GC-LMXB Metallicity

Milky Way Globular Cluster Metallicity and Low-Mass X-ray Binaries: The Red Giant Influence

N. Vulic, P. Barmby, & S. C. Gallagher
Department of Physics & Astronomy, Western University, London, ON, N6A 3K7, Canada
nvulic@uwo.ca
Received; Accepted
Abstract

Galactic and extragalactic studies have shown that metal-rich globular clusters (GCs) are approximately three times more likely to host bright low-mass X-ray binaries (LMXBs) than metal poor GCs. There is no satisfactory explanation for this metallicity effect. We tested the hypothesis that the number density of red giant branch (RGB) stars is larger in metal-rich GCs, and thus potentially the cause of the metallicity effect. Using Hubble Space Telescope photometry for 109 unique Milky Way GCs, we investigated whether RGB star density was correlated with GC metallicity. Isochrone fitting was used to calculate the number of RGB stars, which were normalized by the GC mass and fraction of observed GC luminosity, and determined density using the volume at the half-light radius (). The RGB star number density was weakly correlated with metallicity [Fe/H], giving Spearman and Kendall Rank test -values of 0.00016 and 0.00021 and coefficients and respectively. This correlation may be biased by a possible dependence of  on [Fe/H], although studies have shown that  is correlated with Galactocentric distance and independent of [Fe/H]. The dynamical origin of the -metallicity correlation (tidal stripping) suggests that metal-rich GCs may have had more active dynamical histories, which would promote LMXB formation. No correlation between the RGB star number density and metallicity was found when using only the GCs that hosted quiescent LMXBs. A complete census of quiescent LMXBs in our Galaxy is needed to further probe the metallicity effect, which will be possible with the upcoming launch of eROSITA.

keywords:
galaxies: individual: Milky Way — X-rays: binaries — Galaxy: globular clusters: general — stars: color-magnitude diagrams
pubyear: 2017

1 Introduction

Low-mass X-ray binaries (LMXBs) have companion stars of masses M and are found in the field of a galaxy as well as in globular clusters (GCs). LMXBs form more efficiently in GCs due to increased stellar densities (Katz, 1975; Clark, 1975; Fabian et al., 1975; Pooley et al., 2003), and studies of Milky Way LMXBs found that their formation rate per unit stellar mass is 100 times greater in GCs compared to the field (Katz, 1975; Clark, 1975). Similar results have been found in elliptical galaxies (Sarazin et al., 2003; Jordán et al., 2004; Kim et al., 2006; Sivakoff et al., 2007; Kundu et al., 2007; Humphrey & Buote, 2008; Kim et al., 2009). Numerous relationships exist between GC properties and LMXBs. Globular clusters that are brighter/more massive, more compact (with smaller core radius ), and more metal-rich (redder) favour LMXB formation in both the Milky Way (Grindlay, 1993; Bellazzini et al., 1995) and other nearby galaxies (Kundu et al., 2002; Maccarone et al., 2004; Jordán, 2004; Trudolyubov & Priedhorsky, 2004; Sivakoff et al., 2007; Kundu et al., 2007; Peacock et al., 2010; Paolillo et al., 2011; Kim et al., 2013; Agar & Barmby, 2013; Mineo et al., 2014; Vulic et al., 2014). These studies have confirmed that metal-rich clusters are times more likely to host LMXBs with limiting luminosities erg s for Milky Way and extragalactic observations. The dependence on mass and compactness is straightforward to explain because more stars and a higher density promote stellar interactions that create binaries. However, the metallicity dependence is still a mystery.

Various explanations have been suggested to explain the metallicity dependence, such as magnetic braking in main sequence stars (Ivanova & Kalogera, 2006) or irradiation-induced stellar winds in low-metallicity stars (Maccarone et al., 2004). Bellazzini et al. (1995) was the first to indicate that the larger radii and masses of metal-rich stars would increase the rate of tidal capture in metal-rich GCs, thus increasing the number of LMXBs. Ivanova et al. (2012) posited that the difference in number densities and average masses of red giant stars in metal-rich versus metal-poor extragalactic GCs can explain the difference. Depending on their evolutionary state, GC-LMXBs can have either a main sequence, red giant, or white dwarf companion. Red giants promote dynamical formation of LMXBs via binary exchange interactions and physical collisions, serving as the seeds for dynamical formation of bright LMXBs. A strong argument for red giants being donor stars for neutron star GC-LMXBs with X-ray luminosities erg s is that these systems require companions with higher mass-loss rates. A full population synthesis study is still needed to confirm the red giant scenario, but here we attempt to address the observational effect.

We will use observations of Galactic GCs to compare the number and number density of red giants in clusters with and without LMXBs. In the Milky Way, 18 bright LMXBs are known in 14 GCs (Bahramian et al., 2014). Simulations by Ivanova et al. (2008) have shown that RGB stars are not expected to be donors for most Galactic GC-LMXB systems. However, RGB stars cannot be resolved in extragalactic GC cores, and so we are limited to the Milky Way population. While the prediction of Ivanova et al. (2012) was for bright ( erg s) extragalactic neutron star GC-LMXBs, red giants serve as the seeds for bright ultracompact white dwarf-neutron star systems. In addition, main sequence-neutron star binaries (e. g. that are not X-ray sources) or LMXBs (below the ‘bright’ limit) can evolve into the typical bright persistent LMXBs as observed in extragalactic studies. To assess whether the number of red giants in LMXB-hosting clusters is proportionally larger than in GCs without LMXBs, we will use the method devised by Nataf et al. (2013, hereafter N13). N13 used 72 Galactic GCs to study the red giant branch bump brightness and number counts by combining data from the Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) and Wide-field Planetary Camera 2 (WFPC2) instruments. They found that the ‘bump’ brightness and number have a strong dependence on metallicity, foreshadowing a likely dependence of GC-LMXBs on the number of red giants. They reported the total number of red giants in 48 GCs, which we will use in addition to 61 other GCs to investigate the effect of red giants on the metallicity dependence of LMXBs in Galactic GCs.

