SPECTRAL ENERGY DISTRIBUTIONS AND AGE ESTIMATES OF 104 M31 GLOBULAR CLUSTERS

Globular clusters (GCs) are among the oldest known stellar systems in the universe. They typically have ages similar to those of their host galaxies, thus making them fossils that may provide important information about the formation and evolution of their parent galaxies. In addition, nearly all types of galaxies contain GCs, from dwarfs to giants and from the earliest to the latest types (Fusi Pecci et al. 2005). However, our most in-depth understanding of GC systems has predominantly come from studies of the Milky Way.

M31, located at a distance of ∼780 kpc (Stanek & Garnavich 1998; Macri 2001), is the largest galaxy in the Local Group. By virtue of the natural advantage of being located at a reasonable distance, the galaxy offers us an ideal environment for detailed, resolved investigations of a large GC system, using both Hubble Space Telescope (HST; e.g., Grillmair et al. 1996; Holland et al. 1997; Rich et al. 2005; Perina et al. 2009b) and ground-based observations with large telescopes (e.g., Christian & Heasley 1991).

A large number of studies focusing on the M31 GC system have been performed since Hubble's (1932) original identification of 140 GC candidates in M31. The latest Revised Bologna Catalog of M31 GCs and candidates (hereafter RBC v.3.5; Galleti et al. 2004, 2006, 2007) was updated on 2008 March 27, and contains 1983 objects (509 confirmed and 1049 candidate GCs, 9 controversial objects, 147 galaxies, 6 H ii regions, 245 stars, 5 asterisms, and 13 extended clusters). These objects were observed and discovered by a large number of authors using a variety of observational systems (see, e.g., Vete${\rm \breve{s}}$nik 1962; Sargent et al. 1977; Battistini et al. 1980; Crampton et al. 1985; Barmby et al. 2000). To obtain a homogeneous photometric data set, Galleti et al. (2004) took the observed data of Barmby et al. (2000) as reference and transformed other observations to this standard setup.

An accurate and reliable analysis of star clusters is important for our understanding of the formation, buildup, and evolutionary processes in galaxies. By comparing integrated photometry with models of simple stellar populations (SSPs), recent studies have achieved some success in determining ages and masses of extragalactic star clusters (e.g., de Grijs et al. 2003a, 2003b, 2003c; de Grijs & Anders 2006; Bik et al. 2003; Ma et al. 2006a, 2007a, 2009a; Fan et al. 2006). Ma et al. (2006a) and Fan et al. (2006) derived age estimates for M31 GCs by fitting SSP models (Bruzual & Charlot 2003, henceforth BC03) to their photometric measurements in a large number of intermediate- and broadband filters spanning the spectral range from the optical to the near-infrared (NIR). In particular, Ma et al. (2007a) determined an age for the M31 GC S312 (B379), using multicolor photometry from the near-ultraviolet (near-UV) to the NIR, of 9.5^+1.2_−1.0 Gyr. S312 (B379) is, in fact, among the first extragalactic GCs for which the age was estimated accurately and independently, using main-sequence photometry, at 10^+2.5₋₁ Gyr (Brown et al. 2004). This provides a robust check on our methodology to derive age constraints based on the spectral energy distributions (SEDs) of (simple) stellar systems.

This paper is organized as follows. In Section 2, we present Beijing–Arizona–Taiwan–Connecticut (BATC) observations of our sample GCs and GC candidates, the relevant data-processing steps, and the Galaxy Evolution Explorer (GALEX; far- and near-UV), optical broadband, and Two Micron All Sky Survey (2MASS) NIR data that are subsequently used in our analysis. In Section 3, we derive the ages of our sample clusters by comparing their SEDs with the galev SSP models. We then discuss and summarize our results in Section 4.

