ULTRAVIOLET OBSERVATIONS OF THE GLOBULAR CLUSTER M10 FROM HST AND GALEX: THE BSS POPULATION^*

Blue stragglers stars (BSS) are a common population of any medium-size stellar aggregate such as open (Mathieu & Geller 2009) and globular clusters (GCs), as well as dwarf galaxies (Monelli et al. 2012). They are arguably the most common objects whose nature is not explainable in terms of the canonical evolution of a single star.

In an optical color–magnitude diagram (CMD) BSS appear hotter and brighter than turnoff (TO) stars, thus mimicking a sparse sequence of younger and more massive objects. Observational evidence (see, for example, Shara et al. 1997; Gilliland et al. 1998) showed that BSS are indeed more massive (M ∼ 1.2–2.0 M_☉) than "normal" stars from the same cluster (M ∼ 0.8 M_☉), thus they are thought to be the result of some mechanism responsible for increasing the masses of single stars.

Two main formation scenarios have been proposed over the years: the "collisional" scenario (COL-BSS; Hills & Day 1976) according to which BSS are the end products of stellar mergers induced by collisions between single stars or binary systems, and the "mass-transfer scenario" (MT-BSS; McCrea 1964; Zinn & Searle 1976) in which BSS are the result of mass accretion between two stars in a binary system. These mechanisms are believed to work simultaneously within the same cluster (see the case of M30; Ferraro et al. 2009), with efficiencies that may be a function of environment (Ferraro et al. 1995; Davies et al. 2004). In particular, COL-BSS have higher probabilities to form in the cores of GCs where densities are incredibly high and so is the chance of collisions and interactions. On the contrary, the MT scenario is the dominant formation channel of BSS in very loose systems or in cluster outskirts, where binary systems are more likely to have evolved free of interactions with other stars.

Observational support to this idea comes from the results obtained from data for 47 Tucanae by Ferraro et al. (2006a; see also Lovisi et al. 2010 for M4), where a fraction of BSS has been found to have strong carbon (C) and oxygen (O) abundance anomalies, probably due to mass-transfer processes (Sarna & de Greve 1996).

Being three to four times more massive (independently of the formation mechanism) than the average cluster mass (m ∼ 0.3 M_☉), BSS are heavily affected by dynamical friction and thus they are natural test particles to probe the internal dynamics of stellar aggregates. In particular their radial distribution (Ferraro et al. 1997) has been found to be an important tool to probe the efficiency of dynamical friction (Mapelli et al. 2006; Lanzoni et al. 2007a). This approach has been followed by our group over the past fifteen years leading to the construction of a large collection of BSS radial distributions (see Dalessandro et al. 2008a and references therein) over the full spatial extent of the clusters studied.

By using this data set, Ferraro et al. (2012, hereafter F12) introduced the definition of the "dynamical clock", i.e., a measurement that provides an assessment of the dynamical age of a cluster on the basis of the presence and the position of the minimum of its BSS radial distribution.

Following this interpretation, clusters with a flat radial distribution (ω Centauri—Ferraro et al. 2006b; NGC 2419—Dalessandro et al. 2008b; Palomar14—Beccari et al. 2011) are dynamically young, so that the effect of dynamical friction is still not present. Clusters whose BSS distribution has a single peak at the center (M79—Lanzoni et al. 2007b; M75—Contreras Ramos et al. 2012; M30—Ferraro et al. 2009; M80—F12) are dynamically old, so that the most remote BSS already have drifted toward the cluster center. Finally, intermediate dynamical-age clusters show a bimodal BSS radial distribution with a peak in the cluster center and another one toward the outer regions, thus defining a clear minimum in the distribution. The radial position of this minimum (r_min) has been found to be linked to the efficiency of the dynamical friction and to strongly correlate with the central relaxation time (F12).

In this work, we present a photometric analysis of the Galactic globular cluster (GGC) M10 (NGC 6254) with the aim of studying its structural parameters and the properties of its BSS population. The results will be interpreted in the framework of the scheme proposed by F12 and will be compared with previous results on M10's binary systems content and mass segregation profile (Beccari et al. 2010, hereafter B10; Dalessandro et al. 2011, hereafter D11).

As suggested by Ferraro et al. (1997, 2004), since BSS are relatively warm stars (T_eff  ∼  7000–10, 000 K), the optimal way to observe them is at ultraviolet (UV) wavelengths, where they define a bright and well-defined sequence that is easily distinguishable in the CMD. In fact in the wavelength regime between 1800 Å and 3500 Å, giants, which are the brightest objects at optical and near-infrared bands, give a negligible contribution to the total light. Therefore, stellar crowding is negligible, which makes identification of hot stars very easy.