2 Data

We use data from two large HST surveys of Milky Way GCs. The first was carried out by Piotto et al. (2002) using the F439W and F555W filters on the WFPC2 instrument (WF2/WF3/WF4 each has a resolution of 0.1″ pixel, PC1 has a resolution of 0.046″ pixel). They studied 74 GCs with a wide range of properties by investigating colour-magnitude diagrams (CMDs), which are complete to approximately the main sequence turnoff. The Planetary Camera was centred on the cluster centre in each case. The more recent treasury survey by Sarajedini et al. (2007) and Dotter et al. (2007) used the F606W and F814W filters on the ACS Wide Field Camera instrument (resolution of 0.05″ pixel). Each cluster was centred in the ACS field. The program studied 71 GCs and obtained photometry with for stars down to 0.2 M. The benefit of using these treasury surveys is that in studying various aspects of Galactic GCs the authors produced precise and consistent photometric catalogues. Both catalogues have carried out artificial star tests that confirm completeness on the RGB. N13 used 72 Galactic GCs by combining the ACS and WFPC2 surveys. Because the authors were studying the RGB bump, they only chose clusters that had well-populated RGBs and RGB bumps (), and were not affected by differential reddening. They called this their ‘gold’ sample, which consisted of 48 GCs for which they reported RGB numbers. The remaining 24 GCs that made up their ‘silver’ sample had anomalous RGB bumps. The RGB numbers from the 48 GCs in the gold sample of N13 will be used in our study; we independently determine  for the remaining clusters. Combining the ACS and WFPC2 datasets there are 109 unique Galactic GCs, of which N13 analysed 48. The remaining 61 GCs consist of 34 from the ACS survey and 27 from the WFPC2 survey. To be consistent in our analysis we followed the methods of N13 to obtain RGB numbers for these GCs. First, we summarize some issues regarding the data that have been addressed by N13. The photometric filters used in each survey were different, and thus a standard calibration needed to be adopted. Photometric values were transformed from the F439W/F555W and F606W/F814W filters for WFPC2 and ACS, respectively, into the Johnson () and () planes in the original catalogue papers. A comparison between 13 GCs that were common to both surveys found that the difference in the derived magnitudes was negligible. The magnitudes from both catalogues are not reddening-corrected. Using both ACS and WFPC2 data it is possible that crowding could have been an issue. However, because PC1 was centred on the core of each GC, this effect will be reduced given the similar resolution (to ACS) and concentration of RGB stars in cluster cores.

3 Isochrone Fitting

Before we determined the number of RGB stars, we plotted isochrones for each of the 61 GCs to guide our analysis. We plotted isochrones only to identify the different regions of the CMD, such as the subgiant, red giant, asymptotic giant, and horizontal branches. We do not aim to determine the age, distance, or metallicity of a GC using this method but only to better approximate the RGB. We used the isochrones provided by the Dartmouth Stellar Evolution Database111http://stellar.dartmouth.edu/models, which provides isochrone grids based on the original 2008 version photometric systems (Dotter et al., 2008). We used the ACS Galactic Globular Cluster Survey isochrones that include the BVI/F606W/F814W empirical colours for the ACS dataset. These isochrones were created by Dotter et al. (2007) specifically for the ACS catalogue we use here. We used the empirical BVI colour isochrones from VandenBerg & Clem (2003) for our WFPC2 dataset. All isochrone grids have age intervals of 250 Myr between ages of Gyr, and 500 Myr intervals between ages of Gyr. Metallicities for [Fe/H] range from to , with steps of 0.5 in the range of interest for our work ( to ). The -enhancement [/Fe] is another probe of the metallicity, and in the models it refers to enhancements in the following -capture elements: O, Ne, Mg, Si, S, Ca, Ti. The value of [/Fe] ranges from to 8 in steps of 2. The models assume an initial He mass fraction Y = 0.245 + 1.54Z, with additional grids using Y of 0.33 and 0.40 for [/Fe] of 0.0 and 0.4 (see Table 2 of Dotter et al. (2007) for more details).

To determine the best-fitting isochrones for each of our GCs, we first assumed the metallicity [Fe/H] given by Harris (1996, 2010 edition, hereafter H10)222http://www.physics.mcmaster.ca/Globular.html and found the nearest value of [Fe/H] from the isochrone grid. We then plotted isochrones with ages ranging from 115 Gyr for each of the 10 different combinations of [/Fe] and initial He mass fraction values on our CMDs. The isochrone magnitudes were adjusted for each cluster using its distance from the Sun (H10). Because we used the raw Johnson magnitudes that were not corrected for reddening, we shifted our isochrones based on the values given in H10. For the ACS survey, since we were working in the () plane, we converted the reddening using (Cardelli et al., 1989; Barmby et al., 2000). We obtained and using the standard Galactic extinction law (Cardelli et al., 1989). A number of GCs had all their isochrones shifted away from the main sequence and RGB, with no overlap. This arose from the uncertainty in the distance to a GC and also the conversion factor for reddening, which caused inaccurate values. For these isochrones we shifted the values to account for this effect. We chose the best-fitting CMD that most accurately represented the main sequence, subgiant and red giant branches. We cross-checked the ages determined from isochrone fitting with results from Dotter et al. (2010), who used the HST magnitude plane for isochrone fitting, to ensure our results were consistent. We report the results of our isochrone fitting in Table 1, where the parameters do not reflect precise values for each cluster but instead the values for a specific isochrone.

