The Color-Magnitude Relation for Metal-Poor Globular Clusters in M87: Confirmation From Deep HST/ACS Imaging
Eric W. Peng, Andres Jordan, John P. Blakeslee, Steffen Mieske, Patrick Cote, Laura Ferrarese, William E. Harris, Juan P. Madrid, Gerhardt R. Meurer
aa r X i v : . [ a s t r o - ph . GA ] J u l Accepted for publication in the Astrophysical Journal
Preprint typeset using L A TEX style emulateapj v. 08/22/09
THE COLOR-MAGNITUDE RELATION FOR METAL-POOR GLOBULAR CLUSTERS IN M87:CONFIRMATION FROM DEEP
HST/ACS
IMAGING Eric W. Peng , Andr´es Jord´an , John P. Blakeslee , Steffen Mieske , Patrick Cˆot´e , Laura Ferrarese ,William E. Harris , Juan P. Madrid , and Gerhardt R. Meurer Accepted for publication in the Astrophysical Journal
ABSTRACTMetal-poor globular clusters (GCs) are our local link to the earliest epochs of star formation andgalaxy building. Studies of extragalactic GC systems using deep, high-quality imaging have revealed asmall but significant slope to the color-magnitude relation for metal-poor GCs in a number of galaxies.We present a study of the M87 GC system using deep, archival
HST/ACS imaging with the F606Wand F814W filters, in which we find a significant color-magnitude relation for the metal-poor GCs.The slope of this relation in the I vs. V – I color-magnitude diagram ( γ I = − . ± . M I . −
10, and itssignificance is largest when fitting metal-poor GCs brighter than M I = − .
8, a luminosity which is ∼ ∼ . Subject headings: galaxies: elliptical and lenticular, cD — galaxies: individual(M87) — galaxies: dwarf— galaxies: evolution — galaxies: star clusters – globular clusters: general INTRODUCTION
Globular clusters (GCs) contain the oldest stellar pop-ulations in galaxies, and are in many ways our most ac-cessible link to the earliest, most intense phases of galaxybuilding. The formation of GC systems are clearly linkedto the formation of the galaxies that host them. Well-established correlations show, for instance, that both themean metallicity of the entire GC population and themean metallicities of the well-known metallicity subpop-ulations are correlated with the masses of the hosts (e.g.Brodie & Huchra 1991; Larsen et al. 2001; Peng et al. Based on observations with the NASA/ESA
Hubble Space Tele-scope obtained at the Space Telescope Science Institute, which isoperated by the Association of Universities for Research in Astron-omy, Inc., under NASA contract NAS 5-26555. Department of Astronomy, Peking University, Beijing 100871,China; [email protected] Kavli Institute for Astronomy and Astrophysics, Peking Uni-versity, Beijing 100871, China Departamento de Astronom´ıa y Astrof´ısica, Pontificia Univer-sidad Cat´olica de Chile, Casilla 306, Santiago 22, Chile Harvard-Smithsonian Center for Astrophysics, 60 Garden St.,Cambridge, MA 02138 Herzberg Institute of Astrophysics, National Research Coun-cil of Canada, 5071 West Saanich Road, Victoria, BC V9E 2E7,Canada European Southern Observatory, Alonso de Cordova 3107, Vi-tacura, Santiago, Chile Department of Physics and Astronomy, McMaster University,Hamilton, ON L8S 4M1, Canada Department of Physics and Astronomy, Johns Hopkins Univer-sity, Baltimore, MD 21218 individ-ual metal-poor GCs and their masses (Harris et al. 2006;Strader et al. 2006; Mieske et al. 2006; Spitler et al. 2006;Forte et al. 2007; Cantiello, Blakeslee & Raimondo 2007;Lee et al. 2008; Wehner et al. 2008). This discovery,mainly in the GC systems of massive early-type galaxies,runs counter to the previously held conventional wisdomthat individual GCs do not lie on a mass-metallicity re-lation. Because of their low masses, it is not expectedthat GCs would be able to self-enrich via successive gen-erations of star formation in the way that galaxies do.Recently, however, high-quality color-magnitude dia-grams of some Galactic GCs and LMC star clusters showevidence of multiple stellar populations (e.g. Piotto et al.2007), provoking theoretical work on how star clustersmight be able to retain gas and form successive gener-ations of stars (D’Ercole et al. 2008; Strader & Smith2008; Bailin & Harris 2009). A mass-metallicity relationin metal-poor GCs is also interesting when viewed along-side the mass-metallicity relation for dwarf spheroidalgalaxies (dSphs) in the Local Group (Kirby et al. 2008).Despite their very different structure, GCs and dSphshave similar stellar masses. The brightest metal-poorGCs also appear to overlap in parameter space withobjects that have been dubbed Ultra-Compact Dwarfs(UCDs) or Dwarf-Globular Transition Objects (DGTOs)(e.g. Ha¸segan et al. 2005, Mieske et al. 2008). How it isthat metal-poor GCs fit into the early epochs of galaxy Peng et al.growth, and what their relation is to dwarf galaxies, isstill unclear.The question of whether or not metal-poor GCs lieon a color-magnitude (i.e. mass-metallicity relation) thushas important implications for star cluster and galaxyformation. However, because the relationship betweenmetallicity and optical color is very steep at low metal-licities, discerning this relationship requires high qual-ity data, many GCs, and preferably a large wavelengthbaseline. There have been many independent detectionsof the metal-poor GC color-magnitude relation using avariety of data sets in a number of different galaxies (seereferences above), but a recent paper that analyzes deeparchival
