On the Metallicity-Color Relations and Bimodal Color Distributions in Extragalactic Globular Cluster Systems
aa r X i v : . [ a s t r o - ph ] S e p On the Metallicity-Color Relations and Bimodal ColorDistributions in Extragalactic Globular Cluster Systems
Michele Cantiello , andJohn P. Blakeslee ABSTRACT
We perform a series of numerical experiments to study how the nonlinearmetallicity–color relations predicted by different stellar population models affectthe color distributions observed in extragalactic globular cluster systems. Wepresent simulations in the
U BV RIJ HK bandpasses based on five different setsof simple stellar population (SSP) models. The presence of photometric scatterin the colors is included as well. We find that unimodal metallicity distributionsfrequently “project” into bimodal color distributions. The likelihood of this ef-fect depends on both the mean and dispersion of the metallicity distribution, aswell as of course on the SSP model used for the transformation. Adopting theTeramo-SPoT SSP models for reference, we find that optical–to–near-IR colorsshould be favored with respect to other colors to avoid the bias effect in glob-ular cluster color distributions discussed by Yoon et al. (2006). In particular,colors such as ( V − H ) or ( V − K ) are more robust against nonlinearity of themetallicity–color relation, and an observed bimodal distribution in such colors ismore likely to indicate a true underlying bimodal metallicity distribution. Similarconclusions come from the simulations based on different SSP models, althoughwe also identify exceptions to this result. Subject headings: galaxies: star clusters – galaxies: elliptical and lenticular, cD– globular clusters: general Department of Physics and Astronomy, Washington State University, Pullman, WA 99164. INAF–Osservatorio Astronomico di Teramo, Via M. Maggini, I-64100 Teramo, Italy
1. Introduction
The globular cluster (GC) system of a galaxy provides a unique view into the formationhistory of the galaxy. Apart from some rare exceptions, GCs are known to represent arelatively simple class of objects, with homogeneous ages and chemical compositions for thestars composing each GC. Thus, GCs are at the same time reasonably simple objects, andgood tracers of the early star formation histories of the host galaxy. For these reasons,in recent years a great deal of effort has been made to study the observational propertiesof extragalactic GC systems. As a consequence, many GC features have been discovered,providing valuable constraints on the evolutionary paths of galaxies.One commonly observed property is that the GC populations in galaxies tend to bebimodal in their color distributions. A combination of photometric and spectroscopic ob-servations indicates that GC systems are fairly homogeneous in terms of age, so differencesin color mainly reflect metallicity differences. Thus, the bimodal color distributions haveusually been interpreted as bimodal metallicity distributions; see the reviews by West et al.(2004), Brodie & Strader (2006), and references therein, for further details. However, morerecently some authors (e.g. Richtler 2006; Yoon et al. 2006) have shown that a bimodal colordistribution can be enhanced, or even originated, by the effect of nonlinear metallicity-color(MC hereafter) relations.For instance, Richtler (2006) has shown that the observed MC relation for the Wash-ington system ( C − T ) color, coupled with a Gaussian scatter of 0.08 mag around the meanrelation, can transform a nearly flat GC metallicity distribution into a bimodal ( C − T )distribution. Yoon et al. (2006, YYL06 hereafter), instead, exploited the fact that, whenthe Horizontal-Branch (HB) morphology is realistically modeled in stellar population sim-ulations, the color indices sensitive to stars in this evolutionary stage follow “wavy” MCrelations. Such a nonlinear feature has in fact been observed for the metallicity versus( g − z ) color of GCs in the Milky Way and Virgo ellipticals (Peng et al. 2006). This featurecauses evenly-spaced metallicity bins to be “projected” into larger/narrower color bins, de-pending on the location on the MC relation. YYL06 consequently conclude that it is notnecessary to invoke a bimodal metallicity distribution to have a bimodal color distribution.We will refer to this effect as metallicity projection bias .In this paper we study how nonlinear MC relations can affect the color distributionsobserved in different passbands. Our aim is ( i ) to test how various colors “suffer” from thenonlinear effects described above, and, consequently, ( ii ) to suggest the optimal color(s) forrevealing the presence of real bimodal GC metallicity distributions.We do this by first carrying out multiple sets of simulations based on the Simple Stel- 3 –lar Population (SSP) models developed by the Teramo-SPoT group (Raimondo et al. 2005,SPoT hereafter ). We then perform the same tests using simulations based on four other setsof SSP models and compare the results. Finally, we summarize the most robust conclusionson GC colors and their underlying metallicity distributions from this work.