Globular Cluster Age (Gyr) [Fe/H] [/H] E(BV) E(BV) Shift E(VI) Instrument
Arp 2 13.0 -2.0 0.2 0.15 0.05 0.19 ACS
E 3 13.0 -1.0 0.2 0.33 0.03 0.42 ACS
IC 4499 12.0 -1.5 0.2 0.25 0.02 0.32 ACS
NGC 288 12.5 -1.5 0.4 0.03 0.00 0.04 ACS
NGC 2298 13.0 -2.0 0.2 0.27 0.12 0.33 ACS
NGC 4147 13.0 -2.0 0.2 0.06 0.04 0.08 ACS
NGC 4590 13.0 -2.0 0.2 0.08 0.03 0.09 ACS
NGC 4833 13.0 -2.0 0.4 0.38 0.06 0.48 ACS
NGC 5053 13.5 -2.5 0.2 0.04 0.03 0.05 ACS
NGC 5139 12.0 -1.5 0.2 0.17 0.05 0.21 ACS
NGC 5466 13.0 -2.0 0.2 0.04 0.04 0.04 ACS
NGC 6101 13.0 -2.0 0.2 0.15 0.10 0.19 ACS
NGC 6121 12.5 -1.0 0.4 0.41 0.07 0.52 ACS
NGC 6144 13.5 -2.0 0.2 0.49 0.13 0.62 ACS
NGC 6366 12.0 -0.5 0.2 0.71 0.00 0.89 ACS
NGC 6397 13.5 -2.0 0.2 0.21 0.04 0.27 ACS
NGC 6426 12.0 -2.0 0.2 0.45 0.09 0.56 ACS
NGC 6496 12.0 -0.5 0.2 0.21 0.06 0.26 ACS
NGC 6535 13.0 -2.0 0.2 0.48 0.14 0.60 ACS
NGC 6656 12.5 -1.5 0.2 0.40 0.06 0.50 ACS
NGC 6715 12.0 -1.5 0.2 0.17 0.02 0.21 ACS
NGC 6717 13.0 -1.5 0.2 0.27 0.05 0.34 ACS
NGC 6779 13.5 -2.0 0.2 0.28 0.02 0.35 ACS
NGC 6809 13.5 -2.0 0.2 0.14 0.06 0.18 ACS
NGC 6838 12.5 -1.0 0.2 0.27 0.02 0.34 ACS
NGC 7099 13.0 -2.5 0.2 0.09 0.06 0.11 ACS
Palomar 1 7.0 -0.5 0.2 0.16 0.01 0.20 ACS
Palomar 12 9.5 -1.0 0.0 0.06 0.04 0.08 ACS
Palomar 15 13.0 -2.0 0.2 0.47 0.07 0.59 ACS
Palomar 2 12.0 -1.5 0.2 1.19 -0.05 1.50 ACS
Pyxis 12.0 -1.0 0.2 0.28 0.07 0.35 ACS
Ruprecht 106 10.0 -1.5 0.2 0.23 0.03 0.28 ACS
Terzan 7 8.0 -0.5 0.0 0.08 0.01 0.10 ACS
Terzan 8 13.0 -2.0 0.4 0.16 0.04 0.20 ACS
IC 1257 12.0 -1.5 0.0 0.73 - - WFPC2
NGC 1904 12.0 -1.5 0.6 0.01 - - WFPC2
NGC 2419 12.5 -2.0 0.4 0.08 - - WFPC2
NGC 4372 13.5 -2.0 0.8 0.39 - - WFPC2
NGC 5694 13.5 -2.0 0.8 0.09 - - WFPC2
NGC 5946 13.5 -1.5 0.8 0.54 - - WFPC2
NGC 6235 12.0 -1.5 0.6 0.31 - - WFPC2
NGC 6256 10.0 -1.0 0.0 1.09 - - WFPC2
NGC 6266 12.0 -1.0 0.0 0.47 - - WFPC2
NGC 6273 12.0 -1.5 0.2 0.38 - - WFPC2
NGC 6287 13.5 -2.0 0.8 0.60 - - WFPC2
NGC 6293 13.5 -2.0 0.4 0.36 - - WFPC2
NGC 6316 13.5 -0.5 0.0 0.54 - - WFPC2
NGC 6325 13.5 -1.5 0.6 0.91 - - WFPC2
NGC 6342 13.5 -0.5 0.0 0.46 - - WFPC2
NGC 6355 13.5 -1.5 0.2 0.77 - - WFPC2
NGC 6380 5.0 -1.0 0.8 1.17 - - WFPC2
NGC 6401 12.5 -1.0 0.6 0.72 - - WFPC2
NGC 6440 11.0 -0.5 0.0 1.07 - - WFPC2
NGC 6453 13.5 -1.5 0.0 0.64 - - WFPC2
NGC 6517 9.0 -1.0 0.0 1.08 - - WFPC2
NGC 6522 13.0 -1.5 0.8 0.48 - - WFPC2
NGC 6539 7.0 -0.5 0.0 1.02 - - WFPC2
NGC 6540 12.0 -1.5 0.0 0.66 - - WFPC2
NGC 6544 13.0 -1.5 0.2 0.76 - - WFPC2
NGC 6642 13.5 -1.5 0.8 0.40 - - WFPC2
NGC 6712 12.5 -1.0 0.2 0.45 - - WFPC2
  • Isochrone fitting parameters for the 61 GCs without reported RGB numbers in N13. The age, metallicity ([Fe/H]), and helium enhancement ([/Fe]) are the values used for the best-fitting isochrones and do not reflect precise values for each cluster. The values are taken from H10, while the values were derived using (Cardelli et al., 1989; Barmby et al., 2000). values were only needed for ACS data because CMDs were created in the () plane. This conversion was not accurate for all clusters and therefore an offset in the original ) values for ACS clusters was introduced to properly align the isochrone. This value is shown in the sixth column as Shift. The last column indicates which camera was used to observe the cluster.

Table 1: Isochrone Fitting Parameters

4 Red Giant Branch Star Numbers

In order to determine the number of RGB stars in each GC, , we inspected the CMDs of each cluster individually to create a bounded area that represented the RGB. Following the technique of N13 (D. M. Nataf, priv. comm.), we required the bounding region for the RGB to be as long and wide as possible. We selected the lower bound to be approximately 0.5 magnitudes above the mean brightness of the subgiant branch. This attempts to eliminate any foreground stars that may be contaminating the region. Specifically, some clusters had abrupt subgiant branches where the main sequence and RGB are not well-separated, introducing more contamination from foreground stars near the subgiant branch region of the CMD. The upper bound was selected based on the decreasing density of stars towards the tip of the RGB, and the beginning of the curve in the distribution of stars that represents the start of the asymptotic giant branch. In some cases the horizontal branch could be used as a reference point for the end of the RGB. We limited the width of the parallelogram resulting from the lower and upper bounds for two reasons. First, moving too far blueward of the RGB can result in horizontal branch stars being included in our estimate of . Second, the wider our parallelogram, the higher incidence of foreground stars we can expect to contaminate our sample, further biasing our approximation. In Figure 1 we show the CMD of NGC 7099, a metal-poor GC with minimal extinction and large concentration parameter. The blue parallelogram reflects the criteria just summarized, and includes 332 RGB stars. The CMDs for the remaining ACS and WFPC2 GCs are in Appendices A and B, respectively. In Table 2 we present the  values and the properties for each GC in our study. This includes cluster parameters from H10: absolute V magnitude , metallicity [Fe/H], concentration parameter (), core radius , half-light radius , and the distance from the Sun . The upper and lower limits (UL and LL) on  were derived using for values and Poisson statistics (Gehrels, 1986) for values . We also include the mass and mass-to-light ratios taken from Table 8 (column 6) of McLaughlin & van der Marel (2005, see Section 5.2 for more details). Masses were derived by multiplying by total cluster luminosity derived from .

Figure 1: Colour-magnitude diagram of NGC 7099 in the Johnson plane without reddening correction. The overplotted best-fitting isochrone (purple curve) has parameters given in Table 1. The blue parallelogram corresponds to the conservative estimate of the region where red giant branch stars exist, giving the number of red giant branch stars in the cluster . The open star at top-centre indicates that the cluster hosts a quiescent LMXB. Various cluster parameters from H10, including the absolute magnitude  and concentration parameter are shown at top-left. Average photometric uncertainties are represented by the grey error bar at bottom-right. The CMDs for the remaining ACS and WFPC2 GCs are in Appendices A and B, respectively.