HST imaging (Waters et al. 2009) claims notto find any significant color-magnitude relation in theVirgo cD galaxy M87 (NGC 4486), a galaxy in whichtwo different groups have reported a detection with shal-lower HST data (Mieske et al. 2006; Strader et al. 2006(hereafter S06)), and one group with ground-based data(Forte et al. 2007). Given that M87 represents possi-bly the best combination of proximity and GC numbersfor such a study (McLaughlin 1999; Tamura et al. 2006;Peng et al. 2008), it is important to establish definitivelywhether or not the metal-poor GCs in M87 possess asignificant relationship between color and magnitude.In this paper, we perform an independent analysis ofthe same data set as used by Waters et al. (2009). Most ofthe techniques used for this paper were first described inthe analysis of the ACS Virgo Cluster Survey (ACSVCS;Cˆot´e et al. 2004), particularly for much of the data reduc-tion and catalog generation (Jord´an et al. 2004; Jord´anet al. 2005; Jord´an et al. 2009), and the analysis of thecolor-magnitude relation of blue GCs (Mieske et al. 2006;hereafter ACSVCS XIV). We refer the reader to thesepapers for a more thorough description of our methods. OBSERVATIONS AND DATA REDUCTION
M87 was observed for 50 orbits with the ACS WideField Channel (WFC) in the F606W ( V ) and F814W( I ) filters for a microlens monitoring program ( HST
GO Program 10543, PI Baltz). In all, there were 49usable exposures in F606W and 205 in F814W. Weprocessed these images using the Apsis ACS IDT datapipeline (Blakeslee et al. 2003) to produce summed,geometrically corrected, cosmic ray cleaned images foreach bandpass. Apsis measures the offsets and rota-tions of each individual exposure with respect to a mas-ter catalog that it iteratively constructs from the in-put images. It then uses the measured offsets and ro-tations to combine the images using the Drizzle soft-ware (Fruchter & Hook 2002). For this analysis, we usedthe Gaussian interpolation kernel and an output imagescale of 0 . ′′
035 pix − , thus taking advantage of the verylarge number of dithered exposures to improve the fi-nal resolution. We initially processed the images using pixfrac = 1 . pixfrac = 0 .
5, and although the PSF FWHMwas 10% narrower for the latter case, the differences infitted magnitudes and sizes were completely negligible.Total exposure times for the combined images are 24500 sin F606W and 73800 s in F814W.We assume a distance to the Virgo cluster of 16.5 Mpc(Tonry et al. 2001) with a distance modulus of 31 . ± .
03 mag from Tonry et al. (2001), corrected by the fi-nal results of the Key Project distances (Freedman et al.2001; see discussion in Mei et al. 2005b). The SBF dis-tance to M87 itself is consistent with the galaxy beingat the center of the Virgo cluster (Blakeslee et al. 2009).At this distance, one pixel in the final image thereforecorresponds to 2.80 pc.The M87 halo light dominates the image. In order toobtain accurate photometry of the GC population, wefirst model and remove this light using the elliprof software developed for the SBF survey of Tonry et al.(1997; see also Jord´an et al. 2004). Briefly, elliprof iteratively fits a series of ellipses of varying centers, ellip-ticities, position angles, and Fourier component pertur-bations to the galaxy light distribution. Once the fit hasconverged, it interpolates to construct a smooth model,which we subtract from the image. Figure 1 shows thecentral 1 ′ × ′ portion of the F814W image before andafter model subtraction. THE PHOTOMETRIC CATALOG
Detection and Photometry
Detection was performed with SExtractor (Bertin &Arnouts 1996) on the model subtracted images using aprocedure similar to that described in Jordan et al. (2004;ACSVCS II), including the removal of large-scale modelresiduals with SExtractor as described there. Object de-tection on the final subtracted image was performed us-ing a detection threshold of five connected pixels at a10 σ significance level. The depth of the data is such thatthis high threshold still allows the detection of the greatmajority of GCs present in the field of view, while at thesame time avoiding the detection of SBF and other real,albeit much fainter features. The detections in both theF606W and F814W images were finally matched using amatching radius of 0 . ′′ ǫ ≡ a/b , mea-sured in the F606W and F814W filters to be h ǫ i ≥ I .
