful comments. and Chien Peng for his excellent program Galfit and for helpful conversations regarding the galaxy fitting. | We would like to thank Alessandro Marconi and Tod Lauer for helpful comments, and Chien Peng for his excellent program Galfit and for helpful conversations regarding the galaxy fitting. |
This work is based on observations with the NASAJ/ESATelescope. | This work is based on observations with the NASA/ESA. |
We are grateful for support of this work through grantsHST GO-9851. GO-10516. and GO-10833 from the Space Telescope Science Institute. which is operated by the Association of Universities for Research in Astronomy. Inc.. under NASA contract ΝΑΡΟ-26555. and by the NSF through grant AST-0604066 to The Ohio State University. | We are grateful for support of this work through grants GO-9851, GO-10516, and GO-10833 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555, and by the NSF through grant AST-0604066 to The Ohio State University. |
M.B. gratefully acknowledges support from the NSF through grant AST-0548198 to the University of California. Irvine. and M.V. gratefully acknowledges support fromHST GO-10417 andHST AR-10691. | M.B. gratefully acknowledges support from the NSF through grant AST-0548198 to the University of California, Irvine, and M.V. gratefully acknowledges support from GO-10417 and AR-10691. |
This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Administration and the SIMBAD database. operated at CDS. Strasbourg. France. | This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration and the SIMBAD database, operated at CDS, Strasbourg, France. |
disk inclination and stellar mass. a planct orbiting around RY Tau would produce a less visible gap. | disk inclination and stellar mass, a planet orbiting around RY Tau would produce a less visible gap. |
Iu particular. our observations seenis to exclude he preseuce of planets more massive than 5 Jupiter asses between 10 and 60 AU. | In particular, our observations seems to exclude the presence of planets more massive than 5 Jupiter masses between 10 and 60 AU. |
Civen he higher stellar mass of RY Tau. the miu iue scale for the formation of gaps is one order of magnitude larger than the case of DG Tau (see lower panel of Figure 12)). | Given the higher stellar mass of RY Tau, the minimum time scale for the formation of gaps is one order of magnitude larger than the case of DG Tau (see lower panel of Figure \ref{fig:tau_delta}) ). |
This implies that planets less massive than Jupiter orbiting at more han about 30 AU max not have had enough tine ο fori a eap in the disk. | This implies that planets less massive than Jupiter orbiting at more than about 30 AU may not have had enough time to form a gap in the disk. |
A comparison of the best fit solutions obtained for the wavelengths of 1.3 1011 and 2.8 mun enable us to investigate the dependence of dust opacity on the orbital radius. | A comparison of the best fit solutions obtained for the wavelengths of 1.3 mm and 2.8 mm enable us to investigate the dependence of dust opacity on the orbital radius. |
If the dust opacity is coustanut throughout the disk as assumed in Section L.. the model fitting necessarily leads to the same surface deusitv profile for observatious at two differcut wavelengths. | If the dust opacity is constant throughout the disk as assumed in Section \ref{sec:mod}, the model fitting necessarily leads to the same surface density profile for observations at two different wavelengths. |
Otherwise. differcut SCR) would sugeest a radial variation iu the relative dust opacities at the observed wavelengths. | Otherwise, different $\Sigma(R)$ would suggest a radial variation in the relative dust opacities at the observed wavelengths. |
To understand this poiut. we assmnue that the dust Cluission is optically thin. | To understand this point, we assume that the dust emission is optically thin. |
Iu this case the observations constrain the product X4GQR)<Ay. where XAGR) is the surface density obtained by fittinethe observations at the wavelength A. | In this case the observations constrain the product $\Sigma_{\lambda}(R) \times k_{\lambda}$, where $\Sigma_{\lambda}(R)$ is the surface density obtained by fittingthe observations at the wavelength $\lambda$. |