2. Models simulations
For this study we adopt the SPoT SSP models as our reference models for two reasons.First, these models have proven to match fairly well the observed integrated photometricproperties of galaxies, i.e. colors, surface brightness fluctuation magnitudes, etc., in differentpassbands for a large sample of objects with very different physical properties (Cantiello et al.2005; Raimondo et al. 2005; Cantiello et al. 2007). Second, the SPoT models also providea good match to the observed color–magnitude diagrams (CMDs) for star clusters with awide range of ages and chemical compositions (Brocato et al. 2000; Raimondo et al. 2005).In particular, these models are optimized to simulate the HB spread observed in GalacticGCs.The detailed numerical synthesis of the CMD features is a key point for the aims of thepresent study since, as shown by YYL06, the wavy feature that can produce a “projected”color bimodality is due to a realistic treatment of the HB morphology. It is worth noting herethat this feature is not a peculiarity of the YYL06 models; in fact it was already presentedby Lee et al. (2002, see their Figures 2 and 4) and, as we will show, it is present also in theSPoT models. Not surprisingly, this feature is not noticeable in those models where the HBmorphology is not properly simulated to match the observed Galactic GC properties, as forexample in the Bruzual & Charlot (2003) models, which adopt a fixed red HB morphology.In fact, our reference SPoT models attempt to simulate in a realistic way all features ofthe observed CMD, that is all the stellar evolutionary stages including the fast and brightphases of the Giant Branch stage. These models are computed according to the followingprescriptions: Scalo (1998) Initial Mass Function; solar scaled stellar evolution tracks fromPietrinferni et al. (2004); HB morphology reproduced taking into account the effects due toage, metallicity, and the stellar mass spread due to the stochasticity of the mass-loss alongthe RGB. The RGB mass–loss rate is evaluated according to Reimers’ law (Reimers 1975),with efficiency η RGB = 0 .
4. Thermal pulses are simulated using the analytic formulations byWagenhuber & Groenewegen (1998). Finally, the atmosphere models are from Westera et al.(2002). See Raimondo et al. (2005) for further details. Throughout this paper, we will t = 13 Gyr age models for reference, if not stated otherwise.Figure 1 shows the MC relations from the SPoT models for several different colors.Data for the Galactic GCs are also shown. The optical colors and the [Fe/H] values for theGalactic GCs are taken from the Harris (1996) updated online catalog , while the near-IRphotometric data are from Brocato et al. (1990) and Cohen et al. (2007). As seen in Fig. 1,the models provide a good match to the integrated properties of the Galactic GC system.The “wavy” behavior of the MC relations for the ( V − I ), ( B − I ), ( U − R ), and ( B − V ) colorsis clearly evident. Furthermore, it is worth emphasizing the general nonlinearity of the MCrelations for all the colors shown in the figure. We have developed a procedure to simulate a GC population with an arbitrary metal-licity distribution and number of objects. Throughout this paper, however, we will considerthe case of Gaussian metallicity distributions, and we simulate GC populations composedof 1000 objects. Armed with the MC relations of our reference models, the metallicity dis-tribution of the GC system is randomly populated and projected into a color distribution.Finally, we use the KMM code (McLachlan & Basford 1988; Ashman et al. 1994) to testwhether the GC color distribution is best fit by a single or double Gaussian function.In Figure 2 (left panel), we show the results of one of these simulations. Specifically, inthis case we have simulated a metallicity distribution similar to the one adopted by YYL06,that is a Gaussian with peak at [Fe/H] = − .