5 Normalizations

5.1 Globular Cluster Luminosity and Foreground Contamination

A number of normalizations were required in order to effectively use the  parameter in our analysis. The first and most obvious is for the instrument field of view. For the 109 unique GCs for which  was determined, 71 come from the ACS survey and 38 from the WFPC2 survey. The ACS instrument has a slight parallelogram shape and is comprised of the Wide Field Camera 1 and 2, with a total field of view of 202″ by 202″. The WFPC2 is made up of 4 CCDs, 3 wide field cameras (WF2, WF3, WF4), each with field of view 75″ by 75″, and the Planetary Camera (PC1), having a 32″ by 32″ field of view. Therefore the WFPC2 is essentially a square of area 150″ a side with a piece missing due to the size of PC1. We needed to account for the difference in observed area of each cluster including the different fields of view of ACS and WFPC2. All GCs in the ACS survey were observed twice in each filter, with the fields overlapping each other close to the 100% level. The WFPC2 survey was a snapshot program where the numerous exposures overlapped similar to the ACS survey. We determined the total area observed for each cluster (in pc) by counting the nonzero pixels in the merged images for both the ACS and WFPC2 surveys.

However, the issue was exacerbated because the fraction of each GC observed (physical size) depends on the instrument field of view and the cluster’s distance. Therefore the appropriate correction involved determining the fraction of cluster luminosity observed, , where is observed cluster luminosity and is the total luminosity of the cluster. was calculated by using GC absolute magnitudes333These absolute magnitudes are corrected for foreground Galactic extinction.  from H10. No uncertainties are reported for any of the values and so we adopt a conservative universal uncertainty of 0.2 magnitudes, consistent with the uncertainty of the globular cluster luminosity function peak (Kavelaars & Hanes, 1997). For this calculation and others, we used the reference values from Mamajek (2012) for the Sun444https://sites.google.com/site/mamajeksstarnotes/basic-astronomical-data-for-the-sun of L erg s, M, . The observed cluster luminosities, , were calculated by summing the photometry from each cluster field. Because each star in a field of view has an apparent magnitude associated with it, we converted to flux and determined . By working in the band for all clusters and using to get we remain consistent within one passband. However, by summing the flux from all stars in a given field of view we were also including the contribution from foreground stars, which biases our calculations. This has the opposite effect of extinction in that it would raise our total observed luminosity. To account for this effect we estimated the contamination from Galactic foreground stars using the Besançon models555http://model.obs-besancon.fr/ (Robin et al., 2003). Using the (Galactic) co-ordinates from the centres of the ACS and WFPC2 images (not always the cluster centres), along with the solid angle in deg, we obtained a detailed list of parameters of foreground stars for each cluster. For the solid angle, we used the area for each cluster field of view as described above. The models produce reliable predictions for the luminosity and colour distributions in the optical/near-infrared for the stars expected to be in the field of view. We used the apparent magnitudes and given visual extinctions from the model to determine the total absolute magnitude from foreground stars, (fgstars). Subtracting this foreground flux from the total observed flux allowed us to calculate accurate observed cluster luminosities. represents the actual cluster luminosity after removing the foreground star contamination and correcting for extinction.

For some of the clusters we were not able to accurately determine a value for , likely due to the uncertainty associated with distance, extinction, and the foreground star modelling/photometry. For 3 GCs, namely Lynga 7, Palomar 12, and Terzan 7, we had to remove the brightest star from the photometric catalogue. These stars were magnitudes brighter than the next brightest star, which was part of the smooth distribution of cluster stars. For NGC 6453 and Palomar 2, we used updated extinction values from Schlafly & Finkbeiner (2011) obtained using the NASA/IPAC database666http://irsa.ipac.caltech.edu/applications/DUST/. Our  values vary from , where the lower limit corresponds to NGC 4372, a large, nearby (5.8 kpc) GC that was observed with the small field of view of WFPC2. The upper limit of 97% is for Palomar 1, a very dense GC with small core and half-light radii observed with ACS. In Figure 2 we show the number of RGB stars normalized by the observed GC luminosity vs. metallicity. Clusters with LMXBs are indicated by filled red circles and clusters with qLMXBs by open blue circles. NGC 6440 and NGC 7078 (M15) each have two LMXBs. From our sample of 109 GCs we have 10 bright LMXBs in 8 GCs. We used results compiled by Verbunt & Lewin (2006) and Bahramian et al. (2014) for LMXBs and qLMXBs in Galactic GCs (see Table 2). The uncertainties on [Fe/H] were taken from Carretta et al. (2009). For the five GCs in our sample that didn’t have uncertainties on [Fe/H], IC 1257, Lynga 7, NGC 6426, NGC 6540, and Terzan 8, we set them to the mean uncertainty value of the remaining GCs. The  distribution still needs to be normalized in order to appropriately assess its impact on LMXB formation. We present the values of , , and (fgstars) for each cluster in Table 2.

Figure 2: RGB star number vs. metallicity [Fe/H]. Black plusses represent normal GCs, open blue circles are GCs hosting quiescent LMXBs and filled red circles are GCs hosting bright LMXBs. NGC 6440 and NGC 7078 each have 2 LMXBs. GC names are indicated near each datapoint. The  parameter is expected to scale linearly with mass and thus needs to be normalized by mass in order to assess any potential relationship between RGB stars and LMXBs.

5.2 Globular Cluster Mass

Normalizing  by the fraction of observed luminosity accounts for RGB stars that would have been observed had the field of view been larger. However, even if each GC had , our result would still be biased towards clusters that are more massive, which by extension have a larger number of RGB stars. Because the relative  is important, we needed to normalize  by the mass of each GC. We calculated cluster masses using our value for the total cluster luminosity and the mass-to-light ratio of the cluster. McLaughlin & van der Marel (2005) tabulated band (Table 8, column 6 of their paper) for 148 Galactic GCs, which includes the 109 GCs in our work (see Table 2). The ratios were derived using the code from Bruzual & Charlot (2003) and the disc initial mass function of Chabrier (2003). We used our cluster luminosities to determine the mass of each GC in our sample. In Figure 3 we show the relationship between / and the GC mass.

