Nonlinear Color-Metallicity Relations of Globular Clusters. IX. Different Radial Number Density Profiles between Blue and Red Clusters
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NONLINEAR COLOR − METALLICITY RELATIONS OF GLOBULAR CLUSTERS. IX.DIFFERENT RADIAL NUMBER DENSITY PROFILES BETWEEN BLUE AND RED CLUSTERS
Sang-Yoon Lee , Chul Chung ,
1, 2 and Suk-Jin Yoon
1, 2 Center for Galaxy Evolution Research, Yonsei University, Seoul 03722, Republic of Korea Department of Astronomy, Yonsei University, Seoul 03722, Republic of Korea (Accepted for publication in ApJ)
ABSTRACTThe optical colors of globular clusters (GCs) in most large early-type galaxies are bimodal. Blue andred GCs show a sharp difference in the radial profile of their surface number density in the sense thatred GCs are more centrally concentrated than blue GCs. An instant interpretation is that there existtwo distinct GC subsystems having different radial distributions. This view, however, was challengedby a scenario in which, due to the nonlinear nature of the GC metallicity-to-color transformation forold ( (cid:38)
10 Gyr) GCs, a broad unimodal metallicity spread can exhibit a bimodal color distribution.Here we show, by simulating the radial trends in the GC color distributions of the four nearby giantelliptical galaxies (M87, M49, M60, and NGC 1399), that the difference in the radial profile betweenblue and red GCs stems naturally from the metallicity-to-color nonlinearity plus the well-known radialmetallicity gradient of GC systems. The model suggests no or little radial variation in GC age even outto ∼ R eff . Our results provide a simpler solution to the distinct radial profiles of blue and red GCsthat does not necessarily invoke the presence of two GC subsystems and further fortify the nonlinearityscenario for the GC color bimodality phenomenon. Keywords:
Galaxy evolution (594); Giant elliptical galaxies (651); Elliptical galaxies (456); cD galaxies(209); Globular star clusters (656) INTRODUCTIONGlobular clusters (GCs) play a vital role in under-standing the formation process of their host galaxies be-cause GC formation accompanies star-forming episodesof their hosts, and GCs are easier to observe than fieldstars of their hosts. Among others, a well-establishedobservational phenomenon for GCs, the bimodal opticalcolor distributions in early-type galaxies have shed lighton galaxy and GC formation (e.g., Ostrov et al. 1993;Zepf & Ashman 1993; Gebhardt & Kissler-Patig 1999;Kundu & Whitmore 2001; Larsen et al. 2001; Forte etal. 2005, 2012; Harris et al. 2006, 2017; Peng et al. 2006;Lee et al. 2008a; Blakeslee et al. 2010; Faifer et al. 2011;Forbes et al. 2011; Foster et al. 2011; Liu et al. 2011;Blom et al. 2012; Chies-Santos et al. 2012; Cho et al.2012; Kim et al. 2013a; Usher et al. 2013; Cantiello et al.
Corresponding author: Suk-Jin [email protected] a r X i v : . [ a s t r o - ph . GA ] N ov Lee, Chung & Yoon (R/R eff ) l og Σ G C ( a r c m i n − ) −3.0−2.0−1.00.01.02.03.0 M87 (Tamura+06)V−I observation −3.0−2.0−1.00.01.02.03.0 M49 (Lee+98)C−T observation −3.0−2.0−1.00.01.02.03.0 M60 (Lee+08)C−T observation0 1 2 3−3.0−2.0−1.00.01.02.03.0 NGC 1399 (Cantiello+18)g−i observation Figure 1.
Radial surface number density profiles of blue(open circles) and red (filled circles) GCs in the four giantelliptical galaxies. We use data from Tamura et al. (2006) forM87, Lee et al. (1998) for M49, Lee et al. (2008b) for M60,and Cantiello et al. (2018) for NGC 1399. The dashed anddotted lines are fitted to the blue and red GCs, respectively,following the de Vaucouleurs R / law. In relation to the GC color bimodality, a well-knownphenomenon observed in most GC systems is the sys-tematic variation in the GC color histogram morphol-ogy along the galactocentric radius (Geisler et al. 1996;Kundu et al. 1999; Lee & Kim 2000; Dirsch et al. 2003,2005; Forbes et al. 2004, 2011; Bassino et al. 2006;Tamura et al. 2006; Strader et al. 2011; Blom et al. 2012;Kim et al. 2013a; Escudero et al. 2015, 2018; Harris et al.2016; Ennis et al. 2019; Ko et al. 2019; De B´ortoli et al.2020). For most early-type galaxies, the fraction of red(blue) GCs is highest (lowest) at the galactic center anddecreases (increases) with radius. Accordingly, the sur-face number density of red GCs drops faster than thatof blue GCs as the radius increases (Forbes et al. 2004;Forte et al. 2005; Bassino et al. 2006, 2008; Tamura etal. 2006; Harris 2009b; Faifer et al. 2011; Strader et al.2011; Blom et al. 2012; Pota et al. 2013; Usher et al.2013; Cho et al. 2016; Harris et al. 2016, 2017; Escuderoet al. 2018; Ennis et al. 2019; Ko et al. 2019; De B´ortoliet al. 2020). In Figure 1, we show the surface numberdensity profiles of blue and red GCs in the four largestelliptical galaxies (M87, M49, M60, and NGC 1399) inthe Virgo and Fornax galaxy clusters. The blue and redGCs show a sharp difference in the radial profile in thesense that the red GCs are more centrally concentratedthan blue GCs. This has been generally interpreted asthe presence of two subpopulations having distinct spa-tial occupations.As opposed to the popular belief in the existence ofGC subpopulations with different metallicities, Yoon etal. (2006, hereafter Paper I; see also Richtler 2006) of-fered an alternative explanation, in which the primarydriver of color bimodality is the nonlinear nature of thecolor − metallicity relations (CMRs). They showed thatthe CMRs of old ( >
10 Gyr) GC systems are inflected duemainly to helium-burning horizontal branch (HB) stars,and that the color bimodality can be naturally achievedfrom broad, unimodal metallicity distributions by thenonlinear CMRs. In a series of subsequent papers, thenonlinearity scenario was tested both observationallyand theoretically. Yoon et al. (2011b, hereafter PaperII) and Yoon et al. (2013, hereafter Paper IV) revealedusing M87 (Paper II) and M84 (Paper IV) GC systemsthat the degree of the CMR nonlinearity depends on thechoice of colors ( g − z , u − z , and u − g ) and governs theshape of color histograms. Yoon et al. (2011a, hereafterPaper III) demonstrated that the shape of the metal-licity distribution functions (MDFs) of GC systems arecharacterized by a broad, skewed Gaussian function andare similar to MDFs of both halo field stars and galacticchemical evolution models, alleviating the long-standingdiscrepancy between GC and stellar MDFs. Lee et al. UMBER DENSITY PROFILE OF GLOBULAR CLUSTERS Table 1.