65 dex and dispersion σ [ F e/H ] = 0 . V − I ) panel that the projected color distribution is bimodal. Byrunning the KMM code, we find that, for this specific simulation, all the optical colors andthe ( J − K ) color distributions are significantly bimodal, while the optical to near-infraredcolors, including ( I − H ), have unimodal distributions.As a check to these simulations, we have also made some numerical experiments adoptinga bimodal metallicity distribution. In particular, Figure 2 (right panel) shows a simulationcarried out adopting the bimodal metallicity distribution of the Galactic GC system, obtainedusing the prescriptions of Cˆot´e (1999). In the Figure also the observed metallicity and color ∼ harris/mwgc.dat We consider the ( U − R ) as it is the nearest color the Washington system ( C − T ) color, not providedwith the SPoT models. The ( C − T ) index is interesting because it is known to be one for which the GCsdistribution is bimodal in all of the limited number of observed galaxies (Richtler 2003). − . , − . , − . , − .
15 dex andthree values for the dispersion: σ [ F e/H ] = 0 . , . , .
75 dex. For each of the twelve ([Fe/H], σ [ F e/H ] ) pairs, we have simulated a GC system with a unimodal metallicity distribution andevaluated the colors of each GC according to the adopted MC relations. Afterwards, byusing the KMM code, we estimate the likelihood, P ( bimodal ), that the color distribution isbetter represented by two Gaussians than a single Gaussian, for various color choices. Val-ues of P ( bimodal ) ≈ P ( bimodal ) ≈ P ( bimodal ) for each choiceof mean metallicity and dispersion. The results are also shown graphically in the Figure 3,where solid dots mark the results for simulations without any color errors, and open circlesmark results obtained with the random 10% color scatter. The different rows and columnsrefer to different mean [Fe/H] and σ values, respectively, as labeled.Two considerations emerge from inspection of Figure 3. First, according to the SPoTmodels, the projection effect that causes a unimodal metallicity distribution to be observedas a bimodal color distribution is not a unique characteristic of the HB-sensitive colors. It is,instead, present for most of the analyzed colors. For example, in the case of ( J − K ), almosthalf of the numerical experiments carried out give bimodal color distributions [ P ( bimodal ) ∼ . g − z ) and ( V − I ) colors discussed by YYL06. Although, as shown in Figure 1,different colors are affected differently by nonlinearity in the MC relation.The second consideration that emerges from these simulations regards how the presenceof color scatter (i.e. the photometric uncertainty) can affect the probability of obtaining abimodal color distribution. The addition of color scatter can of course decrease the probabil-ity of bimodality by smoothing out the separation between the peaks. More surprisingly, itcan also make bimodality appear more probable by removing sharp features from the color 6 –distributions, and thus significantly improving the goodness-of-fit of the double Gaussianmodel used by KMM.It is interesting to note that the two extreme metallicities, [Fe/H] = − .
65 and − σ values are in almostall cases more bimodal. Thus, for the combination ([Fe/H] = − σ = 0 . • ( V − I ) ,blue ∼ .
95 and ( V − I ) ,red ∼ .
15, based on the Brodie & Strader (2006)compilation for bright (mainly E and S0) galaxies with M B ≤ − . • ( B − I ) ,blue ∼ .
94 and ( B − I ) ,red ∼ .
06, derived from the Harris et al. (2006) sampleof bright galaxies. • ( I − H ) ,blue ∼ . I − H ) ,red ∼ .
7, from Kundu & Zepf (2007), based on M 87.In order to avoid any bias towards bimodal distributions, we have also considered asrealistic those unimodal color distributions whose peak is equal to the averaged blue andred peak colors reported above. By matching these criteria with the simulations, we havefound that only the subset of simulations with [Fe/H] = − − σ [ F e/H ] = 0 . , . V − I ), ( B − I ),and ( I − H ) colors for the case of ([Fe/H] = − σ [ F e/H ] = 0 .