21. Our catalog has 2459 GCcandidates after rejecting elongated sources. The sourcesleft at this stage are run through KINGPHOT (Jordanet al. 2005), a code that measures structural and pho-tometric parameters by fitting the two-dimensional ACSsurface brightness profiles with PSF-convolved isotropic,single-mass King (1966) models.PSFs for the F606W and F814W bands were obtainedby drizzling the position-dependent set of PSFs con-structed by Anderson & King (2006). The Anderson &King (2006) PSFs are meant to be used on the geometri-cally distorted ACS chips, so they should be drizzled inthe same fashion as the actual data in order to be used onre-sampled, drizzled frames. Reproducing the kernel and pixfrac used is important to determine accurate sizes.In order to measure the structural parameters, we useda fitting radius of 6 pixels (0 . ′′ c , and half-light radius,olor-Magnitude Relation for M87 Metal-Poor GCs 3 Fig. 1.— (Left) The central 1 ′ × ′ of our reduced F814W image. (Right) The same field after the subtraction of a smooth model. Thepoint sources are nearly all globular clusters. Larsen ( V − I) A C S ( V − I) Fig. 2.— (a, left) A comparison between our ( V – I ) photometry(y-axis) and the WFPC2 ( V – I ) photometry of Larsen et al. (2001,x-axis). Black points have σ ( V − I ) ,Larsen < .
05 and gray pointshave errors in the Larsen et al. photometry larger than 0.05 mag.The solid line has slope of unity, while the dashed line is a robustlinear bisector fit to the black points. (b, right) A comparisonbetween our ( V – I ) photometry and the ( g – z ) photometry fromthe ACSVCS. Black and gray points are those with σ ( g − z ) lessthan and greater than 0.05 mag, respectively. The line is a robustlinear bisector fit to the black points. r h in both bandpasses. Note that these magnitudes al-ready include the effect of size. As described in Jordanet al. (2009; ACSVCS Catalogs Paper), the magnitudesstill require an aperture correction due to the fact thatthe PSFs used to fit the data do not extend far enough toinclude all of the light. We used a method identical to theone described in Jordan et al. (2009) to obtain aperturecorrections using mean PSFs constructed up to a radiusof 3 ′′ and used in Sirianni et al (2005) to derive aperturecorrections. Because the magnitudes derived by KING-PHOT already include the effects of the different sizeof each source, the aperture corrections ( A ) are roughlyconstant with r h , and have values of A F606W ≈ .
07 magand A F814 ≈ .
06 mag (we use the measured r h for eachobject, averaged on both bands, to apply the aperturecorrection that applies to that size). Magnitudes werede-reddened using a value of E ( B − V ) = 0 .
023 obtainedfrom the the DIRBE maps of Schlegel et al (1998) andextinction ratios appropriate for a G2 star as presentedin Sirianni et al (2005).To produce our final sample of GCs, we rejected all h (Deep) [pc]110 r h ( A C S V C S ) [ p c ] Fig. 3.—
A comparison between half-light radii ( r h ) measuredin the single-orbit ACSVCS data and r h measured in the deepF606W and F814W ACS images used in this study. Measurementsof the same objects in these two independent data sets agree verywell within the expected errors, showing that the ACSVCS dataprovides the necessary depth and resolution to measure GC sizesat Virgo distance. The dotted line represents a slope of unity. Theslight offset from unity of 0 .
26 pc, which equals 3 milliarcsecondsor less than one tenth of a pixel, is within the expected error fromPSF systematics. objects with magnitude errors greater than 0.5 mag ineither band (116 objects), or with measured half-lightradii larger than 10 pc (140 objects). Nearly all bonafide GCs, which have a mean half-light radius of 2.7 pc(Jord´an et al. 2005), will qualify under this size criterion.In order to make sure, however, that this cut does notaffect our results, we used KINGPHOT to specially fita subset of the extended objects. Because of our in-tial choice of fitting radius, sources with r h >
10 pchave unreliable measurements (see Jord´an et al. 2005for a description of the biases that may arise whenthe fitting radius is less than ∼ r h ). We se-lected the 24 extended objects with I <
22 mag and Peng et al.
TABLE 1Positions and KINGPHOT photometry for M87 GCs
ID RA(J2000) Dec(J2000)
V σ V I σ I (mag)1 187.7432637 12.4052854 25.793 0.034 24.574 0.0512 187.7371764 12.3819827 23.703 0.012 22.696 0.0183 187.7341900 12.3709317 23.293 0.008 22.342 0.0144 187.7331924 12.3676597 22.327 0.019 21.255 0.0225 187.7340066 12.3707719 23.047 0.009 21.927 0.014 Note . — The complete version of this table is in the electronicedition of the Journal. . < ( V − I ) < . V and I is not altogether advisable, as this conversiondepends on the spectrum of the sources, but is neces-sary for comparison purposes. We converted magnitudesto V and I by using the relation between ( V − I ) and( m F606W − m F814W ) presented in Equation (3) of De-Graaff et al (2007), namely ( V − I ) = 1 . m F606W − m F814W ) + 0 .
06, and the following equation from Ta-ble 22 in Sirianni et al., I = m F814W , OBMAG + 25 . − . V − I ) (see discussion in DeGraaff et al. as to whyour adopted color transformation is preferred to eitherthe observed or synthetic transformations presented inSirianni et al; the relation between I and m F814W is lessproblematic, with the observed and synthetic transfor-mations presented in Sirianni et al. being almost identi-cal).The full table of 2250 GC positions and KINGPHOT V and I photometry is presented in Table 1. We set thezeropoint of the astrometry to the International CelestialReference Frame (ICRF; Fey et al. 2004). We did this byfirst matching 1579 matched GCs with the ACSVCS cat-alog and determining the median offsets between the twocatalogs in RA and Dec, both of which were less than 1 ′′ .The dispersion about the median offset between the twocatalogs was very small ( σ = 0 . ′′ ). We then calibratethe astrometry directly to the ICRF by measuring theposition of the nucleus of M87 in the ACSVCS F475Wimage, and compare it to the position measured by Feyet al. (2004) using very long baseline interferometry radioobservations. Photometric and Size Comparisons I Fig. 4.—
The V – I color-magnitude diagram of 2250 M87 glob-ular clusters (dots). Overplotted as diamonds are 18 objectswith r h >
10 pc, some of which are confirmed UCDs or DGTOs(Ha¸segan et al. 2005). Excluding these more extended objects fromour analysis has a no impact on our results.