Observational Data
Galaxy Telescope Filter N GC a Radial Extension (kpc) b Radial Extension ( R eff ) ReferenceM87 HST gz − − V I − − CT − − gz
765 0.3 − − V I
609 0.0 − − CT − − gz
807 0.1 − − g (cid:48) i (cid:48) − − CT − − gz − − BI − − CT − − Note —The radial extension values correspond to the innermost and the outermost GCs in each catalog. a The number of GCs in the catalog. b We take the distance to each galaxy from Blakeslee et al. (2009). (2019, hereafter Paper VIII) reproduced the GC colordistributions of 78 early-type galaxies in the Virgo andFornax galaxy clusters. They showed that ∼
70 % ofthe GC systems fit into the nonlinearity theory and theremaining ∼
30 % are also consistent with the theoryassuming a young GC population diluting the under-lying color bimodality. The nonlinearity scenario wasfurther explored by using spectroscopic absorption-lineindex distributions as a close analogy to the photomet-ric color distributions (Kim et al. 2013b; Chung et al.2016; Kim & Yoon 2017, Papers V, VI, and VII). Theyshowed that the inflected index − metallicity relations ofGCs account for the observed bimodal absorption-line in-dex distributions of M31 GCs (Paper V) and NGC 5128GCs (Paper VII). In the same vein, Paper VI revisitedthe well-known metallicity proxy, Ca II triplet (CaT)index, and showed that the inflected CaT − metallicityrelation is responsible for the observed CaT bimodal-ity of GCs in elliptical galaxies. Most recently, Kim etal. (2020, hereafter Paper X) obtained the spectroscopicmetallicities of ∼
130 GCs of M87 with Subaru/FOCASand confirmed that the CMRs are nonlinear and theMDF is close to a unimodal distribution.According to the nonlinearity theory, neither the ra-dial variation in the color distribution morphology (i.e.,the relative portions of blue and red GCs) nor the radialdifference in the density profiles of blue and red GCs iscaused by two GC subpopulations occupying differentspatial positions. But instead the both radial behav-iors are originated by a combined effect of the nonlin-ear CMRs plus the systematic change of the mean GCmetallicity with galactocentric radius. In this paper,we put our hypothesis to the test on the origin of the different number density profiles of blue and red GCsin giant elliptical galaxies. This paper is organized asfollows. Section 2 describes the observational databaseused in this study. Section 3 gives descriptions of thestellar population model and the GC color distributionmodel. Section 4 compares between the observationsand our simulations in terms of the radial variations inthe color distribution morphology and the difference inthe surface number density profiles of blue and red GCs.In Section 5, we discuss the implications of our results. OBSERVATIONAL DATA2.1.
Information on Individual GC Systems
We analyze the four largest giant elliptical galaxies (M87, M49, M60, and NGC 1399) in the Virgo and For-nax galaxy clusters. They harbor numerous GCs, forwhich we can examine the radial properties. The GCsystems of the four galaxies have been observed fre-quently, and each galaxy has several photometric cat-alogs. For each galaxy, we choose three GC catalogswith more than 500 GCs, for which color informationalong the radial direction is publicly available. Table 1summarizes the photometric GC datasets used in thisstudy.In Figure 2, we show the colors of individual GCsagainst their galactocentric radii. The criterion for di-viding radial bins is to assign an equal number of GCs toeach bin. The mean colors of blue and red GCs and the We refer to the HyperLeda database (http://leda.univ-lyon1.fr/)for the morphological classification and Liu et al. (2011) for thestellar mass of galaxies.
Lee, Chung & Yoon eff g − z M87
Jordan et al. (2009) 1.0 10.0R/R eff V − I M87
Peng et al. (2009) 1.0 10.0R/R eff C − T M87
Forte et al. (2007)1.0 10.0R/R eff g − z M49
Jordan et al. (2009) 1.0 10.0R/R eff V − I M49
Lee & Kim (2000) 1.0 10.0R/R eff C − T M49
Kim et al. (2006)1.0 10.0R/R eff g − z M60
Jordan et al. (2009) 1.0 10.0R/R eff g ′ − i ′ M60
Faifer et al. (2011) 1.0 10.0R/R eff C − T M60
Lee et al. (2008)1.0 10.0R/R eff g − z NGC 1399
Jordan et al. (2015) 1.0 10.0R/R eff B − I NGC 1399
Kim et al. (2013) 1.0 10.0R/R eff C − T NGC 1399
Forte et al. (2007)
Figure 2.