75) are all in good agreementwith the observational values listed above, even though most of these colors are found tohave unimodal color distributions for this particular simulation.By inspecting only the panels for the s elected “realistic” simulations in Figure 3 (thepanels labeled with an “ S ”), one can see that the colors ( B − V ), ( V − I ), and ( B − I ) have,on average, an increased probability of being projected to a bimodal distribution, whilecolors such as ( I − K ), ( V − H )and ( V − K ) have lower probabilities. Thus, if one wants tominimize the bias from the MC projection effect in real observations, i.e. if the contributionto bimodality due to a nonlinear MC relation is to be neglected, then the ( I − K ), ( V − H ),and ( V − K ) colors are to be preferred. 7 –Finally, we must emphasize that the above conclusions do not change if we adopt dif-ferent ages. In fact, although there is some shift in color, the MC profiles are not stronglyaffected even when the t = 5 Gyr models are considered (Figure 1). Since the projectioneffect is due to the shape of the MC relation (that is, to the changing derivative of the rela-tion), and not to the absolute color values, this explains why the outcome of the simulationsdoes not change significantly with age. In more detail, for the Raimondo et al. (2005) modelsat an age of t = 5 Gyr, the “wavy” MC relation is mostly related to the appearance of theHB at metallicities [Fe/H] ∼ < − . . The results presented in the previous Section are based on a particular choice of theMC relations derived from the SPoT SSP models. In order to verify the robustness ofthose results, in this section we perform the same analysis discussed above, but with theMC relations derived from four other sets of SSP models. We consider the Maraston (2005),Anders & Fritze-v. Alvensleben (2003), Bruzual & Charlot (2003) and Lee et al. (2002) mod-els (hereafter Mar05, And03, BC03, and Lee02, respectively).We emphasize that, with the lone exception of the Lee02 models, the quoted models arecomputed with the primary aim of deriving the integrated photometric properties of stellarsystems. This means that, in contrast to the SPoT models, they are not constrained to matchas well with the specific features of observed CMDs. As a consequence, the detailed shapeof the MC relation may not take into account the effect of stars in a particular evolutionaryphase, which is a key point for a detailed modeling of the MC relations. Keeping in mindthis warning, we perform for these models the same analysis discussed above for the SPoTmodels. For these simulations we again adopt a model age of 13 Gyr, except for the Lee02models, which do not include this age, so we use their 14 Gyr models. The results ofthe simulations are presented in Figure 4, where we show only the results for the selected“realistic” simulations, although this choice does not substantially affect the our conclusions.Inspecting the panels of Figure 4, we find some differences with the results based on We have found that the locations of the color peaks change on average ∼ < P ( bimodal )by less than 25% if >
50 up to ∼ P ( bimodal ) are low for the BC03 ( B − V ),( V − I ), and ( B − I ) colors distributions. This result for the BC03 models is not surprising,due to their lack of detailed HB morphology modeling, which is the main cause of the wavyMC relations for these colors. In contrast, the ( J − K ) colors from the BC03 models arealmost always bimodal, a result of some non-linearity in their MC relation unrelated to HBmorphology. On the other hand, the Lee02 models, where nonlinear effects in the MC relationare stronger with respect to other models, generally predict higher P ( bimodal ) values. .By making a cross-check of the results based on these sets of SSP models with theones based on the SPoT models, we find that no one color is completely unaffected by MCprojection bias. However, in almost all cases the ( V − H ) and ( V − K ) colors are predictedto be less affected by this bias. Thus, these mixed optical–IR colors should be preferred forGC studies, since, in normal galaxies, a bimodal distribution in these colors is more likelylinked to an underlying bimodal metallicity distribution.
3. Conclusions
In this work we have performed a series of numerical experiments to simulate the prop-erties of GC populations observed in different photometric colors. Our aim was to studyhow the nonlinear behavior of the MC relations affect a unimodal (Gaussian) metallicitydistribution when it is projected into various optical and near-IR color distributions. Byusing the MC relations from the SPoT models, we have found that a unimodal metallicitydistribution can be projected into a bimodal color distribution in almost any of the colorsconsidered here, depending on the properties of the metallicity distribution, on the particularcolor index, and on the photometric uncertainty of the sample.