Iu the more eeneral case in which the dust opacity depeuds on the orbital radius we can write The left side of this equation contains the opacity discussed iu Section 1. and the surface density derived from the model fitting. | In the more general case in which the dust opacity depends on the orbital radius we can write The left side of this equation contains the opacity discussed in Section \ref{sec:mod} and the surface density derived from the model fitting. |
The right side contains the unknown “true” surface deusity SUR) in the case im which the “truce” dust opacity kA) varies with the radius. | The right side contains the unknown “true” surface density $\tilde\Sigma(R)$ in the case in which the “true” dust opacity $\tilde k_{\lambda}(R)$ varies with the radius. |
The ratio of Equation 6. for two different waveleugths Ay aud Ay leads to Tere we assumed that at each radius the dust opacity can be expressed by a power law hyκ 7. | The ratio of Equation \ref{eq:sigmak} for two different wavelengths $\lambda_0$ and $\lambda_1$ leads to Here we assumed that at each radius the dust opacity can be expressed by a power law $k_{\lambda} \propto \lambda^{-\beta}$ . |
Finally. taking the logarithnuu of this latter equation we cau write where 3.=log(hy,Eslog(ÀAog/A1) and A3(R) has the form If 0vὃν.= Ma, the dust opacity slope is constant throughout the disk aud assumes the value discussed in Section L. | Finally, taking the logarithm of this latter equation we can write where $\beta_c=\log(k_{\lambda_1}/k_{\lambda_0})/\log(\lambda_0/\lambda_1)$ and $\Delta\beta(R)$ has the form If $\Sigma_{\lambda_1}=\Sigma_{\lambda_0}$ , the dust opacity slope is constant throughout the disk and assumes the value discussed in Section \ref{sec:mod}. . |
Otherwise. we cau use the lattercquation to investigate the radial variatiou of .j. | Otherwise, we can use the latterequation to investigate the radial variation of$\beta$ . |
an ultra-relativistic shock. and found that. particles with initially isotropic momenta upstream can increase their energv by a factor of order ΕΣ in the initial shock crossing cycle. | an ultra-relativistic shock, and found that particles with initially isotropic momenta upstream can increase their energy by a factor of order $\Gs^2$ in the initial shock crossing cycle. |
In all subsequent shock crossing eveles. however. we showed that the particle energy typically only doubles. | In all subsequent shock crossing cycles, however, we showed that the particle energy typically only doubles. |
Εις is due to the [act that particles do not have time to re-isotropise upstream before. being overtaken by the shock. which we demonstrated in the specilie cases of a larec-scale. ordered magnetic Ποιά and of small-seale magnetic Iluctuations. | This is due to the fact that particles do not have time to re-isotropise upstream before being overtaken by the shock, which we demonstrated in the specific cases of a large-scale ordered magnetic field and of small-scale magnetic fluctuations. |
We argued. that the maximum energv that can be reached bv repeated: shock crossings at. the unmoclified relativistic blast wave from a GRB fireball is well below the UCLLECKR. range. | We argued that the maximum energy that can be reached by repeated shock crossings at the unmodified relativistic blast wave from a GRB fireball is well below the UHECR range. |
Pre-existing relativistic particles of sullicicnt enerey can nonetheless be boosted to VILECR energies in the first shock crossing evele. | Pre-existing relativistic particles of sufficient energy can nonetheless be boosted to UHECR energies in the first shock crossing cycle. |
For a fireball expanding into a twpical interstellar medium. where ealactic cosmic rays provide the κους particles. we showed. however. that. this process is too inellicient to account for ULLECTU production. | For a fireball expanding into a typical interstellar medium, where galactic cosmic rays provide the seed particles, we showed, however, that this process is too inefficient to account for UHECR production. |