Colors of individual GCs against the radii for three different observations for each galaxy. The blue and red linesrepresent the mean color of blue and red GCs that are determined by the KMM code in each radial bin. The black lines indicatethe mean colors of the entire GCs. The error bars were obtained by carrying out 1000 bootstrapping iterations. red fractions are determined by the KMM code by Ash-man et al. (1994). The mean colors of blue and red GCstend to be bluer as the radial distance increases, exceptin a few cases (e.g., g − z for M49). In Figure 3, we showthe red GC fractions of our sample galaxies as a func-tion of the galactocentric radius. As is well known, thenumber fraction of red GCs declines with radius (e.g.,Harris et al. 2006, 2017; Kim et al. 2013a). Thus, backin Figure 2, the mean colors of the entire (blue + red) GCs (black lines) show steeper decline than the meancolors of blue GCs (blue lines) or red GCs (red lines).Brief information on each galaxy’s observational datasets is given below.2.1.1. M87 (NGC 4486) g − z : the Advanced Camera for Surveys (ACS) VirgoCluster Survey presents a catalog of GC candidates for100 early-type galaxies (Jord´an et al. 2009). The imag-ing was done by ACS on board the Hubble Space Tele- UMBER DENSITY PROFILE OF GLOBULAR CLUSTERS eff R ed G C f r a c t i on ( g − z ) M87
Jordan et al. (2009) 1.0 10.0R/R eff R ed G C f r a c t i on ( V − I ) M87
Peng et al. (2009) 1.0 10.0R/R eff R ed G C f r a c t i on ( C − T ) M87
Forte et al. (2007)1.0 10.0R/R eff R ed G C f r a c t i on ( g − z ) M49
Jordan et al. (2009) 1.0 10.0R/R eff R ed G C f r a c t i on ( V − I ) M49
Lee & Kim (2000) 1.0 10.0R/R eff R ed G C f r a c t i on ( C − T ) M49
Kim et al. (2006)1.0 10.0R/R eff R ed G C f r a c t i on ( g − z ) M60
Jordan et al. (2009) 1.0 10.0R/R eff R ed G C f r a c t i on ( g ′ − i ′ ) M60
Faifer et al. (2011) 1.0 10.0R/R eff R ed G C f r a c t i on ( C − T ) M60
Lee et al. (2008)1.0 10.0R/R eff R ed G C f r a c t i on ( g − z ) NGC 1399
Jordan et al. (2015) 1.0 10.0R/R eff R ed G C f r a c t i on ( B − I ) NGC 1399
Kim et al. (2013) 1.0 10.0R/R eff R ed G C f r a c t i on ( C − T ) NGC 1399
Forte et al. (2007)
Figure 3.
Same as Figure 2, but for the number fractions of the red GCs for each galaxy. scope (HST), and 12,763 GC candidates in g − z wereobtained in the whole galaxy sample. The field of viewof ACS (202 (cid:48)(cid:48) × (cid:48)(cid:48) ) allows gradient measurements forthe radius of (cid:46) V − I : Peng et al. (2009) constructed a photometriccatalog of M87 GCs with F606W ( V ) and F814W( I ) filters using ACS Wide Field Channel. The radialcoverage of this observation is similar to that of Jord´an et al. (2009). The total number of GC candidates in thiscatalog is 2250. C − T : Forte et al. (2007) presented a Washington C and T photometric catalog of the GC system in M87and NGC 1399. The photometric data were obtainedby 4 m telescopes at Kitt Peak National Observatory(KPNO) and Cerro Tololo Inter-American Observatory(CTIO). The radial coverage of this data is bigger thanthose of the two previous datasets. They defined GCcandidates, which satisfy the color and magnitude cri-teria (0 . < C − T < . . < T < .
2) among
Lee, Chung & Yoon
Table 2.
The Empirical Color–Metallicity Relations [Fe/H]= α + β ( X ) + γ ( X ) X α β γ
Reference B − I − V − I − g (cid:48) − i (cid:48) − g − z − C − T − − Note —The ( g (cid:48) − i (cid:48) ) − [Fe/H] relation is obtained from theoriginal ( g (cid:48) − i (cid:48) ) − [Z/H] relation (Faifer et al. 2011), usingthe equation [Fe/H] = log(Z/Z (cid:12) ) − log(X/X (cid:12) ) − α /Fe]= [Z/H] − α /Fe] = 0.3 (Kim et al. 2002). the photometric sources. The number of GC candidatesin M87 from this catalog is 2933.2.1.2. M49 (NGC 4472) g − z : the data are taken from the ACS Virgo ClusterSurvey catalog like M87 and M60. The number of GCcandidates in M49 is 765. V − I : the observational data were obtained fromHST/WFPC2 (Lee & Kim 2000). This observation wasperformed for the central region ( r < (cid:48) ) of the galaxy.The color and magnitude criteria to select GC candi-dates are 0 . < V − I < .
45 and V ≤ V ≤ . C − T : Geisler et al. (1996) and their follow-up work,Lee et al. (1998), and Kim et al. (2006), presented aWashington C and T photometric catalog of the GCsystem in M49 using the KPNO 4 m telescope. The colorand magnitude criteria to select GC candidates are 1.0 ≤ C − T ≤ ≤ T < . r (cid:46) (cid:48) . 2.1.3. M60 (NGC 4649) g − z : the data are taken from the ACS Virgo ClusterSurvey catalog like M87 and M49. The number of GCcandidates is 807. g (cid:48) − i (cid:48) : Faifer et al. (2011) presented g (cid:48) , r (cid:48) , and i (cid:48) imaging with the Gemini North and South telescopesfor the GC system in M60. The photometric data ontotal 1546 GC candidates were obtained by the criteriaof three-color selection (0.4 ≤ g (cid:48) − i (cid:48) ≤ ≤ g (cid:48) − r (cid:48) ≤ ≤ r (cid:48) − i (cid:48) ≤ ≤ i (cid:48) ≤ (cid:38)
50 % at a magnitude of i (cid:48) = 24.30. C − T : Lee et al. (2008b) presented a photometriccatalog of the GCs in M60, based on wide-field Washing-ton CT images. The imaging was done by the KPNO 4 m telescope and completeness is higher than 90 % for T = 22 .
8. The observation covered 16 (cid:48) . × (cid:48) .
4, whichis the most extensive field for M60. We choose the GCsby the criteria of 1 . < C − T < .