2.1. Observations and Data Reduction

We combined high-resolution optical and UV images obtained with the Hubble Space Telescope (HST) and optical and UV wide-field images collected both from ground-based and space telescopes. In particular the data set is composed of

• 1.  
  high-resolution sample—it consists of a combination of images obtained with the Advanced Camera for Surveys (ACS) and the Wide Field Camera 2 (WFPC2) on board the HST. The WFPC2 data set (Prop. 6607, PI: F. R. Ferraro) has been already presented by Ferraro et al. (2003) and it consists of a series of images in the F255W, F336W, and F555W filters.This data set has been supplemented by ACS optical images already used by B10 and D11. In addition, in order to minimize the impact of saturation on bright stars, we supplemented that catalog with short exposure time images: two images in F606W and F814W with exposure time t_exp = 7 s each (Prop. 10775, PI: Sarajedini).As shown in Figure 1, the center of the cluster is located in the Planetary Camera (PC) for the WFPC2 data set and in the gap between the two chips of the ACS data set.
• 2.  
  wide-field sample—it consists of UV wide-field images secured with the Galaxy Evolution Explorer (GALEX; Schiavon et al. 2012; Dalessandro et al. 2012) and optical ground-based wide-field images obtained with the Wide Field Imager (WFI) mounted at the 2.2 m ESO-MPG telescope.The GALEX data set (PI: R. P. Schiavon, GI1 release) has been already presented by Schiavon et al. (2012) and it consists of two circular images of ∼1 deg², one obtained with the FUV channel and t_exp = 1911 s and one with NUV channel with t_exp = 25362 s. These images are aligned and the core of the cluster is approximately located in the center of the detectors.The WFI data set (Prop. 69.D-0582(A), PI: Ortolani) is composed of nine images in the I band, six with t_exp = 30 s and three with t_exp = 3 s, and of nine V-band images, six with t_exp = 50 s and three with t_exp = 5 s.

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The photometric analysis has been carried out by using DAOPHOTII (Stetson 1987) for all the images with the exception of the WFPC2 data set for which ROMAFOT (Buonanno et al. 1983) has been adopted. For the full description of the photometric reduction procedure see Ferraro et al. (2003), B10, and Schiavon et al. (2012).

2.2. Astrometry and Photometric Calibration

The catalogs obtained from each data set were put on the absolute astrometric system using a large number of stars in common with the Guide Star Catalogue (GSC2.3). First, we obtained the astrometric solution for each of the eight WFI chips by using a third-order polynomial solution found by the CataXcorr package.⁵ Since the core regions of GC do not host astrometric standard stars, we used the stars in the WFI catalog as secondary astrometric standards to extend the astrometric solution to the internal regions. All the stars in common with GALEX, and with the high-resolution sample were then used as secondary astrometric standards. Several hundreds of them have been found in each step and this allowed us to find a very accurate astrometric solution with typical uncertainties of about 02 in both right ascension (α) and declination (δ).

More than 200 stars in common with the publicly available "Photometric Standard Fields"⁶ catalog (Stetson 2000) were used to calculate the color equations needed to transform the V and I WFI magnitude into the standard Johnson–Cousin photometric system. The ACS m_F606W and m_F814W magnitudes were calibrated respectively to V and I by using the stars in common with the WFI catalog. In particular, the best linear fits to the star distribution in the (V–m_F606W, V − I) or the (I–m_F814W, V − I) planes have been applied. The same approach has been adopted for the m_F555W WFPC2 magnitudes, while m_F255W and m_F336W have been calibrated to the STMAG photometric system by using the procedure and zero points reported in Holtzman et al. (1995). The NUV ABMAG GALEX magnitudes have been converted to m_F255W by means of Equation (1) obtained by linearly fitting the stars in common in the (m_F255W − NUV, m_F255W − V) plane:

$$\begin{equation} m_{F255W}= {\rm NUV} + 0.02\times (m_{F255W}-V) + 0.39. \end{equation} \tag{ 1 }$$

The final catalog is composed of all stars in the WFPC2 catalog and those detected in the complementary ACS field of view (FOV) (see Figure 1). It also includes the stars in the WFI catalog and external to both the WFPC2 and ACS FOVs (Figure 2). Stars in the WFI catalog and in common with GALEX also have an m_F255W magnitude.