We proposed that the blast wave instead. expands into a pulsar wind bubble produced by the progenitor system. a plausible hypothesis in the neutron star binary merger scenario for GRBs. | We proposed that the blast wave instead expands into a pulsar wind bubble produced by the progenitor system, a plausible hypothesis in the neutron star binary merger scenario for GRBs. |
We showed that for parameters typical of the neutron star binary svstems observed in our Galaxy. relativistic ions in the pulsar wind bubble can be cllicientLy boosted by the blast wave to energies execeding 1072eV. | We showed that for parameters typical of the neutron star binary systems observed in our Galaxy, relativistic ions in the pulsar wind bubble can be efficiently boosted by the blast wave to energies exceeding $10^{20} \, \eV$. |
We argued that these boosted ions would have an do> spectrum. extending. down in. energy to about LOlx.HeV. | We argued that these boosted ions would have an $E^{-2}$ spectrum, extending down in energy to about $10^{18.5} \, \eV$. |
This work was supported by the Netherlands Foundation for ltesearch in Astronomy (ASTRON) project 78171050. | This work was supported by the Netherlands Foundation for Research in Astronomy (ASTRON) project 781–71–050. |
null | $1/r^2$. |
7. | 7. |
Follow tlie same steps to obtain Arl:).:) audDan ).2) at different 7. | Follow the same steps to obtain $\Delta^2_{SZ,G}(l/x(z),z)$ and $\Delta^2_{SZ}(l/x(z),z)$ at different $l$. |
Since [or C'ez(I) at different angular scale f. (1/a?(b2) is determined roughly by ομςςτρ].2p] τρ~ Lis the redshift with peak contribution to Cy. | Since for $C_{SZ}(l)$ at different angular scale $l$, $\langle 1/r^2(l/x,z)\rangle$ is determined roughly by $r(l/x(z_p),z_p)$ $z_p\sim 1$ is the redshift with peak contribution to $C_l$. |
See Fie. 2)). | See Fig. \ref{fig:zcon}) ), |
we can even get some idea about the scale dependeuce of r(&.z). | we can even get some idea about the scale dependence of $r(k,z)$. |
Thus. the total projected SZ autocorrelation give a consistency check ou the reconstructed time resolved power spectrum from the galaxy-5Z cross correlation. | Thus, the total projected SZ autocorrelation give a consistency check on the reconstructed time resolved power spectrum from the galaxy-SZ cross correlation. |
Furthermore. the galaxy. bias and its time depeucence have completely dropped out of the calculation. aud are thus uot expected to affect the results at all. | Furthermore, the galaxy bias and its time dependence have completely dropped out of the calculation, and are thus not expected to affect the results at all. |
Them. iu principle. SZ-galaxy correlation plus $Z CMB tulsotropy provide a cousistent and. powerful method to extract all time evolution inlormation of the IGM pressure power spectrum. | Then, in principle, SZ-galaxy correlation plus SZ CMB anisotropy provide a consistent and powerful method to extract all time evolution information of the IGM pressure power spectrum. |
Noise aud cosmic variance put coustraints ou the feasibility of our procedure. ( | Noise and cosmic variance put constraints on the feasibility of our procedure. ( |
1) Limitation of CMB resolution degrades our method. | 1) Limitation of CMB resolution degrades our method. |
The measured range of & is [fafas).loασ)~[14730002.05:| 3000:/Mpc. | The measured range of $k$ is $[l_1/x(z),l_2/x(z)]\sim[1_1/3000z,l_2/3000z]
h$ /Mpc. |
Here. [h4./5] is the range of the CMB n | Here, $[l_1,l_2]$ is the range of the CMB experiment. |
Iu order to detect the peak of AL . aroun ko= Sh/Npc as shown iu Fig. 3)). z"d-fof9000. | In order to detect the peak of $\Delta_p^2$ ( around $k=
3h$ /Mpc as shown in Fig. \ref{fig:pressure}) ), $z\leq l_2/9000 $. |
dFor CBI (630</x 3500). we are only able to detectz€ 0.L. | For CBI $630\leq
l\leq 3500$ ), we are only able to detect$z\leq 0.4$ . |