Figure 3: The number of RGB stars  normalized by the fraction of observed cluster luminosity  vs. the cluster mass. GC metallicity [Fe/H] is indicated by the colourbar to the right. The strong correlation between the total number of RGB stars in a GC and its mass is evident, as expected. The dashed line shows the weighted least squares fit to the data, which is given in equation 1.

As expected, the number of RGB stars increases with GC mass. The datapoint with a large uncertainty in  is NGC 4372, which happens to be the cluster for which  was 5%, having a large uncertainty of 15% (300% relative). A weighted least-squares fit to the data produced the relationship in equation 1.

(1)

In addition, GC mass has a strong influence on the presence of an LMXB (e.g. Sivakoff et al., 2007; Vulic et al., 2014). Therefore not only are we removing the intrinsic dependence of RGB number on mass but also a parameter (mass, via ) that is known to promote the production of LMXBs. When normalizing by GC mass we obtain the number of RGB stars per unit mass,  M, which we call . In Figure 4 we plot  vs. metallicity using the same format as Figure 2.

Figure 4:  parameter (RGB star number normalized by GC mass) vs. metallicity [Fe/H]. Black plusses represent normal GCs, open blue circles are GCs hosting quiescent LMXBs and filled red circles are GCs hosting bright LMXBs. NGC 6440 and NGC 7078 each have 2 LMXBs. Names of GCs with LMXBs are indicated near each datapoint. The weighted least squares fit (equation 2) is shown, which is consistent with a flat distribution. This result indicates no relationship with the number of RGB stars per M and metallicity of a GC.

Figure 4 shows that  varies very little with metallicity, where only a slightly positive correlation may exist. The much larger uncertainties in the  parameter are a result of the uncertainty in GC masses, which propagate from the values for total cluster luminosity . A weighted least squares fit to the data is shown by the solid line and reproduced in equation 2, where M is the GC mass in terms of M.

(2)

We have effectively removed the bias that would exist in this relationship due to mass and thus have a quantity  that can be independently compared to the metallicity. This is important because a mass-metallicity relationship could also affect our results. In early-type galaxies, the brighter metal-poor GCs show a relationship between mass and metallicity, dubbed the ‘blue tilt’, thought to arise from self-enrichment in GCs (Peng et al., 2006; Harris et al., 2006; Mieske et al., 2006; Strader et al., 2006; Bailin & Harris, 2009). In the Milky Way, a mass-metallicity relationship has not been detected for several reasons (e.g. cluster to cluster scatter in mean [Fe/H], sample size, mass limit), although its existence has not been ruled out (Strader & Smith, 2008). Therefore it is beneficial to remove the dependence on mass to avoid any intrinsic dependence of massive metal-poor Galactic GCs on metallicity. To test whether a statistically significant relationship existed between  and [Fe/H], we split our data into separate groups that represented all GCs, those with LMXB, qLMXBs, and either an LMXB or qLMXB. Performing Spearman’s rank test on each of these groups for the  and metallicity parameters all returned -values , indicating we cannot reject the null hypothesis (i.e. there is no evidence for correlation).

5.3 Globular Cluster Volume

While there is no correlation between  and metallicity, the predictions of Ivanova et al. (2012) were based on the hypothesis that the number densities of RGB stars influence the formation rate of LMXBs. Therefore we must normalize this value by some volumetric quantity. We used the half-light radius (in pc) to determine the volume of a cluster. Uncertainties on were taken from McLaughlin & van der Marel (2005) and were on average , where this mean value was used for GCs without uncertainties.  is a characteristic scale for the size of a GC because it is not affected by dynamical evolution in the same way is. The uncertainty associated with can be large (e.g. Goldsbury et al., 2013), and the small values for many GCs mean that our sample size of RGB stars enters the Poisson regime. is also known to be one of the strongest indicators of LMXB formation via the stellar encounter rate, and we want to exclude parameters that influence LMXB formation. One would expect the majority of RGB stars to be located near the centre of a GC due to mass segregation, as they are among the most massive members of the cluster that appear on the CMD. There are a number of caveats with using to determine the volume within which RGB stars are located. Firstly, not all RGB stars will be located within . Because we only have projected distances of stars and not a 3D distribution, we can’t account for the distance of stars from the GC core along the line of sight. Therefore we cannot determine what fraction of the RGB stars that we have identified will be within . This would affect the number density of RGB stars since the volume within which a percentage of RGB stars resides would be different for each GC. However, while the projected and 3D distributions are not the same, this effect will average out for all clusters. We checked the radial distribution of the RGB stars we identified in each GC and most are not peaked near the core but instead can be approximated by a Gaussian. Using  means we assumed a constant density of RGB stars in the cluster to the half-light radius, which is not accurate given the radial distribution of all stars. This assumption is justified because while the stellar distribution peaks in the core, the peak of the RGB star distribution generally does not, so  as a characteristic size scale for GCs is acceptable in this case. Secondly, is another parameter, like mass, that influences the formation of LMXBs, where GCs with smaller (more compact) have been shown to preferentially host LMXBs in the Milky Way (Bregman et al., 2006) and other galaxies (Sivakoff et al., 2007; Jordán, 2004; Peacock et al., 2010; Vulic et al., 2014). The stellar encounter rate , which influences LMXB production, has a stronger correlation with LMXB occurrence when calculated using the core radius as opposed to (e.g. Peacock et al., 2010; Bahramian et al., 2013; Agar & Barmby, 2013). Even so, by using we would introduce an additional confounding effect in attempting to find a relationship between the RGB star density and [Fe/H]. This is a difficult degeneracy to remove since any measurement of the RGB density requires an estimation of the volume. In addition, has been shown to be weakly negatively correlated with [Fe/H] in M31 GCs (Barmby et al., 2007), while Vanderbeke et al. (2015) found tentative evidence for a correlation between  and [Fe/H] in Galactic GCs. Vanderbeke et al. (2015) state that this trend is caused by metal-rich GCs being more centrally concentrated than metal-poor GCs. Studies have found that most GC populations have metal-rich GCs that are on average 20% ( pc) smaller than metal-poor GCs, likely due to different dynamical histories (e.g. Kundu & Whitmore, 1998; Larsen et al., 2001; Jordán et al., 2005; Harris, 2009; Paolillo et al., 2011). Vanderbeke et al. (2015) concluded that the origin of the size difference () is related to the Galactocentric distance and not [Fe/H]. Miocchi et al. (2013) studied 26 Galactic GCs and also confirmed that the correlation between half-mass radius and Galactocentric radius does not depend on other cluster properties. Both studies confirm a purely dynamical origin for the correlation, suggesting tidal stripping from the bulge/disc was responsible for the correlation. If indeed  is independent of [Fe/H] and is only correlated with Galactocentric distance, then the location of a GC (and not ) influences its metallicity. Therefore, we calculated the RGB density using  and show its relationship with [Fe/H] in Figure 5.