Because the quality of the photometry is one of thecore issues for this analysis, we present comparisonsbetween this photometry and those from two previousstudies. First, we compare to the V and I photome-try from the deep HST/WFPC2 study of Larsen et al.(2001). This study used the F555W and F814W fil-ters and transformed to V and I . We matched 757 ob-jects between the two catalogs that were within a ra-dius of 0 . ′′
2. The WFPC2 field of view is smaller thanthat of ACS/WFC, and contains fewer objects overall.Figure 2a shows the comparison between the two pho-tometric catalogs. We fit the objects with low error( σ ( V − I ) Larsen < .
05 mag) with a robust linear bisec-tor to obtain ( V − I ) ACS = 0 .
015 + 0 . V − I ) Larsen ,a relation that very nearly has a slope of unity, show-ing that our photometry is consistent with that from theLarsen et al. (2001) study.Next, we compare to the ACS F475W and F850LP(hereafter g and z ) photometry from the ACSVCS. Fig-ure 2b shows this comparison using a matched cata-log between the two data sets created with a matchingradius of 0 . ′′
1. The ( V – I ) and ( g – z ) colors are well-correlated, and a robust linear bisector fit to the highsignal-to-noise data ( σ ( g − z ) < .
05) produces the rela-tion ( V − I ) = 0 .
944 + 0 . { ( g − z ) − } (normalized to( g − z ) = 1 for convenience). This is nearly identical tothe relation fit by Peng et al. (2006b). Again, the shal-lower and deeper data are consistent within the internaluncertainties of both data sets.Lastly, we compare the measured half-light radii, r h be-tween the ACSVCS data and the much higher signal-to-noise ACS data in this study. The ability to measure thesizes of the GCs is not only scientifically interesting in itsown right, but is critical for photometry because the mag-nitudes are affected by the derived r h . Figure 3 showsthe comparison between r h measured independently inthe two data sets. We find that there is excellent corre-lation and agreement between half-light radii measuredin the shallower ACSVCS data and those measured inthe current deep ACS data for the same objects. Thereolor-Magnitude Relation for M87 Metal-Poor GCs 5 Fig. 5.—
Color-magnitude diagram of M87’s GC system from the deep HST imaging set. KMM fit results are indicated, analogous toFigures 1 and 2 of ACSVCS XIV. Left panel corresponds to a luminosity bin size of N=150, right panel to N=100. We fit a linear relation tothe KMM blue peak position. The dashed lines indicate fit to data points with − < M I < − . < I < . is a slight offset of median 0.26 pc between the measuredradii, which is consistent with the expected systematicuncertainty from the different PSFs used in the differentfilters. This offset is equal to 0 . ′′
003 on the sky, or lessthan 0.1 pixels on the ACS/WFC detector. Both Kundu(2008) and Waters et al. (2009) claim that the single-orbit ACSVCS data might not be deep enough for anaccurate measure of GC size, but Jord´an et al. (2005) al-ready used simulations to show that accurate sizes can bemeasured in the ACSVCS data, and we now confirm thisempirically using the deeper data in the present study. THE GC COLOR-MAGNITUDE DIAGRAM AND FITTEDRELATIONS
Fitting the Color-Magnitude Relations
In Figure 4 we present the ( V – I ) M87 globular clustercolor-magnitude diagram (CMD). The two color subpop-ulations, blue and red, are clearly visible, with a divisionaround ( V – I ) ≈ .
05. The typical error in ( V – I ) for GCswith I < .
5, is σ ( V − I ) < .
02 mag. We have alsooverplotted the 18 extended objects with r h >
10 pcto show where they lie in the CMD. The brightest fiveobjects with colors similar to the metal-poor GCs areUCD/DGTOs identified by Ha¸segan et al. (2005). Thefollowing analysis does not include the extended objects,although we have performed the analysis on the com-bined sample and find virtually no difference in the re-sults.We analyzed the luminosity dependence of the GCcolors in this CMD in an identical fashion as inACSVCS XIV. In brief, we apply the heteroscedasticmode of
KMM to the CMD, subdivided into luminos-ity bins containing the same number of data points. Weuse two different bin sizes of N=100 and N=150 to quan-tify how much the result depends on the specific binningchosen. The fitted mean positions of the blue and redpeaks are plotted over the respective CMDs in Figure 5,as a function of magnitude. Apart from varying the bin size, we also choose two different pairs of initial guessesfor the blue and red peak: ( V – I )= 0 . V – I )= 1 . − < M I < − . . < I < . KMM peakpositions for all pairs of initial guesses, bin sizes and lim-iting magnitudes.For each bin size, the slope γ I = d ( V − I ) dI is adoptedas the mean of the value derived from the two pairs ofinitial guesses. The errors of the fit are derived from re-sampling the points using the observed scatter aroundthe fitted relation for the dispersion. The difference be-tween the slopes derived from peak positions of the twodifferent initial guesses was negligible compared to theformal fit errors. In Table 2 we give the resulting val-ues of the slope γ I for both the blue and red peak, forthe two bin sizes, and for the average of the two. In theend, the fitted value for the slope is robust to the exactchoice of bin size. For the remainder of this paper, weuse the average γ I of the fits in the two bin sizes, giving γ I, blue = − . ± . γ I, red = +0 . ± . γ I, blue by0.001, which is much smaller than the uncertainty. Wehave also checked the color-magnitude diagram using theSExtractor mag auto aperture photometry to make surethat the color-magnitude relation is not affected by ourGC selection in general. Of the objects rejected by thesize criterion, nearly all are either too faint ( I > . V − I ) > .