AMIBA will measure/<"d2820 SouthPoleSubinillimeterTelescope(2003) wil Ineasure /«100t). | AMIBA will measure $l\leq 28500$ and \citet{10m} will measure $l \leq 40000$. |
They will mu"allow us to ineasure the gas power spectrum up to zo3 aud z—f. respectively. ( | They will allow us to measure the gas power spectrum up to $z\sim 3$ and $z\sim 4$, respectively. ( |
2) errors impose [further coustraints. | 2) Observational errors impose further constraints. |
Suppose that the galaxy survey covers a fraction fe; of the sky aud the 7-th survey region (For example. if the redshift accuracy is Az. then we can divide the galaxies iuto redshilt bins with QXz<Ac. Acσσ€2.Nz. ete. ) | Suppose that the galaxy survey covers a fraction $f_G$ of the sky and the $i$ -th survey region (For example, if the redshift accuracy is $\Delta z$, then we can divide the galaxies into redshift bins with $0 \leq z \leq \Delta z$, $\Delta z \leq z \leq 2 \Delta z $, etc. ) |
have AN; observed galaxies. | have $N_i$ observed galaxies. |
The CMB observation covers afraction fey), of sky aucl the Cy) is averaged over the band [/—Al/2./+.NE/2]. | The CMB observation covers afraction $f_{cmb}$ of sky and the $C_l$ is averaged over the band $[l-\Delta l/2,l+\Delta l/2]$. |
Then the galaxy number count causes the Poisson error: (3) The cosmic variance of the Cy also cause errors. | Then the galaxy number count causes the Poisson error: (3) The cosmic variance of the $C_l$ also cause errors. |
Recalling that Cy=Soapna),/(253-1) aud μη7XOFx bd. we get: 81, is the deusity NEM oversinoothing scale 2 ~h/Mpe. | Recalling that $C_l=\sum a_{lm}a_{lm}^*/(2l+1)$ and $a_{lm} \propto \delta T \propto b_p \delta$ , we get: Here, $\sigma^2_R$ is the density dispersion over smoothing scale $R\sim h/$ Mpc. |
We already. use the typical value of S, LOaud σ=σρίς1)~10. | We already use the typical value of $S_4
\sim 40$ and $\sigma^2_R(z=1) \sim 10$ . |
The correspoucing error caused iu ó3; is: A Recalling ALx O3. requiringa LOY accuracy on ALS would impose that (a) 10*. tha | The corresponding error caused in $\phi_M$ is: Recalling that $\Delta^2_{SZ} \propto \phi_M^2$ , requiringa $40\%$ accuracy on $\Delta^2_{SZ}$ would impose that (a) $f_G \times
min(N_i)\geq 10^3$ . |
tEach survey Ὁ must be large enough. in order to contain sullicient.number | Each survey regions must be large enough in order to contain sufficientnumber |
the Vireo Cluster Survev: VCC 1226. VCC 1316. VCC 1978. VCC 381. and VCC 798. | the Virgo Cluster Survey: VCC 1226, VCC 1316, VCC 1978, VCC 881, and VCC 798. |
These 10-pixel magnitudes were (hen corrected to a nominal infinite aperture using values of —0.10 ing and —0.12 in : (Sinanni 2005: this paper describes the photometric calibration ol ACS), | These 10-pixel magnitudes were then corrected to a nominal infinite aperture using values of $-0.10$ in $g$ and $-0.12$ in $z$ (Sirianni 2005; this paper describes the photometric calibration of ACS). |
Finally. the magnitudes were transformed to the AB svstem using zeropoints [rom sSiranni (26.068 and 24.862 [or g and z. respectively). and corrected. for Galactic reddening using the maps of Schlegel Finkbeiner. Davis (1993). | Finally, the magnitudes were transformed to the AB system using zeropoints from Sirianni (26.068 and 24.862 for $g$ and $z$, respectively), and corrected for Galactic reddening using the maps of Schlegel Finkbeiner, Davis (1998). |
Alost GCs at the distance of Virgo are well-resolved in ACS imaging. | Most GCs at the distance of Virgo are well-resolved in ACS imaging. |
Hall-light. radii (rj) for GC candidates were measured on g images (since (he g PSF is more centrally concentrated) using the routine (Larsen 1999). | Half-light radii $r_h$) for GC candidates were measured on $g$ images (since the $g$ PSF is more centrally concentrated) using the routine (Larsen 1999). |
For each object. Nine models with fixed e=30 (lor ο=ΙΓ νο) aud varving ry, were convolved wilh a distant-depencdent empirical PSF derived from bright isolated stars in the images to find the best-fit rj. | For each object, King models with fixed $c=30$ (for $c=r_{tidal}/r_{core}$ ) and varying $r_h$ were convolved with a distant-dependent empirical PSF derived from bright isolated stars in the images to find the best-fit $r_h$. |