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2.3. Center of Gravity and Density Profile

We determined the center of gravity C_grav of M10 by averaging the positions α and δ of selected stars (see below) lying in the FOV of the WFPC2/PC, as previously done in other works by our group (see Dalessandro et al. 2009 for example). We choose the center listed by Goldsbury et al. (2010) as the initial guess for our iterative procedure (Montegriffo et al. 1995). In order to avoid spurious or incompleteness effects, we performed three different measurements by using three subsamples of stars respectively with V < 19, V < 18.5, and V < 18. The resulting C_grav is the average of three measurements thus obtained and it is located at α_J 2000 = 16^h57^m892, δ_J2000 = −4°05'5807 (R.A. = 254.2871636 decl. = −4.0994655). C_grav is located at ∼35 northwest from the one published by Goldsbury et al. (2010). We checked that this difference does not have any impact on the present analysis.

Taking advantage of the wide radial coverage of our photometric catalog which extends to distances from C_grav to r ∼ 1400'', we constructed the star count density profile for the full cluster extent. We considered only stars with 14 < V < 19 in the different data sets (see Figure 3). We divided the total FOV in 28 concentric annuli centered on C_grav and reaching r = 1300''. Each annulus was then split into a number of sub-sectors (two or four depending on the maximum angular coverage constrained by the WFI FOV). In each sub-sector the density was estimated as the ratio between star counts and area. The density assigned to a given annulus is the average of the densities computed in each sub-sector. The error assigned to each density measure is defined as the dispersion from the mean of the sub-sectors composing the considered annulus. The resulting density profile is shown in Figure 4. The three outermost points have almost the same density, defining a plateau, which was used to define the background density level (∼2 stars arcmin⁻²).

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We performed a fit of the profile by using a single-mass King model (King 1966). The best-fit model is shown in Figure 4 and the derived values of the core radius r_c = 41 ± 1'', concentration c = 1.41 ± 0.03, and tidal radius r_t = 1053 ± 100''⁷ are reported. The concentration obtained from our best fit is in good agreement with those found by Harris (1996—edition 2010; c = 1.40) and McLaughlin & van der Marel (2005; c = 1.41), while r_c is slightly smaller than previous estimates (r_c = 51'' from Harris 1996; r_c = 464 from McLaughlin & van der Marel 2005) based on surface brightness profiles fitting. In an upcoming paper (P. Miocchi et al. 2013, in preparation), we will present a detailed comparison between observed density profiles and different theoretical models for a large sample of GGCs. For the case of M10, multi-mass King models and Wilson models (Wilson 1975) result in a significantly lower quality fit than the best solution described above.

In order to study the BSS radial distribution, we need to select both BSS and at least one reference star population.

3.1. BSS Selection

As explained in Section 2, CMDs involving UV photometry provide the best means for one to study the hottest stellar populations like BSS in GCs. In particular, the m_F255W filter from HST/WFPC2 allows for an excellent contrast between BSS and main-sequence TO stars (see also Figure 1 in Ferraro 2006c). In order to make the selection between different samples as homogeneous as possible, we used the (m_F255W, m_F255W − V) CMD. In this way, selection of BSS from WFPC2 and WFI/GALEX photometry was based on the same criteria.

As shown in Figures 5 and 6, in order to avoid possible contamination from TO and subgiant branch (SGB) stars, we adopted a limiting magnitude m_F255W = 20 (that is ∼1 mag brighter than the cluster TO). In addition, in order to limit the contamination from possible blends with the red giant branch (RGB) stars, we restricted our sample to stars bluer than (m_F255W − V) = 2.5. The boxes shown in Figures 5 and 6 illustrate this selection. These limits have been fixed on the basis of the quality of both the WFPC2 and the WFI/GALEX NUV CMDs. With these criteria we selected 47 and 48 BSS in the WFPC2 and WFI/GALEX FOVs, respectively.

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The complementary ACS is the only catalog for which we do not have UV band measurements. We guarantee the homogeneity of the BSS selection by translating the m_F255W magnitude cut into the V band. The adopted magnitude limit m_F255W = 20 corresponds to V ∼ 18. We adopted this magnitude cut to select BSS in the ACS FOV. Also in this case, an additional constraint on the (V − I) color has been adopted ((V − I) < 0.8). In this way we selected 25 additional BSS in the complementary ACS FOV (Figure 7).

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We obtained a rough estimate of the possible Galaxy field star contamination by counting the number of stars located in our catalog at distances larger than r_t and lying in the adopted (V, V − I) selection box. We find only one object over an area of about 150 arcmin² (corresponding to ∼0.01 stars arcmin⁻²).