4, 19 . < T < . r > (cid:48) , which were suggested by Lee et al. (2008b).The final number of GC candidates in our sample is1539. 2.1.4. NGC 1399 g − z : the data are taken from the ACS Fornax ClusterSurvey (Jord´an et al. 2015), and the criteria to selectbona fide GCs are the same as the ACS Virgo ClusterSurvey catalog. The total number of GCs is 1075. B − I : Kim et al. (2013a) presented multiband ( U , B , V , and I ) photometry for NGC 1399 GCs with theCTIO 4 m telescope. The field of view (36 (cid:48) × (cid:48) ) of theirobservation covered almost the entire GC system in thisgalaxy. The total number of GC is 2037 with U < C − T : the data are taken from Forte et al. (2007),and the color and magnitude criteria are the same asthe M87 case. The total number of GCs is 1920.2.2. Radial Metallicity Gradients of GC SystemsDerived from Empirical Color–MetallicityRelations
In this study, we adopt the empirical CMRs to deter-mine the mean [Fe/H] of the GC systems of our sam-ple galaxies. Table 2 summarizes the adopted empiricalCMRs and their references.In Figure 4, we present the radial metallicity gradientsof GC systems derived from the empirical CMRs. Theeffective radius ( R eff ) is used as a unit of radii to make acomparison among the four different galaxies. The R eff values of galaxies are obtained from the Third ReferenceCatalog of Bright Galaxies (RC3 ; de Vaucouleurs et al.1991). The metallicities of the GC systems in the fourgalaxies decrease with radius, which is consistent withprevious studies (e.g., Geisler et al. 1996; Kundu et al.1999; Rhode & Zepf 2001). The [Fe/H] gradient for thecombined sample (gray solid line) is best described by[Fe / H] = − .
32 log ( R/R eff ) − . . (1)The mean [Fe/H] of M87 GCs decreases faster along theradial sequence than the least-squares fit to the wholesample. The stronger GC metallicity gradient of M87than the other three galaxies is consistent with the lit-erature (e.g., Liu et al. 2011). https://heasarc.gsfc.nasa.gov/W3Browse/all/rc3.html UMBER DENSITY PROFILE OF GLOBULAR CLUSTERS SIMULATIONS OF GLOBULAR CLUSTERS3.1.
Models for Simple Stellar Populations
The simple stellar population simulations in this pa-per are based on the Yonsei Evolutionary PopulationSynthesis (YEPS) model (Paper I; Chung et al. 2013,2017). The model used the Yonsei-Yale (Y ) stellar li-brary (Yi et al. 2001; Kim et al. 2002; Yi et al. 2003)to produce all stages of stars from the main sequence tothe red giant branch (RGB), as well as HB and post-HBstars. Flux libraries are required to obtain the inte-grated spectral energy distribution of each GC, and ourmodel employed the library of Westera et al. (2002).For the initial mass function, our fiducial model usedthe Salpeter function (Salpeter 1955). After significantmass loss, RGB stars have a thin hydrogen envelope andfurther evolve into HB stars that are prominent in bluelight. Thus, the mass loss is an essential factor in HBmodeling. We adopted Reimers’s (1977) formula for themass loss during the RGB stage and calibrated the mass-loss rate parameter by comparing the HB morphologiesof simple stellar population models to those of observedGCs in the Milky Way. Readers are referred to Chung etal. (2013, 2017) for a detailed description of the YEPSmodel including its ingredients and input parameters.3.2. Models for GC Color Distributions
Figure 5 shows how we make the models for GCcolor distribution morphologies based on the simple stel-lar population models (Section 3.1). The left columnpresents the models of GC g − z distributions for differ-ent ages (12, 13, and 14 Gyr), where color bimodality isevident. As we showed in Figure 1 of Paper VIII, ourmodel suggests that bimodality in color diminishes forstellar populations younger than 12 Gyr. We use themean metallicity at a given galactocentric radius (from0.5 R eff to 20 R eff ) based on the empirical metallicitygradient of Equation (1). At each radial position, weassume a simple Gaussian MDF centered at the mean[Fe/H] value, as presented by the distribution along they-axes of the insets of the left column. We convert theMDFs to the model GC color distribution histogramsvia our theoretical CMRs. The properties of the colordistributions, such as the mean colors of blue and redGCs and the red GC fraction, are acquired by the KMMcode assuming the homoscedastic case. In the middlecolumn, the mean colors of blue and red GCs changealong the radii depending on the radial metallicity vari-ation. As the radial distance increases, the mean colorsof blue and red GCs shift toward blue, which is commonin observations (see Figure 2). We will compare in Sec-tion 4.1 our model to the observations in terms of theradial variation in the mean colors of blue and red GCs. In the right column, the model shows the systematic ra-dial variation in the red GC fraction in the sense thatthe red fraction increases as the mean metallicity of theMDF increases.It is noteworthy that for different ages, even with thesame MDF, the model color distributions show differ-ences in (a) the mean colors of blue and red GCs and(b) the red GC fraction. This is because the detailedshape (i.e., the color of the inflected position and thedegree of inflection) of the CMRs varies systematicallywith their ages (see Figure 1 of Paper VIII for moredetails). The inflection point of a CMR moves towarda redder color when a model age gets older. In addi-tion, the inferred age of a GC system gives the age ofthe oldest stellar populations in its host galaxy. Par-ticularly for early-type galaxies, the spectroscopic agesof the central field stellar population of galaxies (e.g.,Kuntschner et al. 2010) concur with those of their GCsystems (e.g., Cohen et al. 1998). This notion opens upa new possibility of galaxy age dating by exploiting theobserved color distribution morphologies of extragalac-tic GC systems. As pointed out in Paper VIII, this agedetermination technique is based on photometry ratherthan spectroscopy, and it has precision as good as (cid:46) ± − metallicity degeneracy of the stel-lar population compared to other age-dating methodsusing galactic integrated colors and spectra (see PaperVIII for details). To determine the age of GC systems,we construct color distribution models of various agesfrom 8 to 15 Gyr by 0.1 Gyr intervals. We will applythis methodology to our sample GC systems and infertheir radial age gradient in Sections 4.1 and 4.2. RESULTS AND ANALYSIS4.1.
Radial Variation in the GC Color DistributionMorphology
In Figures 6 −
9, for the four sample galaxies, ourmodels are compared with the radial variation of theobservational color distribution morphologies. In Fig-ure 6(a), we present our model prediction of CMRs for12, 13, and 14 Gyr. The simple Gaussian MDFs with σ [Fe / H] GC = 0 . Lee, Chung & Yoon eff -2.0-1.5-1.0-0.50.00.5 < [ F e / H ] > G C M87
Jordan+09Peng+09Forte+07
M49
Jordan+09Lee+00Kim+06
M60
Jordan+09Faifer+11Lee+08
N1399
Jordan+15Kim+13Forte+07
Figure 4.