2.1. GC Sample Selection

To obtain photometry in 15 intermediate-band filters of the BATC photometric system for 61 GCs and GC candidates in the RBC v.3.5, for which few measurements are presently available in any photometric system, Fan et al. (2009) mined the BATC survey archive for observations obtained between 1995 February and 2008 March. The resulting set of observations covers approximately 6 deg². For the purpose of estimating accurate cluster ages, we selected clusters for which the metallicities and reddening values had been estimated accurately, independently, and homogeneously in previous studies (Huchra et al. 1991; Barmby et al. 2000; Perrett et al. 2002; Fan et al. 2008); see Section 2.6. We selected classes 1, 2, 3, and 8 (1580 objects) from Column "f" in the RBC v.3.5, which include GCs, candidate GCs, controversial objects, and extended clusters. This resulted in an initial selection of 366 objects. Jiang et al. (2003) and Ma et al. (2006a, 2009a) obtained multicolor photometry for 180 of these GCs and GC candidates. In this paper, we consider the remaining 186 objects. Caldwell et al. (2009) published an updated catalog of 1300 objects in M31, including 670 likely star clusters, with the remaining objects being stars or background galaxies once thought to be clusters (see Tables 3 and 5 of Caldwell et al. 2009). From a comparison with Caldwell et al. (2009), we find that 66 objects are either stars or background galaxies. Therefore, the final sample of M31 GCs and GC candidates analyzed in this paper includes 120 objects. However, we cannot obtain accurate photometric measurements for 16 of these objects because of either a nearby very bright object (B065 and B344D), very faint fluxes superimposed onto a bright background (B119, B396, NB16, and V031), or a location very close to (or blend with) another object (B150D, B176, B256D, B302, B345, B366, B381, B391, and B397), leading to compromised photometric measurements. Object B330 is both faint and located very close to a brighter object. Thus, here we analyze the multicolor photometric properties of 104 GCs and GC candidates. Figure 1 shows their spatial distribution across the M31 fields observed with the BATC multicolor system.

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2.2. BATC Intermediate-band Photometry

2.3. GALEX UV, Optical Broadband, and 2MASS NIR Photometry

2.4. Comparison with Previously Published Photometry

To check our photometry, we transformed the BATC intermediate-band system to the UBVRI broadband system using the relationships between these two systems derived by Zhou et al. (2003):

$$\begin{equation} B=m_{d}+0.2201(m_{c}-m_{e})+0.1278\pm 0.076 \quad \mbox{and} \end{equation} \tag{ 1 }$$

$$\begin{equation} V=m_{g}+0.3292(m_{f}-m_{h})+0.0476\pm 0.027. \end{equation} \tag{ 2 }$$

B-band photometry can be derived from the BATC c, d, and e bands, while V-band magnitudes can be obtained from the BATC f, g, and h bands. Figure 2 shows a comparison of the B and V photometry of our M31 sample objects with previous measurements from Barmby et al. (2000) and Galleti et al. (2004). The mean B and V magnitude differences—in the sense of this paper minus Barmby et al. (2000) or Galleti et al. (2004)—are 〈ΔB〉 = −0.077 ± 0.022 mag and 〈ΔV〉 = −0.047 ± 0.033. Our magnitudes are in good agreement with previous V-band determinations. However, a significant disagreement becomes apparent in the B band for objects with B > 17.5 mag. This disagreement has its origin in the difference between our photometry and that of Galleti et al. (2004). In fact, our B-band photometry agrees well with that of Barmby et al. (2000), even for B > 17.5 mag objects (except for one sample cluster). Referring to Jiang et al. (2003) and Ma et al. (2009a), we also see that our photometric values are fully consistent with Barmby et al. (2000). In Ma et al. (2009a), the analysis of the majority of the GCs was based on the photometric data of Barmby et al. (2000), so even in the B band the agreement is good: see Figure 3 of Ma et al. (2009a). We excluded B257 from the comparison, because its V-band magnitude is too faint compared with the magnitudes obtained in the other bands (see Table 3). In fact, from the observed SEDs, this photometric measurement is unusually far away from the best-fitting integrated SEDs (see Section 3 for more details). This data point was taken from Table 4 of Barmby & Huchra (2001), and the offset may be a typical error. Based on the BATC f, g, and h magnitudes, we obtain V = 17.76 mag for B257. Note that the B-band magnitude of this cluster as listed in Table 4 of Barmby & Huchra (2001) is 11.907, which is too bright for any reasonable SED and may also be a typical uncertainty.