Figure 5: RGB star density vs. metallicity [Fe/H]. The volume was calculated assuming spherical GCs with radius . Black plusses represent normal GCs, open blue circles are GCs hosting quiescent LMXBs and filled red circles are GCs hosting bright LMXBs. NGC 6440 and NGC 7078 each have 2 LMXBs. Names of GCs with LMXBs are indicated near each datapoint. The solid line shows the weighted least squares fit (equation 3), which has a steeper slope than the  best fit. This stems from the fact that GCs with smaller are more massive. The link between  and LMXBs is evident as the metal-rich LMXB-hosting GCs (red circles) are among the GCs with the highest RGB star number density at a given [Fe/H]. The correlation is biased by the intrinsic dependence of RGB star density on (compactness), however this degeneracy is difficult to remove.

The RGB star number density shows a stronger correlation with metallicity than does . A weighted least-squares fit to the data produced the relationship in equation 3.

(3)

Using Spearman’s rank test we found a -value of 0.00016 and coefficient . Our -value means we can reject the null hypothesis that the data is drawn from a random distribution, and the coefficient indicates a moderate linear relation. We also used the Kendall rank test and found a -value of 0.00021 and coefficient . Kendall’s rank test is not as sensitive to uncertainty as Spearman’s rank test but is more accurate for nonlinear correlations. The GCs with LMXBs preferentially have larger RGB star number densities as we expected based on their relation with , and all GC-LMXBs are located above the line of best fit in Figure 5. The qLMXBs are more prevalent in the metal-poor population and have larger mean RGB star number densities than the rest of the metal-poor population. However, GC 47 Tucanae (NGC 104), for example, has 5 qLMXBs, and so the qLMXB distribution in our Figures does not accurately represent number statistics for individual qLMXBs but instead of the clusters within which they reside. A detailed analysis of this population is beyond the scope of this work.

In Figure 6 we plot the unnormalized RGB star density (i.e. RGB stars not divided by GC mass) against metallicity. This quantity best represents the number density of RGB stars as defined in Ivanova et al. (2012). Because there is no evidence of a mass-metallicity relation for Galactic GCs, the fact that RGB stars are highly correlated with mass should not cause a metallicity effect. However, the explicit dependence of volume on , which in turn affects LMXB formation and can influence metallicity, remains. In equation 4 we present the weighted least squares fit from Figure 6. A Spearman Rank test gave a -value of 0.0035 and coefficient , indicating a slightly less significant correlation compared to the mass-normalized case.

Figure 6: RGB star density (not normalized by GC mass) vs. metallicity [Fe/H]. The volume was calculated using the cluster half-light radius and a spherical distribution for the GC. Black plusses represent normal GCs, open blue circles are GCs hosting quiescent LMXBs and filled red circles are GCs hosting bright LMXBs. NGC 6440 and NGC 7078 each have 2 LMXBs. Names of GCs with LMXBs are indicated near each datapoint. The solid line shows the weighted least squares fit (equation 4), which has a steeper slope than the RGB number density normalized by GC mass. As stated for Figure 5, affects LMXB formation and GC metallicity. The GCs with the largest RGB star density at a given metallicity are more likely to host LMXBs.
(4)

In Table 2 we report our values for the RGB fraction  and indicate whether the GC hosts an X-ray source. Where upper and lower limits (UL and LL) are indicated, Poisson statistics (Gehrels, 1986) are used for values while is used for values .