Radial variation of (cid:104) [Fe / H] (cid:105) GC of our sample GC systems. (cid:104) [Fe / H] (cid:105) GC are derived from empirical CMRs. Theradius for each galaxy is normalized by its effective radius. The gray solid line shows the least-squares fit to the combined data. d N / d ( g - z ) eff eff t=12Gyr d N / d ( g - z ) t=13Gyr d N / d ( g - z ) t=14Gyr [ F e / H ] [ F e / H ] [ F e / H ] R ed G C f r a c t i on ( g - z ) R ed G C f r a c t i on ( g - z ) eff R ed G C f r a c t i on ( g - z ) g - z Blue: a= 1.063, b= -0.061Red: a= 1.491, b= -0.056 g - z Blue: a= 1.003, b= -0.058Red: a= 1.411, b= -0.054 eff g - z Blue: a= 0.928, b= -0.056Red: a= 1.338, b= -0.052
Figure 5. (Left column) Radial variations of our model color distributions in g − z color. Top, middle, and bottom panelsrepresent the GC color distribution models of 12, 13, and 14 Gyr, respectively. The color code shows the radial variation ofthe mean [Fe/H] of GCs, which is defined in Equation (1) and the radial variation of color distribution functions. The insetsshow the theoretical CMRs, and the red lines represent the pertinent age. (Middle column) The radial color gradient of blueand red GCs. The blue dotted and red dashed lines are the best linear fit to the mean colors of blue (blue open triangles) andred (red open squares) GCs, respectively. The mean colors are calculated by the KMM code and a , b are the coefficients in g − z = a + b log ( R/ R eff ). (Right column) The radial red GC fraction gradient. The black circles present the red GC fractionsdetermined by the KMM code. UMBER DENSITY PROFILE OF GLOBULAR CLUSTERS −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] (a) N / N ( b l ue pea k ) x C (b) N / N ( b l ue pea k ) x C (c) −1.4−1.2−1.0−0.8−0.6 < F e / H > G C (d) g − z o f pea ks (e) eff R ed G C f r a c t i on (f) −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] N / N ( b l ue pea k ) x C N / N ( b l ue pea k ) x C −1.4−1.2−1.0−0.8−0.6 < F e / H > G C V − I o f pea ks eff R ed G C f r a c t i on −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] N / N ( b l ue pea k ) x C N / N ( b l ue pea k ) x C −1.4−1.2−1.0−0.8−0.6 < F e / H > G C C − T o f pea ks eff R ed G C f r a c t i on −1.5−1.0−0.50.0 [ F e / H ] Jordan et al. (2009) g−zPeng et al. (2009) V−IForte et al. (2007) C−T1
M87 eff A ge ( G y r) Figure 6.
Upper left set of panels: the g − z color distribution of M87 with respect to the radius. The observational dataare taken from Jord´an et al. (2009). (a) The black lines present the YEPS color − [Fe/H] relations for 12 Gyr (dotted line), 13Gyr (solid line), and 14 Gyr (dashed line). Gaussian distributions on the y-axis with red, green, and blue colors show modelmetallicity distributions. The values of the mean [Fe/H] of GCs are adopted from the observations shown in (d). (b) Thebest-matched color distribution models from comparing with observed red GC fractions shown in (f). (c) The observed colordistributions with Gaussian kernels with σ (color) = 0.05. (d) − (f) The black circles are the observed mean [Fe/H] of GCs, themean colors of blue and red GCs, and the fraction of red GCs as a function of radius. The model results are marked by diamondswith the same colors as (a) − (f). The dotted, solid, and dashed lines in (e) and (f) are the isoage models corresponding to themodel color − [Fe/H] relation in (a). Upper right set of panels: M87 in V − I . The observational data are taken from Peng et al.(2009). Lower left set of panels: M87 in C − T . The observational data are taken from Forte et al. (2007). Lower right set ofpanels: radial variation of (cid:104) [Fe / H] (cid:105) GC and (cid:104) Age (cid:105) GC of M87. Lee, Chung & Yoon −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] N / N ( b l ue pea k ) x C N / N ( b l ue pea k ) x C −1.4−1.2−1.0−0.8−0.6 < F e / H > G C g − z o f pea ks eff R ed G C f r a c t i on −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] N / N ( b l ue pea k ) x C N / N ( b l ue pea k ) x C −1.4−1.2−1.0−0.8−0.6 < F e / H > G C V − I o f pea ks eff R ed G C f r a c t i on −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] N / N ( b l ue pea k ) x C N / N ( b l ue pea k ) x C −1.4−1.2−1.0−0.8−0.6 < F e / H > G C C − T o f pea ks eff R ed G C f r a c t i on −1.5−1.0−0.50.0 [ F e / H ] Jordan et al. (2009) g−zLee & Kim (2000) V−IKim et al. (2006) C−T1
M49 eff A ge ( G y r) Figure 7.
Same as Figure 6, but for M49. Observational data are taken from Jord´an et al. 2009 (upper left set of panels),Lee & Kim 2000 (upper right set of panels), and Kim et al. 2006 (lower left set of panels).
GC fractions with the model grids. Remarkably, the in-flected CMRs plus the radial GC metallicity gradient re-produce well the systematic radial trend of the GC colordistribution morphologies. Figures 6(e) and (f) show theradial variations in the mean colors of blue and red GCsand in the red GC fraction, respectively. The observedmean colors of blue and red GCs and the observed redGC fraction are placed well within our model grids of (cid:104)
Age (cid:105) GC = 12 −
14 Gyr. The top-right and bottom-leftsets of panels are for the other observational datasets us-ing different colors and covering different radial zones.The bottom-right set of panels shows the mean [Fe/H](upper) and the inferred age (lower) as functions of theradius of the host galaxy. The format of Figure 6 is repeated for Figures 7 −
9. Inwhat follows, we make comments on the result for eachgalaxy (Figures 6 − g − z and V − I ); however, the mean age estimations are entirelyconsistent with each other. The observed field in C − T is a more outer region than those of the two otherobservations, yet the inferred age is similar to the agesfrom the other two. The mean colors of the blue GCsshow a reasonable agreement between the observationsand models. For C − T , however, the mean colors of UMBER DENSITY PROFILE OF GLOBULAR CLUSTERS −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] N / N ( b l ue pea k ) x C N / N ( b l ue pea k ) x C −1.4−1.2−1.0−0.8−0.6 < F e / H > G C g − z o f pea ks eff R ed G C f r a c t i on −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] N / N ( b l ue pea k ) x C ′ −i ′ N / N ( b l ue pea k ) x C −1.4−1.2−1.0−0.8−0.6 < F e / H > G C g ′ − i ′ o f pea ks eff R ed G C f r a c t i on −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] N / N ( b l ue pea k ) x C N / N ( b l ue pea k ) x C −1.4−1.2−1.0−0.8−0.6 < F e / H > G C C − T o f pea ks eff R ed G C f r a c t i on −1.5−1.0−0.50.0 [ F e / H ] Jordan et al. (2009) g−zFaifer et al. (2011) g ′ −i ′ Lee et al. (2008) C−T1
M60 eff A ge ( G y r) Figure 8.