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2.5. Metallicities and Reddening Values

An SSP is defined as a single generation of coeval stars characterized by the same parameters, including metallicity, age, and stellar initial mass function (IMF). SSP models are calculated on the basis of a set of evolutionary tracks of stars of different initial masses, combined with stellar spectra at different evolutionary stages. In this paper, and following Ma et al. (2009a), we compare the SEDs of our sample objects with the galev SSP models (e.g., Kurth et al. 1999; Schulz et al. 2002; Anders & Fritze-v. Alvensleben 2003) to estimate their ages. The galev SSPs are based on the Padova isochrones (covering wavelengths from 91 Å to 160 μm) and a Salpeter (1955) stellar IMF with lower and upper mass limits of 0.10 M_☉ and 50–70 M_☉, respectively (the latter depending on metallicity). These models cover ages from 4 Myr to 16 Gyr, with an age resolution of 4 Myr for ages younger than 2.35 Gyr, and 20 Myr for older ages. We convolved the theoretical SSP SEDs with the GALEX, broadband UBVRI, BATC intermediate-band, and 2MASS JHK_s filter response curves to obtain synthetic UV, optical, and NIR photometry (Ma et al. 2009a). The synthetic magnitude in the AB magnitude system for the ith filter is

$$\begin{equation} m_i=-2.5\log \frac{\int _{\nu }F_{\nu }\varphi _{i} (\nu){\rm d}\nu }{\int _{\nu }\varphi _{i}(\nu){\rm d}\nu }-48.60, \end{equation} \tag{ 3 }$$

where F_ν is the theoretical SSP SED (which is a function of age and metallicity) and φ_i is the response curve of the ith filter. The galev SSP models include five initial metallicities, Z = 0.0004, 0.004, 0.008, 0.02 (solar), and 0.05. For other metallicities, the relevant spectra can be obtained by linear interpolation of the appropriate model spectra for any of these five metallicities. For metallicities below Z = 0.0004, we use the Z = 0.0004 model (Ma et al. 2009a).

To determine the most compatible galev SSP model for a given observed SED, we adopted a χ² minimization test,

$$\begin{equation} \chi ^2=\sum _{i=1}^{25}{\frac{\big[m_{\nu _i}^{\rm intr}-m_{\nu _i}^{\rm mod}(t)\big]^2}{\sigma _{i}^{2}}}, \end{equation} \tag{ 4 }$$

where $m_{\nu _i}^{\rm mod}(t)$ is the magnitude in the ith filter of a theoretical SSP at age t, while $m_{\nu _i}^{\rm intr}$ is the intrinsic (observed and corrected) magnitude in the same filter. The interstellar extinction curve A_ν is taken from Cardelli et al. (1989), R_ν = A_V/E_{B − V} = 3.1. σ_i is the magnitude uncertainty in the ith filter, defined as

$$\begin{equation} \sigma _i^{2}=\sigma _{{\rm obs},i}^{2}+\sigma _{{\rm mod},i}^{2}. \end{equation} \tag{ 5 }$$

Here, σ_obs,i and σ_mod,i are the observational uncertainty and that associated with the model itself, respectively. Charlot et al. (1996) estimated σ_mod,i by comparing the colors obtained from different stellar evolutionary tracks and spectral libraries. We adopt σ_mod,i = 0.05 mag, following Wu et al. (2005), Ma et al. (2006a, 2009a), and Fan et al. (2006). The SED fits of our sample GCs and GC candidates are shown in Figure 3.