1) to impact our analysis of themetal-poor GCs. We have performed our analysis includ-ing all sources that make our initial SExtractor detectionthreshold, and find that doing so does not change ourconclusions.We emphasize that these observations are extremelydeep, and that the scatter in the color-magnitude dia-gram is caused by physical variations in color, not by Peng et al.
TABLE 2Color-magnitude trends for blue and red globularclusters belonging to M87, determined with
KMM fits
Sample γ I, blue γ I, red N=100, M I,faint = − . − . ± . . ± . M I,faint = − . − . ± . . ± . Average − . ± . . ± . γ I = d ( V − I ) dI of theblue and red GC subpopulations, as derived from linear fitsto KMM determined peak positions (see text and caption ofFigure 5). Errors are from random resampling of the datapoints using their measured dispersion around the fit. photometric error. Therefore, the uncertainty in themeasurement of the color-magnitude relation is intrin-sic to the population of GCs, and cannot be improvedwithout more GCs.
The Slope Dependence on Limiting Magnitudes
We also investigate this dependence of the slope onlimiting magnitudes in order to find the luminosity rangeover which the correlation is most prevalent. There havebeen previous suggestions that the slope in the blue GCsis more strongly defined by the more luminous GCs (Har-ris et al. 2006; Harris 2009). We quantify this more di-rectly by performing our analysis using a range of faintand bright limiting magnitudes.In Figure 6, we fit the blue GCs in the same way asdescribed above, but varying the faint magnitude cutwithin the range − . < M I < − .
5, in steps of 0.1 mag.These fits show that the slope is consistently at thesame value when fitting only the brightest GCs and isat maximum significance when the blue GC faint limit is M I < − .
8. This corresponds to a luminosity 1.1 magfainter than the Gaussian mean of the GC luminosityfunction for blue, metal-poor GCs, and 0.8 mag fainterthan the GCLF turnover for all GCs (see Appendix A).In Figure 7, we fit the blue GCs in the same wayas described above, but varying the bright magnitudecut within the range − . < M I < − .
0, in steps of0.2 mag. In this figure, the fitted slope rapidly declinesas the most luminous GCs are excluded from the fit. Itis clear that slope is driven by the bright blue GCs with M I . − M I = − .
8, about 1 mag below the Gaus-sian mean of the blue GCLF. The metal-rich GCs possessno significant slope. DISCUSSION
Comparisons to Previous Estimates
There have now been many estimates of the slope ofthe metal-poor GC color-magnitude relation, but theyhave often been done in different filter systems with dif-ferent instruments. More importantly, these slopes are
Fig. 6.—
We show the fitted slope ( γ I ) as a function of thefaint end limiting magnitude of the metal-poor GCS used in thefit ( M I,cut,faint ). We find that the color-magnitude relation has asimilar slope for all samples down to M I,cut,faint ≈ − . Fig. 7.—
We show the fitted slope ( γ I ) as a function of thebright end limiting magnitude of the metal-poor GCS used in thefit ( M I,cut,bright ). We find that the color-magnitude relation isdriven by the most luminous GCs, or those with M I . −
10. Forthis plot, we assumed M I,cut,faint = − . usually transformed into a mass-metallicity relation us-ing a metallicity-color relation derived from either Galac-tic GCs or stellar population synthesis models. Althoughtransforming to physical quantities is important for un-derstanding the ultimate origin of this phenomenon, westress that for comparisons between different studies it isthe slopes in observed quantities (color and magnitude)that should be compared rather than in the transformedquantities (metallicity and mass). This is for the sim-ple reason that transformations between different filtersets and colors are much more precisely known than thetransformation from color to metallicity. Direct compar-olor-Magnitude Relation for M87 Metal-Poor GCs 7isons in mass-metallicity space that do not take this intoaccount can produce misleading results, as we will de-scribe below for the case of Waters et al. (2009).The fits in ACSVCS XIV used a limiting magnitudeof M z = − .
7, which closely matches a magnitude limitof M I = − . gz photometry is on the AB sys-tem while V I is VEGAMAG). Thus, for the purposesof our comparison, we will use the average of the mea-sured slope values fitted to samples with a limiting mag-nitude of M I = − .