Same as Figure 6, but for M60. Observational data are taken from Jord´an et al. 2009 (upper left set of panels),Faifer et al. 2011 (upper right set of panels), and Lee et al. 2008b (lower left set of panels). blue GCs of the models are redder by 0.1 − g − z and V − I agree well with our model grids of (cid:104) Age (cid:105) GC = 12 − g − z showmore irregular shapes than other observations due totheir small numbers. The mean colors of blue GCs ofthe models are redder than the observation by ∼ C − T . In Figure 8, for M60, the observed g − z distributions show the feature of small numbers. Theages from g − z and g (cid:48) − i (cid:48) colors are well within our12 −
13 Gyr model grids. For the C − T color, the abso-lute values of ages are slightly older than the two other cases. In Figure 9, for NGC 1399, the comparison of thered GC fractions between the observations and modelsindicates that the age variation along the radius is neg-ligible. The mean colors of blue and red GCs in C − T do not match well with our model grids (12 −
14 Gyr).Generally, our models related to the short-wave bands( C and B bands) predict slightly redder peaks than theobservations. This may be due to the still incompletemodeling for hot HB and post-HB stars.The radial gradient of the mean colors of blue andred GCs is a controversial issue (see Figure 2). A num-ber of observations (Geisler et al. 1996; Harris 2009a,b;Forbes et al. 2011; Liu et al. 2011; Forte et al. 2012;Forbes & Remus 2018) reported that the mean colors2 Lee, Chung & Yoon −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] N / N ( b l ue pea k ) x C N / N ( b l ue pea k ) x C −1.4−1.2−1.0−0.8−0.6 < F e / H > G C g − z o f pea ks eff R ed G C f r a c t i on −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] N / N ( b l ue pea k ) x C N / N ( b l ue pea k ) x C −1.4−1.2−1.0−0.8−0.6 < F e / H > G C B − I o f pea ks eff R ed G C f r a c t i on −2.5−2.0−1.5−1.0−0.50.00.5 [ F e / H ] N / N ( b l ue pea k ) x C N / N ( b l ue pea k ) x C −1.4−1.2−1.0−0.8−0.6 < F e / H > G C C − T o f pea ks eff R ed G C f r a c t i on −1.5−1.0−0.50.0 [ F e / H ] Jordan et al. (2015) g−zKim et al. (2013) B−IForte et al. (2007) C−T1
NGC 1399 eff A ge ( G y r) Figure 9.
Same as Figure 6, bur for NGC 1399. Observational data are taken from Jord´an et al. 2015 (upper left set ofpanels), Kim et al. 2013a (upper right set of panels), and Forte et al. 2007 (lower left set of panels). of both blue and red GCs get bluer with galactocentricradius. Some found the radial gradient for either red orblue group (Forte et al. 2001; Strader et al. 2011; Harriset al. 2016; Caso et al. 2017) or no gradient for bothgroups (Harris et al. 2009, 2017). Back in Figure 5, ourmodel shows shallow radial color gradients for both blueand red GCs in optical g − z colors. In the case of the13 Gyr model, when we adopt the [Fe/H] gradient ofour sample galaxies (Equation (1)), the g − z color gra-dients (∆( g − z ) / ∆ log R ) of the blue and red GCs are − .
06 and − .
05, respectively, for 0.5 − R eff . Liu etal. (2011) analyzed GC systems in 76 early-type galax-ies in the ACS Virgo Cluster Survey and Fornax ClusterSurvey data. Excluding those classified as unimodal dis- tributions, they found the mean g − z color gradient ofblue and red GCs in their 39 galaxies to be − . ± . − . ± .
01, respectively. For the four giant ellipti-cals (M87, M49, M60, and NGC 1399), the mean valuesof the blue and red GCs gradients are − . ± .
01 and − . ± .
01, respectively. Considering the difference in measuring the gradient, our model prediction agreeswell with the result of Liu et al. (2011). Liu et al. (2011) divided GCs in the entire radial range into theblue and red GCs using a simple color cut determined by theKMM test, while we perform the KMM test for every radial bin.See Liu et al. (2011) for more details. See also Villaume et al.(2020) for an explanation that the simple color cut can bias thegradient measurement.
UMBER DENSITY PROFILE OF GLOBULAR CLUSTERS eff A ge ( G y r) M87
Jordan+09Peng+09Forte+07
M49
Jordan+09Lee+00Kim+06
M60
Jordan+09Faifer+11Lee+08
N1399
Jordan+15Kim+13Forte+07
Figure 10.
Radial variation of the inferred GC ages of our sample galaxies. The gray solid line shows the least-squares fit tothe whole data.