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In Section 3, we determined the ages of 104 GCs and GC candidates in M31. The results are tabulated in Table 5. Figure 4 shows the age distribution of the sample clusters, from which we conclude that, except for 20 clusters, the ages of most sample GCs are between 1 and 5 Gyr, with a peak at ∼2 Gyr. The "usual" complement of well-known old GCs (i.e., GCs of similar age as the majority of the Galactic GCs) is also present. In addition, while fitting SSP models to the observed data, we found that some photometric data of a small number of clusters cannot be fitted with any SSP models. We therefore did not use these deviating photometric data points to obtain the best fits. This applies to the GALEX far-UV data of B138D, the 2MASS K_s, H, and J magnitudes of B142D, B181D, and B289D, respectively, the B-band and 2MASS H fluxes of B245D, and the V-band magnitude of B257.

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Other authors have also considered the age distribution of the GCs in M31. For example, Barmby et al. (2000) discovered that M31 contains GCs exhibiting strong Balmer lines and A-type spectra, from which one infers that these objects must be very young. Beasley et al. (2004) and Puzia et al. (2005) confirmed this conclusion. Burstein et al. (2004) and Fusi Pecci et al. (2005) carefully studied the sample of young M31 GCs. Very recently, Caldwell et al. (2009) determined the ages and reddening values of 140 young clusters in M31 by comparing the observed spectra with models, and found that these clusters are less than 2 Gyr old, while most clusters have ages between 10⁸ and 10⁹ yr. Perina et al. (2009a) estimated an age for VDB0-B195D of ∼25 Myr based on HST/WFPC2 color–magnitude diagrams (CMDs). The ages of the M31 clusters determined in this paper are in general agreement with previous determinations, which we will show in more detail below on the basis of comparisons between our determinations and previous age estimates for individual objects.

The most direct and most accurate method to determine a cluster's age is by means of main-sequence photometry, since the absolute magnitude of the main-sequence turnoff is a strong function of age. Williams & Hodge (2001a, 2001b) estimated ages of many young disk clusters in M31 based on HST/WFPC2 CMDs and isochrone fitting to either the main-sequence or luminous evolved stars. Only one of their clusters (B315) is in common with our sample. They obtained an age of ∼0.1 Gyr for this cluster, while we determined it to be approximately 0.5 Gyr old. Both age determinations are mutually consistent within the uncertainties. Caldwell et al. (2009) compared their ages with those of Williams & Hodge (2001a, 2001b) and concluded that both sets of age determinations were in good agreement. We therefore compare our ages with Caldwell et al. (2009) for the seven clusters we have in common with their sample (B018, B307, B316, B448, B475, B483, and V031; see Table 6). It is evident that they are largely internally consistent. Puzia et al. (2005) also presented spectroscopic ages, metallicities, and [α/Fe] ratios for 70 M31 GCs based on Lick line-index measurements. A cross-correlation with Puzia et al.'s (2005) sample shows that we have 21 clusters in common. A direct comparison shows that the ages of Puzia et al. (2005) are systematically older than ours. This surprising result prompted us to compare the ages of clusters in common between Puzia et al. (2005) and other authors (Williams & Hodge 2001a, 2001b; Beasley et al. 2004; Caldwell et al. 2009). We found similar systematic offsets (for details, see also Ma et al. 2009a).