8, which is γ I = − . γ z = d ( g − z ) dz = − . ± . γ z = − . ± . V and I bandpasses used for this study? We have alreadyabove in Section 3.2 matched 1637 objects in commonbetween our current catalog and the ACSVCS catalogfor M87. The fit between V – I and g − z presentedabove for these objects yields a slope of 0.534. Likewise, I = z − .
342 + 0 . g − z ). Therefore, to transformfrom γ z to γ I we use the relation: γ I = γ z d ( V − I ) d ( g − z ) dzdI = γ z × . . γ z (1)For γ z = − . ± .
015 from ACSVCS XIV, we thereforeexpect γ I = − . ± . γ I = − . ± . g and z imaging is perfectly consistent with that derived fromthe deep, 50-orbit V and I observations analyzedhere. m − m versus g − z : Depth, WavelengthBaseline, and the Color-Magnitude Relation The advantage of the ACS data analyzed in this pa-per and in Waters et al. (2009) is the unparalleled depthcompared to other imaging of M87. However, for thepurpose of detecting a mass-metallicity relation in themetal-poor GCs, this data has the singular disadvantageof a short wavelength baseline. Because the filters areF606W and F814W, the baseline is shorter than eventhe traditional V and I to which the instrumental colorsare transformed. Given the transformations used in thispaper ( m − m ) ∝ . g − z ). Thus, the errorsin ( m − m ) need to be 0.445 times smaller than in( g – z ) to achieve the same metallicity sensitivity, corre-sponding to a higher S/N by a factor of 2.25. In the caseof the observations used here, the median ratio betweenthe error in ( m – m ) and the ACSVCS error in ( g – z ) for objects in common is 0.229. These observationsare thus in principle between 1.7 and 2 times more sensi-tive to metallicity than the ACSVCS observations untilscatter in the color become dominated by systematic er-ror at the bright end, or by the intrinsic scatter in coloramong GCs (the latter is the case for our observations).Although the ratio of HST orbits is 50:1, the short wave-length baseline of the filters used and the intrinsic scatterof color among GCs explains why these observations arenot nearly as much of an improvement over the ACSVCSas one might initially expect.
The Discrepancy with Waters et al. (2009)
The main conclusion of Waters et al. (2009) was thatthey did not detect a color-magnitude relation for themetal-poor GCs in M87 using deeper imaging than hadpreviously been analyzed. In this paper, however, wehave performed an independent analysis and reductionof the same archival data, and we find a color-magnituderelation with the exact slope expected from the resultsof ACSVCS XIV and S06. In this section, we makethree comments on the claims, results, and methodologyadopted by Waters et al. (2009).
The Color-Magnitude Relation of Blue GCs is not anObservational Artifact.
Both Waters et al. (2009) and Kundu (2008) make theargument that the color-magnitude relation previouslydetected for blue GCs is due to improperly performingstandard aperture photometry of resolved GCs. The ba-sic claim is that if metal-poor GCs have a size-luminosityrelation where more luminous GCs are larger, then ap-plying a single aperture correction to all objects leads tobiases in color that correlate with magnitude. This claimis can be disproven in three ways.First, both this study and the ACSVCS XIV studyof the GC color-magnitude relation use photometry that always explicitly take into account the size of the GC . Asexplained above, and in Jord´an et al. (2005, 2009), weuse model magnitudes derived from PSF-convolved Kingmodel fits.Second, Kundu (2008) and Waters et al. (2009) fur-ther claim that the ACSVCS data is not deep enoughto measure the sizes of GCs at Virgo distance. As hasbeen shown using simulations (Jord´an et al. 2005) andnow comparing to the deep ACS data analyzed in thispaper, reliable sizes and photometry can in fact be de-rived from the shallower ACSVCS data used as the basisfor previous detections of the blue GC color-magnituderelation. Moreover, the scatter in the size-luminosity re-lation for GCs is much more important than its slope,which is shallow and only relevant for the highest lumi-nosity GCs.Third, a simple test shows that even if one were toperform standard aperture photometry on resolved GCsof different sizes, the resulting bias in color is much toosmall to create the observed color-magnitude relation.Jord´an et al. (2009) performed simple 4 pixel radius aper-ture photometry on PSF-convolved King models with arange of sizes. They found that although the total fluxof GCs can be significantly underestimated for r h > < r h <
30 pc, the ( g – z ) aperture correction deviates byonly +0 . − . from the r h = 3 pc fiducial. For this kindof simple photometry, the different sizes of the PSFsin F475W and F850LP indeed cause the measured ( g – z ) color to become increasingly biased to the red upto a maximum of 0.004 mag at r h ∼ reverses direction and the mea-sured GC colors start becoming biased to the blue. Thiscan be explained because for larger sizes, we enter theregime where the size difference between the PSFs inthe two filters are small compared to the size of the GC(10 pc ∼ . ′′
125 at Virgo). Therefore, even for simple4-pixel aperture photometry, there is no conspiracy be- Peng et al.tween size and magnitude that can artificially producethe color-magnitude relation in the blue GCs. This ex-plains how slopes determined from different studies —those accounting for GC size (ACSVCS XIV, this pa-per), or simply applying an average aperture correction(S06), or with galaxies at different distances (Harris et al.2006), or with data from the ground where GCs are un-resolved (e.g. Forte et al. 2007; Wehner et al. 2008) —all find similar results. (See also a discussion on aperturecorrections in Harris 2009; Harris et al. 2009).