This € is (vpical of non core-collapsed GC's in the Milkv Way (Trager. Nine. Djorgovski 1995). | This $c$ is typical of non core-collapsed GCs in the Milky Way (Trager, King, Djorgovski 1995). |
We experimented with allowing e to vary. but it was poorly constrained [or most GCs. | We experimented with allowing $c$ to vary, but it was poorly constrained for most GCs. |
However. the adopted ο in has little effect on the derived rj, (Larsen 1999). | However, the adopted $c$ in has little effect on the derived $r_h$ (Larsen 1999). |
To convert these measured sizes into physical units. galaxy distance estimates are required. | To convert these measured sizes into physical units, galaxy distance estimates are required. |
We used (hose derived from surface brightness fluctuation measurements in the literature when possible: these were available from Tonry (2001) for the bright galaxies and [rom Jerjen (2004) for several dEs. | We used those derived from surface brightness fluctuation measurements in the literature when possible: these were available from Tonry (2001) for the bright galaxies and from Jerjen (2004) for several dEs. |
For the remainder of the galaxies we used a fixed distance of 17 Alpe. which is the mean of the ellipticals in Tonry Due to the depth of the images (+2 25). some of the fields sulfer significant contamination from Ioreground stars ancl especially background galaxies. | For the remainder of the galaxies we used a fixed distance of 17 Mpc, which is the mean of the ellipticals in Tonry Due to the depth of the images $z \ga 25$ ), some of the fields suffer significant contamination from foreground stars and especially background galaxies. |
Using the gEs and several of the more populous dEs as fiducials. we chose the following structural cuts to reduce interlopers: 0.55 < sharp < 0.9. 20.5« round <(0.5. and 1«ry (pc) <13. where the sharp and round parameters awe from DAOPIIOT. | Using the gEs and several of the more populous dEs as fiducials, we chose the following structural cuts to reduce interlopers: 0.55 $<$ sharp $<$ 0.9, $-0.5 <$ round $< 0.5$, and $1 < r_h$ (pc) $< 13$, where the sharp and round parameters are from DAOPHOT. |
A laree upper limit lor rj is used since the size nmeasurenienis skew svslematically larger for fainter GCs. | A large upper limit for $r_h$ is used since the size measurements skew systematically larger for fainter GCs. |
We further applied a color eut of 0.5 «g-—z«20(203 mag to each blue and red of the limiting metallicities expected [or old GCs: Jordáun 2004) and an error limit < 0.15 mag. | We further applied a color cut of $0.5 < g-z < 2.0$ $> 0.3$ mag to each blue and red of the limiting metallicities expected for old GCs; Jordánn 2004) and an error limit $<$ 0.15 mag. |
In practice. this magnitude limit excluded most GC's within the innermost few aresee of the brightest galaxies (whose GC svslelus are quite populous). | In practice, this magnitude limit excluded most GCs within the innermost few arcsec of the brightest galaxies (whose GC systems are quite populous). |
Finally. we visually inspected all GC candidates. and excluded those which were obviously background galaxies. | Finally, we visually inspected all GC candidates, and excluded those which were obviously background galaxies. |
Our criteria are illustrated visually in Figure 1 for the bright dE VCC 1087. which displavs a good mix of actual GCs and contaminants. | Our criteria are illustrated visually in Figure 1 for the bright dE VCC 1087, which displays a good mix of actual GCs and contaminants. |
These cuts remove nearly all foreground stars. | These cuts remove nearly all foreground stars. |
However. compact galaxies (or compact star-Iorming regions within lareer galaxies) with the appropriate colors can masquerade as GCs. | However, compact galaxies (or compact star-forming regions within larger galaxies) with the appropriate colors can masquerade as GCs. |
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