This result is due to the fact that all the MC relations are by and large nonlinear.To reduce the possibility of this bias in real data, and thus help ensure that an observedbimodal color distribution is due to a bimodal metallicity, one should choose a color whoseMC relation is nearly linear. Since, for the grid of colors that we have considered here, thereis no such “unbiased” color, the best colors to use are those that are most robust againstthis effect. Using the SPoT models, we have concluded that optical–to–near-IR colors arethe best choices to disclose real bimodal metallicity distributions. We chose the 14 Gyr Lee02 models specifically because the “wavy” feature is more pronounced; thisallows us to highlight better the influence of such features on the color distributions. The MC relations forthe Lee02 preferred 12 Gyr models give results more similar to the SPoT ones. V − K ), ( V − H ), and similarcolors. One other result of these simulations is that photometric uncertainties can affect, insurprising ways, the probability of obtaining a bimodal color distribution from the KMMalgorithm. Thus, decreasing the statistical errors in real color data can help to avoid falsedetection of significant bimodality.Further information on metallicity bimodality can of course come from the analysis ofspectroscopic data for a significant number of GCs in galaxies with observed color bimodal-ity. However, such observations are time consuming, and only feasible for relatively nearbyobjects. In addition, certain spectroscopic indices may themselves be affected by similarnonlinear relations with metallicity.In conclusion, we confirm ( V − H ) and ( V − K ) as good colors to reveal (nearly) unbi-ased bimodal metallicity distributions in extragalactic GC systems. Future data on large GCsamples in individual galaxies, including optical and near-IR photometry, as well as spec-troscopy, coupled with further advances in stellar population modeling, should finally resolvethis issue. Until that time, the interpretation of bimodal color distributions will remain, atleast in part, ambiguous.We thank the anonymous referee for helping us to improve this paper with useful sug-gestions. We would like to thank Eric Peng, Pat Cˆot´e, and Gabriella Raimondo for usefulcomments. This research was supported by the NASA grant AR-10642, and the paper wascompleted under the sponsorship of a INAF-OA Teramo grant. 10 – Fig. 1.— The Teramo-SPoT models compared to observational data. The models refer tothree different ages: 5 Gyr (dashed lines), 11 Gyr (dotted lines) and 13 Gyr (solid lines,reference models). The gray dots mark Galactic GC data. 11 – [Fe/H]-2 -1.5 -1 -0.5 0 0.500.050.10.150.20.25 1B-V 1 V-I2 2.5 3 3.5V-H1.5 2 2.500.050.10.150.20.25 B-I 1 1.5 2I-H 0.5 1J-K2 2.5 3 3.500.050.10.150.20.25 V-K 1 1.5 2 2.5U-RSPoT [Fe/H]-2.5 -2 -1.5 -1 -0.5 000.050.10.150.20.25 0.5 1B-V 1 V-I1.5 200.050.10.150.20.25 B-I 1 1.5 2U-R 2 2.5 3V-H2 2.5 300.050.10.150.20.25 V-K 1 1.5I-H 0.5 1J-KSPoT
Fig. 2.—
Left panel:
The color histograms obtained from a unimodal (Gaussian) metallicitydistribution with mean [Fe/H] = − . σ [Fe / H] = 0 . J − K ) color distributions are bimodal based on the KMMalgorithm, while for the other colors a double Gaussian distribution does not significantlyimprove the fit to the data. Right panel:
Simulation of a bimodal metallicity distribution(solid lines), chosen to match the Galactic GC distribution. The observed color histogramsfor the Galactic GCs are also shown with dotted lines (the observed metallicity distributionis shown in the upper left panel with dotted histogram). The parameters used for thesimulated distribution are [Fe/H] low = − . σ [ F e/H ] ,low = 0 .
30 dex, and [Fe/H] high = − . σ [ F e/H ] ,high = 0 .
27 dex, with a photometric uncertainty of 10%, and the N low to N high ratiois 2. 12 –
Fig. 3.— The probability P ( bimodal ) of having a bimodal color distribution startingfrom a unimodal Gaussian metallicity distribution is shown for different color indicesand various metallicity distributions. Left/middle/right panels refer to simulations with σ = 0 . , . , .