Globular Cluster [Fe/H] Concentration (UL) (LL) (fgstars) Mass Mass (UL) (LL) X-ray Source
mag pc pc pc mag M/L M/L M M
Arp 2 -5.29 -1.75 0.88 9.900 14.725 28600 125 11.180 11.180 0.270 0.179 12.56659 1.867 0.156 2.15E+04 4.34E+03 4.334 0.303 0.303 -
E 3 -4.12 -0.83 0.75 4.406 4.948 8100 18 6.754 5.177 0.465 0.239 16.66471 2.303 0.230 9.02E+03 1.89E+03 3.633 0.291 0.271 -
IC 1257 -6.15 -1.70 1.55 1.818 10.181 25000 107 10.344 10.344 0.394 0.079 9.50870 1.867 0.155 4.74E+04 9.58E+03 3.758 0.131 0.131 -
IC 4499 -7.32 -1.53 1.21 4.594 9.351 18800 260 16.125 16.125 0.573 0.119 14.02200 1.874 0.154 1.40E+05 2.82E+04 3.511 0.129 0.129 -
Lynga 7 -6.60 -1.01 0.95 2.094 2.548 7300 329 18.138 18.138 0.819 0.279 15.64936 2.524 0.276 9.70E+04 2.08E+04 3.617 0.176 0.176 -
NGC 0104 -9.42 -0.72 2.07 0.471 4.150 4500 2416 49.153 49.153 0.403 0.161 14.01694 2.348 0.239 1.21E+06 2.55E+05 3.694 0.197 0.197 qLMXB
NGC 1261 -7.80 -1.27 1.16 1.660 3.224 16300 808 28.425 28.425 0.838 0.228 10.10437 1.928 0.158 2.24E+05 4.51E+04 3.634 0.148 0.148 -
NGC 1851 -8.33 -1.18 1.86 0.317 1.795 12100 1241 35.228 35.228 0.850 0.231 13.02692 1.981 0.166 3.75E+05 7.58E+04 3.591 0.148 0.148 LMXB
NGC 1904 -7.86 -1.60 1.70 0.600 2.439 12900 446 21.119 21.119 0.398 0.171 10.74033 1.877 0.154 2.30E+05 4.64E+04 3.687 0.207 0.207 qLMXB
NGC 2298 -6.31 -1.92 1.38 0.974 3.079 10800 184 13.565 13.565 0.876 0.217 13.16012 1.870 0.157 5.50E+04 1.11E+04 3.582 0.142 0.142 -
NGC 2419 -9.42 -2.15 1.37 7.689 21.384 82600 1229 35.057 35.057 0.209 0.039 10.13530 1.903 0.161 9.82E+05 1.99E+05 3.777 0.121 0.121 -
NGC 2808 -9.39 -1.14 1.56 0.698 2.234 9600 3308 57.515 57.515 0.810 0.220 12.33190 2.018 0.172 1.01E+06 2.06E+05 3.605 0.148 0.148 -
NGC 288 -6.75 -1.32 0.99 3.495 5.773 8900 190 13.784 13.784 0.434 0.290 11.59449 1.972 0.165 8.70E+04 1.76E+04 3.702 0.305 0.305 qLMXB
NGC 3201 -7.45 -1.59 1.29 1.853 4.419 4900 214 14.629 14.629 0.345 0.094 11.97579 1.876 0.154 1.58E+05 3.18E+04 3.594 0.150 0.150 -
NGC 0362 -8.43 -1.26 1.76 0.450 2.051 8600 1060 32.558 32.558 0.715 0.152 8.28431 2.013 0.171 4.17E+05 8.47E+04 3.550 0.128 0.128 qLMXB
NGC 4147 -6.17 -1.80 1.83 0.505 2.695 19300 209 14.457 14.457 0.940 0.200 10.37009 1.869 0.157 4.84E+04 9.79E+03 3.663 0.131 0.131 -
NGC 4372 -7.79 -2.17 1.30 2.953 6.597 5800 76 8.718 8.718 0.055 0.157 11.04971 1.898 0.161 2.18E+05 4.43E+04 3.802 1.244 1.244 -
NGC 4590 -7.37 -2.23 1.41 1.738 4.524 10300 253 15.906 15.906 0.461 0.177 12.41205 1.893 0.160 1.48E+05 3.00E+04 3.569 0.191 0.191 -
NGC 4833 -8.17 -1.85 1.25 1.920 4.627 6600 483 21.977 21.977 0.410 0.099 9.50870 1.868 0.156 3.05E+05 6.17E+04 3.587 0.139 0.139 -
NGC 5024 -8.71 -2.10 1.72 1.822 6.821 17900 1155 33.985 33.985 0.668 0.139 10.08142 1.884 0.159 5.06E+05 1.02E+05 3.534 0.127 0.127 -
NGC 5053 -6.76 -2.27 0.74 10.528 13.210 17400 70 8.367 8.367 0.260 0.068 10.74033 1.931 0.164 8.60E+04 1.74E+04 3.496 0.153 0.153 -
NGC 5139 -10.26 -1.53 1.31 3.585 7.563 5200 2598 50.971 50.971 0.197 0.122 10.13530 1.872 0.154 2.09E+06 4.23E+05 3.800 0.283 0.283 qLMXB
NGC 5272 -8.88 -1.50 1.89 1.098 6.854 10200 1325 36.401 36.401 0.553 0.219 11.86501 1.877 0.154 5.89E+05 1.19E+05 3.609 0.194 0.194 qLMXB
NGC 5286 -8.74 -1.69 1.41 0.953 2.484 11700 1951 44.170 44.170 0.870 0.221 10.15669 1.868 0.155 5.15E+05 1.04E+05 3.638 0.141 0.141 -
NGC 5466 -6.98 -1.98 1.04 6.656 10.705 16000 128 11.314 11.314 0.359 0.069 11.04971 1.919 0.163 1.05E+05 2.12E+04 3.532 0.127 0.127 -
NGC 5634 -7.69 -1.88 2.07 0.660 6.304 25200 434 20.833 20.833 0.415 0.086 12.76173 1.873 0.157 1.96E+05 3.98E+04 3.726 0.127 0.127 -
NGC 5694 -7.83 -1.98 1.89 0.611 4.072 35000 634 25.179 25.179 0.537 0.101 10.42474 1.871 0.157 2.23E+05 4.52E+04 3.724 0.121 0.121 -
NGC 5824 -8.85 -1.91 1.98 0.560 4.202 32100 1383 37.189 37.189 0.506 0.122 15.46308 1.870 0.157 5.71E+05 1.16E+05 3.680 0.138 0.138 qLMXB
NGC 5904 -8.81 -1.29 1.73 0.960 3.862 7500 968 31.113 31.113 0.432 0.378 10.40342 1.958 0.163 5.76E+05 1.16E+05 3.590 0.391 0.391 qLMXB
NGC 5927 -7.81 -0.49 1.60 0.941 2.464 7700 1103 33.211 33.211 0.684 0.184 15.77700 2.926 0.345 3.43E+05 7.50E+04 3.673 0.151 0.151 -
NGC 5946 -7.18 -1.29 2.50 0.247 2.744 10600 344 18.547 18.547 0.590 0.404 9.61522 1.918 0.157 1.26E+05 2.54E+04 3.666 0.311 0.311 -
NGC 5986 -8.44 -1.59 1.23 1.422 2.965 10400 1229 35.057 35.057 0.677 0.160 10.13912 1.876 0.154 3.93E+05 7.92E+04 3.665 0.136 0.136 -
NGC 6093 -8.23 -1.75 1.68 0.436 1.774 10000 1286 35.861 35.861 0.816 0.222 10.33998 1.867 0.155 3.22E+05 6.51E+04 3.690 0.148 0.148 qLMXB
NGC 6101 -6.94 -1.98 0.80 4.345 4.704 15400 278 16.673 16.673 0.549 0.106 10.42474 1.869 0.157 9.83E+04 1.99E+04 3.712 0.124 0.124 -