Radial Gradient of the GC Ages
The inflection point of a CMR is located at a reddercolor for an older age model. As a consequence, for agiven MDF, an older CMR produces a lower red GCfraction (see Figure 5). This is the principle behind theage dating based on the GC color distribution morphol-ogy. In this regard, we find that the red GC fractionis a more robust age indicator than the mean colors ofblue and red GCs, especially for the short-wave bandcolors (e.g., C − T ) that are more vulnerable to theincompleteness of the model ingredients (Section 4.1).We thus prefer using the former over the latter. It isfair to note that the mean metallicities of GC systemsmay be affected by the detailed shape of CMRs that isstill somewhat uncertain. With overestimated (under-estimated) mean [Fe/H], the age inferred from the redGC fraction would be higher (lower) than the true age.In Figure 10, we show the inferred ages of the GC sys-tems as a function of the radius normalized by R eff . Thisis a combined figure of the lower panels of the bottom-right sets of panels in Figures 6 −
9. The inferred ages ofthe GC systems are distributed around 13 Gyr and donot show a significant radial gradient. The age variationwithin each galaxy is as low as 1 Gyr. No evidence of theradial age gradient implies that the radial variation inthe color distribution morphology arises predominantlydue to the mean [Fe/H] gradient rather than due to theage gradient. 4.3.
Radial Number Density Profiles of Blue and RedGCs
Figure 11 compares our models for the radial surfacenumber density profiles of blue and red GCs with the ob-servations. The radial profile models are generated bycombining (a) the radial variation in the GC color distri-bution morphologies depending on the observed [Fe/H]gradient of GCs (as shown in Section 4.1) and (b) theobserved radial number density gradient of the entire(blue + red) GCs. Table 3 gives the observed [Fe/H]gradient and the observed surface number density gra-dients. The age of the GC systems is assumed to be 13Gyr. In the left column, the observed number densityprofiles show that the blue and red GCs have differentslopes. Conventionally, the difference in the radial den-sity profile between blue and red GCs has been ascribedto their distinct origins and spatial distributions (e.g.,Forbes et al. 2004; Strader et al. 2011).In the right column, however, our model reproducesthe different slope of the number density profiles of theblue and red GCs naturally. Our model predictions showthat the intersecting points of the two profiles are lo-cated at the slightly more inner region of galaxies thanthose of observations. The difference seems due to theuncertainty of the empirical [Fe/H] − color relations. Wealso note that the simulated difference in the slope be-tween blue and red GCs for each galaxy slightly differsfrom the observation. According to our simulation, evenif the total (blue + red) number density profile of GCs4 Lee, Chung & Yoon
Table 3.
The Number Density Profiles of Total GCs and the Empirical [Fe/H] − Radius Relations
Galaxy Σ = α + β ( R/R eff ) / [Fe / H] = δ + γ ( R/R eff ) / α β Data Source δ γ
M87 3.821 − − − − − − − − − − Note —The empirical [Fe/H] − radius relations are fitted to the mean [Fe/H] of our sample datasets binned into three radialregions for each sample. is the same, the steeper the metallicity gradient is, themore significant the difference in the slope between theblue and red GCs is. The remarkable agreement be-tween our models and observations leads us to concludethat the difference in the radial profile between blue andred GCs stems naturally from the combined effect ofthe radial metallicity gradient of GC systems plus themetallicity-to-color nonlinearity. We, therefore, proposethat there is no need for assuming the distinct origins ofthe blue and red GCs to explain their observed differencein the radial surface number density profile. DISCUSSIONWe have demonstrated that our theoretical model re-produces the observed radial variations in terms of (a)the GC color distribution morphologies such as relativeportions of blue and red GCs and (b) the surface num-ber density of blue and red GCs. Our results provide analternative, more cohesive solution to the distinct radialdensity profiles of blue and red GCs that does not neces-sarily invoke two GC subsystems and thus reinforces thenonlinear-CMR scenario for the GC color bimodality.Our simulation shows that the radial variation in theensemble average of GC ages is within 1 Gyr out to theradial range of ∼ R eff . This implies that GCs through-out the wide radial extent were created in a coeval man-ner for our giant elliptical galaxies. A number of studiesreported that the radial age gradient of field stars inearly-type galaxies is almost flat (Mehlert et al. 2003;Kuntschner et al. 2006; S´anchez-Bl´azquez et al. 2006,2007; Spolaor et al. 2008; Montes et al. 2014) with anegative metallicity gradient (e.g., Santucci et al. 2020).The inferred age distributions of field stars are based onlong-slit and integral field unit spectroscopy and mostlyconfined to the central region of galaxies ( (cid:46) R eff ). Bycontrast, our methodology using the GC color distribu-tion allows us to investigate the age variation of the widerange ( ∼ R eff ). No or little radial gradient in ages ofboth GCs and field halo stars suggests that GC systemsand their parent galaxies have shared a more commonhistory than previously thought (see Paper III). Several studies have reported that observational prop-erties of unresolved halo field stars, such as the surfacelight profile (Bassino et al. 2008; Forbes et al. 2012; Dur-rell et al. 2014; Escudero et al. 2018), ellipticity (Park& Lee 2013; Kartha et al. 2014), and kinematics (Schu-berth et al. 2010; Strader et al. 2011; Pota et al. 2013;Fahrion et al. 2020), are often more similar to those ofred GCs than blue GCs. These findings have been re-garded as the clues that there are two distinct GC sub-populations and the red subpopulation shares a moreintimate history with field stars of a host galaxy. On thecontrary, our nonlinearity scenario suggests that manythousands of building blocks were involved in making asingle massive galaxy. Such a notion leaves little roomfor the existence of just two GC groups in individualgalaxies. In this regard, Paper III showed that the trueMDF of GCs is of a unimodal, skewed Gaussian shapewith a metal-poor tail, similarly to that of field stars,suggesting that both GCs and field stars underwent acontinuous chemical enrichment with a short timescale(2 ∼ <
40 kpc), furthersupporting a common origin of GCs and halo field starsof galaxies. From our point of view, the observed meanproperties of field stars are better represented by metal-rich stars that occupy the majority of field stars at andaround the peak of their MDFs. It is the red GC groupthat has a metallicity value similar to metal-rich fieldstars. Thus, naturally, the red GCs better follow theproperties of unresolved field stars than the blue GCs.As described in our previous papers (Papers II, III,and IV), even with identical MDFs, the color distribu-tion morphology would vary depending on colors usedin observations. This is because the exact CMR shapedepends on the color. Given such color-dependent varia-tion of GC color distributions, the radial density profilesof blue and red GCs should vary when different colorsare used, even for the same galaxy. Durrell et al. (2014)
UMBER DENSITY PROFILE OF GLOBULAR CLUSTERS (R/R eff ) l og Σ G C ( a r c m i n − ) −3.0−2.0−1.00.01.02.03.0 M87V−I observation −3.0−2.0−1.00.01.02.03.0 M49C−T observation −3.0−2.0−1.00.01.02.03.0 M60C−T observation0 1 2 3−3.0−2.0−1.00.01.02.03.0 NGC 1399g−i observation M87 V−I model M49C−T model M60C−T model0 1 2 3 NGC 1399 g−i model Figure 11.