We have determined the ages of M31 GCs and GC candidates in a series of previous papers (Jiang et al. 2003; Ma et al. 2006a, 2006b, 2007a, 2009a, 2009b; Fan et al. 2006) based on the same method as used in the present paper, i.e., by constructing SEDs of known M31 GC candidates and using the SED shapes to estimate cluster ages. In the first paper of this series, Jiang et al. (2003) estimated the ages of 172 M31 GC candidates based on photometric measurements in 13 BATC intermediate-band filters and the SSP models of Bruzual & Charlot (1996, unpublished, hereafter BC96). Subsequently, Fan et al. (2006) obtained new age estimates for 91 GCs from the Jiang et al. (2003) sample, based on improved photometric data including intermediate- and broadband magnitudes from the optical to the NIR, and the SSP models of BC03. Ma et al. (2006b) then estimated the ages of 33 M31 GC candidates using photometry in 13 BATC intermediate-band filters and the BC03 SSP models, while Ma et al. (2009a) determined the ages of 35 M31 GCs and GC candidates based on photometry including far- and near-UV GALEX observations, UBVRI, 13 BATC intermediate-band filters, and 2MASS JHK_s, combined with the galev SSP models. Ma et al. (2006a, 2007a, 2009b) determined the ages of three specific M31 GCs (037-B327, S312, and G1) based on the BC03 SSP models and a large number of photometric measurements. We determined the ages of these three M31 GCs for special reasons: S312 is among the first extragalactic GCs whose age was estimated accurately using main-sequence photometry, while 037-B327 and G1 are among the most massive GCs in the Local Group. They have been speculated to be nucleated dwarf galaxies instead of genuine GCs (see for detailed discussions Ma et al. 2006c, 2007b). In this series of seven articles, we published ages for 331 different M31 GCs and GC candidates. Figure 5 shows the age distribution of these 331 objects. We see that ∼40 clusters are younger than 1 Gyr. The ages range from <1 to 20 Gyr (the upper age limit in the BC96 and BC03 SSP models). A population of young clusters, peaking at ∼3 Gyr, is also apparent.

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Figure 6 shows the absolute magnitudes of our sample of M31 GCs and GC candidates as a function of their age. The crosses indicate that the ages are from Jiang et al. (2003), Ma et al. (2006a, 2006b, 2007a, 2009a), and Fan et al. (2006), which were obtained based on the SSP models of BC96 or BC03, while the circles mean that the ages are from Ma et al. (2009a) and the present paper, obtained on the basis of the galev SSP models. The dashed and solid lines represent SSP models with Z = 0.004 taken from BC03 and galev, respectively, for masses of 10², 10³, 10⁴, 10⁵, and 10⁶ M_☉ and assuming a Salpeter stellar IMF. The V-band photometry is from the RBC v.3.5. The absolute magnitudes have been corrected for extinction (Barmby et al. 2000; Fan et al. 2008), except for 037-B327, S312, and G1, the reddening values of which are from Ma et al. (2006a), Ma et al. (2007a), and Ma et al. (2009b), respectively. We adopt a distance modulus of (m − M)₀ = 24.47 mag (McConnachie et al. 2005). Figure 6 shows that the majority of the clusters have masses between 10³ and 10⁶ M_☉.

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The distribution of absolute V magnitude of GCs in M31 is shown in Figure 7. Overall, the distribution has a cutoff at the faint end with a magnitude limit of about −5.5 mag (with a few fainter clusters still visible, probably because of advantageous positions, e.g., observable through a hole in the extinction distribution). The various cluster ages are separated in Figure 8, which are (1) very young (t < 1 Gyr), (2) young (1Gyr ⩽ t < 4 Gyr), (3) intermediate-age (4Gyr ⩽ t < 10 Gyr), and (4) old GCs and GC candidates (t ⩾ 10 Gyr). We do not see a clear trend between age and brightness. However, the youngest clusters are not the most massive objects, implying that the conditions in the M31 have not been conducive to massive cluster formation in the recent past.

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We converted the absolute magnitudes of our M31 GC sample to photometric masses using the appropriate age-dependent mass-to-light ratios provided by the BC03 and galev SSP models. The GC mass versus age diagram is shown in Figure 9. The crosses indicate that the ages are from Jiang et al. (2003), Ma et al. (2006a, 2006b, 2007a, 2009a), and Fan et al. (2006), and the masses were obtained based on the SSP models of BC03, while the circles mean that the ages are from Ma et al. (2009a) and the present paper, and the masses were obtained on the basis of the galev SSP models. Overplotted is the fading limit, assuming M_V,limit = −5.5 mag and evolutionary fading based on the Z = 0.004 BC03 (dashed line) and galev (solid line) models, assuming a Salpeter stellar IMF. Figure 9 shows that our observational (∼50%) completeness limit describes the lower mass limit of the entire GC sample up to the oldest ages very well. Similarly, the upper envelope of the points in Figure 9 is likely a result of the "size-of sample effect" (e.g., Gieles & Bastian 2008, and references therein). It is clear, however, that massive star cluster formation halted abruptly in the disk of M31 approximately 1 Gyr ago. Given that massive (>10⁴ M_☉) young (<1 Gyr old) clusters will be significantly brighter than the much older GC-type counterparts in M31, we would have expected any such young massive clusters to have been detected in M31, yet they have not.