The Color-Magnitude Diagram of Waters et al.(2009) shows Significant Scatter.
Despite the high signal-to-noise of these deep ACSF606W and F814W observations, the M87 GC color-magnitude diagram presented in Figure 2 of Waters et al.(2009) appears to contain a large amount of scatter. Thisis in contrast to the CMD presented in this paper whichuses the same data (Figure 4), as well as the ( g – z ) CMDsin Figure 1 of ACSVCS XIV, and in Figure 4 of S06. Inparticular, we draw the reader’s attention to the manybright blue sources in the Waters et al. CMD, those with I <
22 and ( V − I ) < .
9, of which there are at least46 shown. By contrast, our catalog generated from thesame imaging contains only 2 objects (6 before the var-ious cuts described in Section 3.1) in the equivalent re-gion (
I <
22 and ( V − I ) < .
8, because we adopt theDeGraaff et al. (2007) transformation for V and I as op-posed to the one from Sirianni et al. (2005), resulting ina ∼ . V − I ) > .
3. Given theshort wavelength baseline of this filter set, any increasein the photometric scatter would make it extremely diffi-cult to detect a color-magnitude relation in the blue GCsof γ I ≈ . The Importance of Comparing Color-MagnitudeRelations Instead of Mass-Metallicity Relations.
There are many transformations between GC color andmetallicity in the literature, based on different data sets.Most studies either derive an empirical relation from theknown colors and metallicities of Galactic globular clus-ters, or they use models of simple stellar populations.What has become clear over the years is that the relation-ship between optical color and metallicity for old stellarpopulations is nonlinear, and becomes increasingly steepfor metal-poor objects ([Fe/H] . −
1) (Cohen et al. 2003,Peng et al. 2006a, Cantiello & Blakeslee 2007). This isexactly the color and metallicity regime with which weare concerned in this paper and in all studies of metal-poor GCs. Although it is necessary and even desirable to trans-form color-magnitude relations into mass-metallicity re-lations, it is important that observational comparisons bedone directly , rather than through the minefield of dif-ferent metallicity-color relations. Waters et al. (2009) donot compare colors directly, but instead attempt to sim-ulate slopes in their data starting with mass-metallicityrelations. The [Fe/H]–( V – I ) relationship assumed byWaters et al. (2009), however, is inconsistent with the[Fe/H]–( g – z ) relations assumed in ACSVCS XIV andS06; ( V – I ) is less sensitive than to [Fe/H] than ( g – z ),particularly at low metallicity. This leads Waters et al.to conclude that the expected slope would be much moreeasily seen in their data than it actually is. Furthermore,their simulated CMD takes the brighter GCs as fixed andoffsets GCs with I >
20 to the blue. If they had insteadfixed the GCs around the GCLF turnover and then off-set brighter (
I <
23) GCs to the red the expected trendwould be more difficult to detect. As a result, they gener-ate a large gap between the blue and red GC populationsthat, in their Figure 3a, bears no resemblance to a realCMD. If previous authors had observed such a CMD toderive a color-magnitude relation, there would be littleargument about its existence. The simulations of Mieskeet al. (2006), which were performed in color space alone,are better suited to testing the sensitivity of observationsto any color-magnitude relation.
Substructure in the Color-Magnitude Diagram
Having established the existence of a color-magnituderelation for metal-poor GCs, it is still not clear whatits underlying cause might be. The high photometricaccuracy of this data set, however, shows some tantaliz-ing hints at substructure in the color-magnitude diagramshown in Figure 4, especially in the blue GCs. Whilethere is an obvious ridge of blue GCs that appears to bedriving the color-magnitude relation for 21 < I < V − I ) ≈ . I ≈ .
5. Given the precarious-ness of transforming from broadband color to metallicityfor stellar populations with [Fe/H] . − CONCLUSIONS
We present an analysis of the color-magnitude dia-gram and luminosity functions for globular clusters in theVirgo cD galaxy, M87, using deep, archival
HST/ACS imaging in the F606W and F814W filters. We report anindependent detection at high significance (4 σ ) of a color-magnitude relation for the blue GCs, which was previ-ously reported for this galaxy using shallower data fromthe ACSVCS (Mieske et al. 2006; S06). The measuredslope in ( V – I ) is entirely consistent with the previouslypublished values in ( g – z ). This finding is contrary to arecent independent reduction and analysis of the samedeep archival data by Waters et al. (2009) who claim tofind no relation.We fit the color-magnitude relation for a range of faintand bright limiting magnitudes, M I , to test the idea thatolor-Magnitude Relation for M87 Metal-Poor GCs 9the bright GCs drive the relation. We find that theslope is driven by GCs brighter than M I ≈ −
10, andis most significant for samples including GCs brighterthan M I = − .