75 dex, respectively (see upper labels). Different rows refer to different meanmetallicities, as labeled. High (low) values of P ( bimodal ) mean that the color distribution issignificantly bimodal (unimodal). Filled dots mark numerical experiments without any colorscatter, and open circles show simulations including a 10% color scatter. Although all thesimulated metallicity distributions are unimodal, about 45% of these color distributions arefound to be bimodal. The four panels with the “ S ” label refer to the simulations that bestmatch with observed GC color ranges. 13 – Fig. 4.— Same as Figure 3, but for MC relations taken from other sets of SSP models(labeled at the top of each set of panels). Only the results for the simulations matching withobserved GC colors are shown. 14 –
REFERENCES
Anders, P., & Fritze-v. Alvensleben, U. 2003, A&A, 401, 1063 (And03)Ashman, K. M., Bird, C. M., & Zepf, S. E. 1994, AJ, 108, 2348Brocato, E., Caputo, F., di Giorgio, A. M., Santolamazza, P., & Richichi, A. 1990, Memoriedella Societa Astronomica Italiana, 61, 137Brocato, E., Castellani, V., Poli, F. M., & Raimondo, G. 2000, A&AS, 146, 91Brodie, J. P., & Strader, J. 2006, ARA&A, 44, 193Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000 (BC03)Cantiello, M., Blakeslee, J. P., Raimondo, G., Mei, S., Brocato, E., & Capaccioli, M. 2005,ApJ, 634, 239Cantiello, M., Raimondo, G., Blakeslee, J. P., Brocato, E., & Capaccioli, M. 2007, ApJ, 662,940Cohen, J. G., Hsieh, S., Metchev, S., Djorgovski, S. G., & Malkan, M. 2007, AJ, 133, 99Cˆot´e, P. 1999, AJ, 118, 406Harris, W. E. 1996, AJ, 112, 1487Harris, W. E., Whitmore, B. C., Karakla, D., Oko´n, W., Baum, W. A., Hanes, D. A., &Kavelaars, J. J. 2006, ApJ, 636, 90Kundu, A., & Zepf, S. E. 2007, ApJ, 660, L109Lee, H.-c., Lee, Y.-W., & Gibson, B. K. 2002, AJ, 124, 2664 (Lee02)Maraston, C. 2005, MNRAS, 362, 799 (Mar05)McLachlan, G. J., & Basford, K. E. 1988, Mixture models. Inference and applications toclustering (Statistics: Textbooks and Monographs, New York: Dekker, 1988)Peng, E. W. et al. 2006, ApJ, 639, 95Pietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2004, ApJ, 612, 168Raimondo, G., Brocato, E., Cantiello, M., & Capaccioli, M. 2005, AJ, 130, 2625 (SPoT)Reimers, D. 1975, Memoires of the Societe Royale des Sciences de Liege, 8, 369
Table 1. Simulations of GC population [Fe/H], σ ( B − V ) ( V − I ) ( B − I ) ( I − H ) ( I − K ) ( J − K ) ( V − H ) ( V − K ) ( U − R ) ( B − H ) ( B − K ) (dex) blue red P b blue red P b blue red P b blue red P b blue red P b blue red P b blue red P b blue red P b blue red P b blue red P b blue red P b GC simulations without color scatter − − − − − − − − − − − − − − − − − − − − − − − − a For each color, the location of the blue and red color peaks is reported, together with the value P b which represents the likelihood that the color distribution is better fitted by a bimodal colordistribution [in the text referred to as P ( bimodal )].
16 –Richtler, T. 2003, in LNP Vol. 635: Stellar Candles for the Extragalactic Distance Scale, ed.D. Alloin & W. Gieren, 281–305Richtler, T. 2006, Bulletin of the Astronomical Society of India, 34, 83Scalo, J. 1998, in Astronomical Society of the Pacific Conference Series, Vol. 142, The StellarInitial Mass Function (38th Herstmonceux Conference), ed. G. Gilmore & D. Howell,201–+Wagenhuber, J., & Groenewegen, M. A. T. 1998, A&A, 340, 183West, M. J., Cˆot´e, P., Marzke, R. O., & Jord´an, A. 2004, Nature, 427, 31Westera, P., Lejeune, T., Buser, R., Cuisinier, F., & Bruzual, G. 2002, A&A, 381, 524Yoon, S.-J., Yi, S. K., & Lee, Y.-W. 2006, Science, 311, 1129 (YYL06)