3.2. The Reference Populations

In order to analyze the BSS radial distribution we first compared its cumulative radial distribution to those of the reference populations.

We took into account the effect of contamination by statistically decontaminating the selected populations. In particular, we divided the FOV into five concentric annuli centered on C_grav and for each of them we randomly subtracted a number of stars constrained by the average field densities quoted in the previous sections. The cumulative radial distribution of the statistically decontaminated populations is shown in Figure 8. As apparent, BSS (solid line) are more centrally concentrated than RGBs and HBs (dashed and dotted lines, respectively). We assessed the statistical significance of the observed difference between the radial distribution of the three populations by means of a Kolmogorov–Smirnov test. We found that BSS and HB have a probability P = 92% (corresponding to ∼1.7σ) to be extracted from different parent populations, and BSS and RGB have P > 99.9% (corresponding to a significance larger than 3σ).

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For a more quantitative analysis, we divided the total FOV into the same five annuli used before. The number of stars of each decontaminated population are reported in Table 1. In each of them we estimated the ratio between the number of decontaminated BSS and reference population stars in each annulus ($N_{{\rm BSS}}^{{\rm ann}}$/$N_{{\rm ref}}^{{\rm ann}}$). The radial distribution is clearly bimodal (see Figure 9), strongly peaked in the central regions, decreasing at intermediate radii and rising again outward. As expected for "normal" cluster populations, the number ratio between the reference populations N_HB/N_RGB does not show any peculiar and significant trend.⁹ As discussed in the Introduction, the BSS bimodal distribution is a common feature of most of the GCs studied so far (see F12).

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Table 1. Decontaminated Number Counts of BSS, RGB, and HB Stars and Fractions of Sampled Light

rint	rext	NBSS	NRGB	NHB	$L_{{\rm samp}}^{{\rm ann}}$/$L_{{\rm samp}}^{{\rm tot}}$
0''	50''	43	183	78	0.24
50''	150''	46	328	125	0.43
150''	300''	16	171	47	0.20
300''	550''	3	80	23	0.10
550''	1150''	4	24	7	0.03

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As a further check we compared the distribution of the double normalized ratio (Ferraro et al. 1993)

$$\begin{equation} R_{{\rm POP}}=\frac{N_{{\rm POP}}^{{\rm ann}}}{N_{{\rm POP}}^{{\rm tot}}} \Bigg/\frac{L_{{\rm samp}}^{{\rm ann}}}{L_{{\rm samp}}^{{\rm tot}}}, \end{equation} \tag{ 2 }$$

where $L_{{\rm samp}}^{{\rm ann}}$ and $L_{{\rm samp}}^{{\rm tot}}$ are the light sampled in each annulus and in the field covered by the observations, respectively (Table 1).

Figure 10 shows that the distributions of HB and RGB stars follow that of the cluster sampled light and R_HB/RGB = 1, as expected by stellar evolution theory (Renzini & Buzzoni 1986) for post-MS stars, while the distribution of R_BSS is bimodal. The normalized ratio at the cluster center is found to be R_BSS ∼ 1.8, which is in good agreement with values found for the central peaks of other GGCs (F12). The minimum of the distribution is located at r_min ∼ 10.35r_c. In the cluster outskirts the normalized ratio is R_BSS ∼ 1, which is what one should expect to find for binary systems and their by-products evolved in isolation (see Section 5).

Simple analytical models (Mapelli et al. 2004, 2006; Leigh et al. 2011) have shown that the observed radial distribution of BSS is well reproduced by modeling the dynamical friction acting on the binary population. By using Equation (1) in Mapelli et al. (2004, see also Binney & Tremaine 1987) and the best-fit King model obtained in Section 2.3, we estimated the distance at which a star as massive as 1.2 M_☉ (estimated average mass for a BSS; Shara et al. 1997) would have already sunk into the cluster core because of dynamical friction. It is predicted to be r ∼ 11r_c, nicely matching the observed minimum in the BSS radial distribution.