Comparison between observations (left column) and models (right) of the surface number density profiles. Theopen and filled circles are the number density of blue and red GCs, respectively. The dashed and dotted lines are the least-squaresfit to the blue and red GCs, respectively. The observational number density profiles (left column) are the same as Figure 1. Themodel number density profiles (right column) are calculated by combining (a) the modeled radial profile of the number ratio ofblue and red GCs and (b) the observed radial profile of the total (blue + red) GC number density (M87: Tamura et al. 2006;M49: Lee et al. 1998; M60: Lee et al. 2008b; NGC 1399: Cantiello et al. 2018). Lee, Chung & Yoon obtained the number density profiles of blue and redGCs in M87 and compared their result (from g (cid:48) − i (cid:48) )with the result (from V − I ) of Tamura et al. (2006)for the same galaxy. The blue GC profiles of the twostudies showed a similar slope, but the red GC profileswere different. Durrell et al. ascribed the discrepancyto the different criteria for dividing blue and red GCs.However, we suspect that the used colors also affect thedifference between the two results. In this vein, the vari-ation of the number density profiles due to the changeof observed colors can be estimated based on multibandphotometry of GCs. For instance, Kim et al. (2013a)provided U BV I colors of the GC systems in the Fornaxgalaxy cluster. In their Figure 15, the red GC fractionin U − B shows a different gradient from that in othercolors for NGC 1399. A clearer difference in the densityprofile according to the different choice of colors is ex- pected for the optical/NIR color combination. Severaloptical/NIR studies reported that the number fractionsof blue and red GCs vary with colors (Blakeslee et al.2012; Chies-Santos et al. 2012; Cho et al. 2016). Thus,with the upcoming James Webb Space Telescope, thehigh-S/N NIR data on a large number of GC systemswill be crucial to test our explanation for the differentradial density profiles of blue and red GCs as well as thecolor bimodality itself.S.-J.Y. acknowledges support by the Mid-career Re-searcher Program (No. 2019R1A2C3006242) and theSRC Program (the Center for Galaxy Evolution Re-search; No. 2017R1A5A1070354) through the NationalResearch Foundation of Korea. The updated data ( CT )for NGC 4472 are kindly provided by Eunhyeuk Kim.REFERENCES Ashman, K. M., Bird, C. M., & Zepf, S. E. 1994, AJ, 108,2348Ashman, K. M., & Zepf, S. E. 1992, ApJ, 384, 50Barmby, P., Huchra, J. P., Brodie, J. P., et al. 2000, AJ,119, 727Bassino, L. P., Faifer, F. R., Forte, J. C., et al. 2006, A&A,451, 789Bassino, L. P., Richtler, T., & Dirsch, B. 2008, MNRAS,386, 1145Beasley, M. A. 2020, Reviews in Frontiers of ModernAstrophysics; From Space Debris to Cosmology, 245Beasley, M. A., Trujillo, I., Leaman, R., et al. 2018, Nature,555, 483Blakeslee, J. P., Cantiello, M., & Peng, E. W. 2010, ApJ,710, 51Blakeslee, J. P., Cho, H., Peng, E. W., et al. 2012, ApJ,746, 88Blakeslee, J. P., Jord´an, A., Mei, S., et al. 2009, ApJ, 694,556Blom, C., Spitler, L. R., & Forbes, D. A. 2012, MNRAS,420, 37Brodie, J. P., & Strader, J. 2006, ARA&A, 44, 193Cantiello, M., Blakeslee, J. P., Raimondo, G., et al. 2014,A&A, 564, L3Cantiello, M., D’Abrusco, R., Spavone, M., et al. 2018,A&A, 611, A93Caso, J. P., Bassino, L. P., & G´omez, M. 2017, MNRAS,470, 3227Chies-Santos, A. L., Larsen, S. S., Cantiello, M., et al. 2012,A&A, 539, A54 Cho, H., Blakeslee, J. P., Chies-Santos, A. L., et al. 2016,ApJ, 822, 95Cho, J., Sharples, R. M., Blakeslee, J. P., et al. 2012,MNRAS, 422, 3591Chung, C., Yoon, S.-J., Lee, S.-Y., et al. 2013, ApJS, 204, 3Chung, C., Yoon, S.-J., Lee, S.-Y., et al. 2016, ApJ, 818,201Chung, C., Yoon, S.-J., & Lee, Y.-W. 2017, ApJ, 842, 91Cohen, J. G., Blakeslee, J. P., & Ryzhov, A. 1998, ApJ,496, 808Cˆot´e, P., Marzke, R. O., & West, M. J. 1998, ApJ, 501, 554Cˆot´e, P., West, M. J., & Marzke, R. O. 2002, ApJ, 567, 853De B´ortoli, B. J., Bassino, L. P., Caso, J. P., et al. 2020,MNRAS, 492, 4313de Vaucouleurs, G., de Vaucouleurs, A., Corwin, H. G., Jr.,et al. 1991, Third Reference Catalogue of Bright Galaxies(New York: Springer)Dirsch, B., Richtler, T., Geisler, D., et al. 2003, AJ, 125,1908Dirsch, B., Schuberth, Y., & Richtler, T. 2005, A&A, 433,43Durrell, P. R., Cˆot´e, P., Peng, E. W., et al. 2014, ApJ, 794,103Ennis, A. I., Bassino, L. P., Caso, J. P., et al. 2019,MNRAS, 488, 770Escudero, C. G., Faifer, F. R., Bassino, L. P., et al. 2015,MNRAS, 449, 612Escudero, C. G., Faifer, F. R., Smith Castelli, A. V., et al.2018, MNRAS, 474, 4302Escudero, C. G., Faifer, F. R., Smith Castelli, A. V., et al.2020, MNRAS, 493, 2253