8, or 1 mag fainter than the mean ofthe blue GCLF, or 0.8 mag fainter than the mean ofthe total GCLF. This suggests that there is a mass scaleat which the correlation between mass and metallicitybegins, and is qualitatively consistent with a scenariowhere self-enrichment drives the relation (Bailin & Har-ris 2009).All of our photometry is performed using the Kingmodel fitter, KINGPHOT (Jord´an et al. 2005), and ex-plicitly takes into account the size of each object. Weshow that the half-light radii previously measured usingKINGPHOT on the shallower ACSVCS data in Jord´anet al. (2005) are well-correlated with the new, more ac-curate measurements.We explain that the color-magnitude relation seen inthe metal-poor GCs cannot be an observational arti-fact involving aperture corrections, as argued by Kundu(2008) and Waters et al. (2009). All of our photometry explicitly uses the fitted size of the object to derive totalmagnitudes and colors. We also show that even if onewere to use a fixed aperture correction for all GCs (as inS06 and Harris et al. 2006), the magnitude of the bias ismuch too small to create the observed color-magnituderelations.We thank Søren Larsen for sharing his
HST/WFPC2 photometry of M87 GCs. E. W. P. gratefully acknowl-edges the support of the Peking University Hundred Tal-ent Fund (985). A. J. acknowledges support from theChilean Center of Excellence in Astrophysics and Asso-ciated Technologies, and from the Chilean Center for As-trophysics FONDAP 15010003. This research has madeuse of the NASA/IPAC Extragalactic Database (NED)which is operated by the Jet Propulsion Laboratory, Cal-ifornia Institute of Technology, under contract with theNational Aeronautics and Space Administration.Facilities: HST(ACS,WFPC2)
APPENDIX
THE GC LUMINOSITY FUNCTIONS OF M87 GC POPULATIONS
The quality and completeness of our photometry also allows us to fit the luminosity function of the M87 GCs. Thecolor-magnitude diagram in Figure 4 hints that the luminosity functions of the blue and red GC subpopulations havedifferent means and widths. We quantify this by fitting the I -band luminosity functions of the GC subpopulationswith two different functions: a Gaussian and an evolved Schechter function (see Jord´an et al. 2007). We fit onlyGCs with I <
24 mag, a limit above which neither contamination nor completeness is a problem, but which is still & σ fainter than the mean in a Gaussian parametrization. We divide blue from red GCs at ( V − I ) = 1 .
04, thecolor at which a GC is equally likely to belong either to the blue or red subpopulation according to a double Gaussianhomoscedastic fit using the Kaye’s Mixture Model (KMM; McLachlan & Basford 1988; Ashman, Bird, & Zepf 1994).The results of our fits are presented in Table 3, and the luminosity distributions with fits are shown in Figure 8. Wenote that although we have plotted the GC magnitude distributions in bins, the fits were performed on the unbinneddata using maximum likelihood estimation. There appears to be an excess of faint objects at
I >
24 mag which arelikely to be compact background galaxies.The best-fit Gaussian parameters of the total population are µ I = 22 . ± .
05 and σ = 1 . ± .
04. This is nearlyidentical to the measurement by Kundu et al. (1999) of µ I,K = 22 . ± .
06 and σ I,K = 1 . ± .
11. Using adistance to M87 of 16.5 Mpc ( m − M = 31 . µ M I = − . ± .
05 mag.The Gaussian mean of the blue GC subpopulation is expected to be brighter than that of the red GC subpopulatonif the GC mass function is universal across metallicity (e.g., Ashman, Conti, & Zepf 1995; Puzia et al. 1999; Jord´anet al. 2002; Jord´an et al. 2007). When fitting the individual subpopulations, we find that µ I,blue = 22 . ± .
06 magand µ I,red = 22 . ± .
09 mag (or µ M I = − .
85 mag and − .
32 mag, respectively). This difference, µ I,blue − µ I,red = − .
43 mag, is consistent with what Puzia et al. (1999) find for the GC system of M49.The Gaussian widths of the GCLFs for the two subpopulations are also different. We measure σ I,blue = 1 . ± .
05 mag and σ I,red = 1 . ± .
06 mag. The LF of the blue GCs is narrower than that for the red GCs, but is not asnarrow as the mean widths for GCLFs of early-type dwarf galaxies in the Virgo and Fornax clusters, which can have σ ∼ . β = 2, as was done in Jord´an et al. (2007).The evolved Schechter function then has two free parameters, which we represent as m c , the absolute magnitude ofthe exponential “cutoff” associated with the bright end of the Schechter function, and δ , the absolute magnituderepresenting the average mass loss per cluster over a Hubble time (for details, see Jord´an et al. 2007, Section 3.2). Thefitted parameters for all GCs (with I <
24 mag) are m c,I = − . ± .
23 mag and δ I = − . ± .
08 mag. For the blueand red subpopulations, we find that m c,I,blue = − . ± .
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TABLE 3Best-fit parameters for I -band GC Luminosity Functions Sample Gaussian Evolved Schechter µ I µ M I σ I, all m c,I δ I All 22 . ± . − . ± .
05 1 . ± . − . ± . − . ± . . ± . − . ± .
06 1 . ± . − . ± . − . ± . . ± . − . ± .
09 1 . ± . − . ± . − . ± . V − I ) = 1 .
04 mag. Fits are performed onGCs with
I <
24 mag. Absolute magnitudes assume m − M = 31 ..