As clearly stated in F12, different BSS radial distributions are the observational evidence of different stages of the cluster dynamical history. As time passes, the distance from the cluster center at which dynamical friction has been effective on BSS (and their progenitors) increases, and so does the position of the minimum in the observed radial distribution. In particular, when mass segregation and dynamical friction start to segregate binaries (and their by-products) into the cluster center, a central peak in the BSS distribution occurs. Since the action of dynamical friction and mass segregation progressively extends to larger and larger distances from the center, the dip left by the massive objects that sunk to the bottom of the potential becomes visible at progressively increasing radii. In the meanwhile, the most remote BSS are still evolving in isolation in the outer regions of the cluster with nearly the same initial frequency (this generates the rising branch of the observed bimodal BSS distributions). Hence because of the dynamical friction effect, the dip of the distribution progressively moves outward with increasing (dynamical) age of the cluster. In a highly evolved cluster, we can expect that virtually all the binaries and their by-products (at any distance from the cluster center) have sunk into the cluster core, thus generating a single central peak in the BSS radial distribution, as observed for example in NGC 1904 (Lanzoni et al. 2007b).

F12 show that the BSS radial distribution is a good tool to rank the dynamical stage reached by stellar systems, thus allowing a direct measure of cluster dynamical age purely from observed properties. In F12, M10 is classified as a Family II GC. This family is populated by clusters with intermediate dynamical ages. In addition, the r_min value found for M10 positions it toward the dynamically older end of Family II clusters. F12 showed that the core relaxation time (as well as the half-mass relaxation time) is a linear function of r_min. This behavior allowed the definition of the "dynamical clock": clusters with relaxation times of the order of the age of the universe show no sign of BSS segregation (hence the radial distribution is flat and r_min is not defined). For decreasing relaxation times, the radial position of the minimum increases progressively.

The structural parameters obtained in the present work for M10 are slightly different from those adopted by F12. Following the approach used by the authors, we detail here the calculations for the core relaxation time and the position of M10 in the "dynamical clock" scheme on the basis of the results obtained in Section 2.3.

The core relaxation time (t_rc) was computed by using Equation (10) in Djorgovski (1993):

$$\begin{equation} t_{rc} = 1.491 \times 10^7\ {\rm yr} \times \frac{0.5592}{\ln (0.4 N_\star)} \frac{\sqrt{\rho _{M,0}}}{\langle m_\star \rangle } r_c^3, \end{equation} \tag{ 3 }$$

where N_⋆ is the total number of stars in the cluster, ρ_{M, 0} is the central mass density in M_☉ pc⁻³, and r_c is the core radius in pc. The values quoted in Djorgovski (1993) for a number of parameters were adopted, namely, the average stellar mass 〈m_⋆〉 = 0.3 M_☉, the stellar mass-to-light ratio in the V band M/L_V = 3, and the Sun V-band absolute magnitude M_☉V = 4.79. The number of stars N_⋆ has been obtained as the ratio between the total cluster mass M_tot and 〈m_⋆〉. M_tot has been calculated by using the M/L_V value quoted above, a bolometric correction factor for the V band of 1.4, and the total luminosity L_V. The latter has been derived from the integrated V magnitude of the cluster V_t = 6.60 (Harris 1996), and the distance modulus (M − m)₀ = 13.38 and reddening E(B − V) = 0.28 quoted in Ferraro et al. (1999). The central mass density has been obtained as ρ_{M, 0} = μ_V/(p × r_c), where μ_V is the central surface brightness in L_☉/pc², p is a parameter which depends on the cluster King concentration c as in Equation (6) of Djorgovski (1993). To compute these parameters we used the μ_V = 17.70 mag arcsec⁻² quoted by Harris (1996) and corrected for extinction, and the concentration (c = 1.41) and core radius (r_c = 41'') obtained from the best-fit King model.

In Figure 11, we highlight the new position of M10 in the (t_rc/t_H,r_min) logarithmic plane. As already discussed, M10 represents together with a few other GCs, a sort of bridge between Family II and Family III (triangles; Figure 11). In fact r_min is quite distant from the cluster center, but the BSS radial distribution is still bimodal.

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In recent studies about both the mass segregation profile (B10) and the radial distribution of binary stars (D11), we have obtained similar results to the ones reported in the present work. In particular the radial distributions of binary stars and BSS show a very similar behavior at least at distances in which binaries have been analyzed (r < 300''). Indeed they both show clear evidence that in M10 energy equipartition has been achieved and heavier stars are moving on inner orbits.

We thank the anonymous referee for the careful reading and useful comments that improved the presentation of this work. This research is part of the project COSMIC-LAB (http://www.cosmic-lab.eu) funded by the European Research Council (under contract ERC-2010-AdG-267675). R.P.S. acknowledges support from the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., on behalf of the international Gemini partnership of Argentina, Australia, Brazil, Canada, Chile, and the United States of America.