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Using these 331 GCs and GC candidates with homogeneously determined ages, we can now investigate their spatial distribution. We use an X, Y projection to refer to the relative positions of the objects. Our adopted X coordinate projects along M31's major axis, where positive X increases toward the northeast, while the Y coordinate extends along the minor axis of the M31 disk, increasing toward the northwest. To obtain the relative coordinates of the M31 clusters, we adopted α₀ = 00^h42^m4430 and δ₀ = +41°16'090 (J2000.0) for M31's center, following Huchra et al. (1991) and Perrett et al. (2002). Formally,

$$\begin{equation} X=A\sin \theta +B\cos \theta \quad {\rm and} \end{equation} \tag{ 6 }$$

$$\begin{equation} Y=-A\cos \theta +B\sin \theta, \end{equation} \tag{ 7 }$$

where A = sin(α − α₀)cos δ and B = sin δcos δ₀ − cos(α − α₀)cos δsin δ₀. We adopt a position angle of θ = 38° for the major axis of M31 (Kent 1989). We divided the GCs and GC candidates into four age groups: (1) very young (t < 1 Gyr), (2) young (1Gyr ⩽ t < 4 Gyr), (3) intermediate-age (4Gyr ⩽ t < 10 Gyr), and (4) old GCs and GC candidates (t ⩾ 10 Gyr). Figure 10 shows their spatial distributions. Although our sample of M31 GCs and GC candidates is not complete (in spatial, radial terms, given that we are limited by the six observed fields), we note that there is a tendency for young GCs and GC candidates to be nearly uniformly distributed around M31. The majority of old GCs appear to occupy the central regions of the galaxy, although this restricted distribution may be caused by selection biases. Figure 11 shows the number of GCs and GC candidates as a function of projected radial distance from the M31 center, confirming our conclusions derived from Figure 10. Figure 12 displays the cluster ages as a function of projected radial distance. The crosses indicate that the ages are from Jiang et al. (2003), Ma et al. (2006a, 2006b, 2007a, 2009b), and Fan et al. (2006), which were obtained using the BC96 or BC03 SSP models, while the circles indicate that the ages are from Ma et al. (2009a) and the present paper, obtained on the basis of the galev SSP models. Figure 12 shows that young GCs and GC candidates are distributed nearly uniformly, and that most of the old GCs (and candidates) are more concentrated.

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This paper presents photometry of 104 M31 GCs and GC candidates in 15 intermediate-band filters of the BATC photometric system. The ages of the clusters were obtained by comparing the photometric data with the theoretical synthesis models. The ages of our sample clusters cover a large range, although most clusters are younger than 10 Gyr. Combined with the ages obtained in our series of previous papers focusing on the M31 GC system, we present the full M31 GC age distribution. The results show that the M31 GC system contains populations of young and intermediate-age GCs, as well as the "usual" complement of well-known old GCs, i.e., GCs of similar age as the majority of the Galactic GCs. In addition, young GCs (and GC candidates) are distributed nearly uniformly in radial distance from the center of M31, while most old GCs (and GC candidates) are more strongly concentrated.

We are indebted to the referee for thoughtful comments and insightful suggestions that improved this paper significantly. This work was supported by the Chinese National Natural Science Foundation (grants 10873016, 10633020, 10603006, and 10803007) and by National Basic Research Program of China (973 Program; grant 2007CB815403).