NGC 6121 -7.19 -1.16 1.65 0.742 2.771 2200 140 11.832 11.832 0.236 0.087 9.61522 1.991 0.168 1.32E+05 2.67E+04 3.654 0.186 0.186 qLMXB
NGC 6139 -8.36 -1.65 1.86 0.441 2.497 10100 904 30.067 30.067 0.382 0.104 8.13620 1.868 0.155 3.63E+05 7.34E+04 3.814 0.148 0.148 qLMXB
NGC 6144 -6.85 -1.76 1.55 2.434 4.220 8900 232 15.232 15.232 0.533 0.265 9.92719 1.867 0.155 9.04E+04 1.83E+04 3.683 0.235 0.235 -
NGC 6171 -7.12 -1.02 1.53 1.043 3.221 6400 323 17.972 17.972 0.402 0.109 13.52426 2.089 0.186 1.30E+05 2.65E+04 3.792 0.150 0.150 -
NGC 6205 -8.55 -1.53 1.53 1.280 3.490 7100 1252 35.384 35.384 0.535 0.145 9.16737 1.881 0.154 4.36E+05 8.78E+04 3.730 0.148 0.148 qLMXB
NGC 6218 -7.31 -1.37 1.34 1.103 2.471 4800 380 19.494 19.494 0.361 0.464 11.91284 1.892 0.155 1.40E+05 2.82E+04 3.876 0.565 0.565 -
NGC 6229 -8.06 -1.47 1.50 1.065 3.194 30500 734 27.092 27.092 0.547 0.102 10.87180 1.904 0.156 2.81E+05 5.66E+04 3.680 0.120 0.120 -
NGC 6235 -6.29 -1.28 1.53 1.104 3.345 11500 137 11.705 11.705 0.572 0.149 9.92719 1.912 0.157 5.52E+04 1.11E+04 3.637 0.148 0.148 -
NGC 6254 -7.48 -1.56 1.38 0.986 2.496 4400 574 23.958 23.958 0.489 0.133 8.89801 1.885 0.154 1.63E+05 3.28E+04 3.857 0.148 0.148 -
NGC 6256 -7.15 -1.02 2.50 0.060 2.577 10300 246 15.684 15.684 0.653 0.189 10.60710 2.419 0.254 1.54E+05 3.27E+04 3.388 0.158 0.158 -
NGC 6266 -9.18 -1.18 1.71 0.435 1.820 6800 1210 34.785 34.785 0.307 0.109 9.58422 1.950 0.161 8.07E+05 1.63E+05 3.689 0.178 0.178 qLMXB
NGC 6273 -9.13 -1.74 1.53 1.101 3.379 8800 985 31.385 31.385 0.321 0.077 9.22696 1.868 0.155 7.38E+05 1.49E+05 3.619 0.137 0.137 -
NGC 6284 -7.96 -1.26 2.50 0.312 2.937 15300 644 25.377 25.377 0.276 0.075 10.89594 1.938 0.160 2.61E+05 5.26E+04 3.952 0.149 0.149 -
NGC 6287 -7.36 -2.10 1.38 0.793 2.023 9400 205 14.318 14.318 0.396 0.104 8.75438 1.892 0.160 1.46E+05 2.97E+04 3.548 0.147 0.147 -
NGC 6293 -7.78 -1.99 2.50 0.138 2.459 9500 427 20.664 20.664 0.374 0.101 8.91537 1.876 0.158 2.14E+05 4.33E+04 3.727 0.148 0.148 -
NGC 6304 -7.30 -0.45 1.80 0.360 2.437 5900 824 28.705 28.705 0.733 0.200 8.39241 2.567 0.284 1.88E+05 4.04E+04 3.776 0.151 0.151 -
NGC 6316 -8.34 -0.45 1.65 0.514 1.966 10400 513 22.650 22.650 0.208 0.054 8.89052 2.625 0.295 5.01E+05 1.08E+05 3.693 0.148 0.148 -
NGC 6325 -6.96 -1.25 2.50 0.068 1.429 7800 198 14.071 14.071 0.251 0.082 9.82771 2.007 0.170 1.07E+05 2.18E+04 3.866 0.170 0.170 -
NGC 6341 -8.21 -2.31 1.68 0.628 2.463 8300 730 27.019 27.019 0.686 0.186 9.95255 1.929 0.164 3.27E+05 6.63E+04 3.513 0.148 0.148 qLMXB
NGC 6342 -6.42 -0.55 2.50 0.124 1.805 8500 216 14.697 14.697 0.343 0.089 8.63129 2.484 0.267 8.09E+04 1.73E+04 3.892 0.149 0.149 -
NGC 6352 -6.47 -0.64 1.10 1.352 3.339 5600 280 16.733 16.733 0.475 0.271 9.07131 2.419 0.254 8.25E+04 1.75E+04 3.854 0.265 0.265 qLMXB
NGC 6355 -8.07 -1.37 2.50 0.134 2.355 9200 321 17.916 17.916 0.220 0.058 9.85393 1.888 0.155 2.81E+05 5.67E+04 3.715 0.145 0.145 -
NGC 6356 -8.51 -0.40 1.59 1.054 3.558 15100 1253 35.398 35.398 0.391 0.078 10.68691 2.703 0.309 6.03E+05 1.31E+05 3.726 0.128 0.128 -
NGC 6362 -6.95 -0.99 1.09 2.498 4.532 7600 287 16.941 16.941 0.546 0.149 8.73967 2.160 0.200 1.15E+05 2.36E+04 3.661 0.150 0.150 -
NGC 6366 -5.74 -0.59 0.74 2.209 2.973 3500 97 9.849 9.849 0.357 0.154 10.60710 2.282 0.225 3.97E+04 8.30E+03 3.835 0.213 0.213 qLMXB
NGC 6380 -7.50 -0.75 1.55 1.078 2.346 10900 450 21.213 21.213 0.715 0.195 8.52676 2.703 0.309 2.38E+05 5.16E+04 3.422 0.153 0.153 -
NGC 6388 -9.41 -0.55 1.75 0.346 1.497 9900 4003 63.269 63.269 0.791 0.215 9.88980 2.552 0.281 1.31E+06 2.80E+05 3.589 0.151 0.151 LMXB
NGC 6397 -6.64 -2.02 2.50 0.033 1.940 2300 111 10.536 10.536 0.350 0.117 9.58422 1.879 0.159 7.49E+04 1.52E+04 3.627 0.175 0.175 qLMXB
NGC 6401 -7.90 -1.02 1.69 0.771 5.889 10600 447 21.142 21.142 0.174 0.048 8.65301 2.135 0.195 2.72E+05 5.59E+04 3.975 0.150 0.150 -
NGC 6402 -9.10 -1.28 0.99 2.137 3.517 9300 942 30.692 30.692 0.232 0.063 9.66426 1.915 0.157 7.36E+05 1.48E+05 3.742 0.148 0.148 -
NGC 6426 -6.67 -2.15 1.70 1.558 5.513 20600 215 14.663 14.663 0.527 0.173 9.22696 1.925 0.164 7.89E+04 1.60E+04 3.714 0.170 0.170 -
NGC 6440 -8.75 -0.36 1.62 0.346 1.187 8500 1399 37.403 37.403 0.303 0.083 9.87176 2.981 0.354 8.30E+05 1.82E+05 3.745 0.152 0.152 LMXB
NGC 6441 -9.63 -0.46 1.74 0.439 1.923 11600 5777 76.007 76.007 0.785 0.214 10.09970 2.656 0.301 1.66E+06 3.60E+05 3.646 0.151 0.151 LMXB
NGC 6453 -7.22 -1.50 2.50 0.169 1.485 11600 719 26.814 26.814 0.775 0.211 10.00285 1.883 0.154 1.28E+05 2.58E+04 3.860 0.148 0.148 -
NGC 6496 -7.20 -0.46 0.70 3.123 3.353 11300 223 14.933 14.933 0.164 0.039 8.75438 2.497 0.270 1.67E+05 3.56E+04 3.912 0.142 0.142 -
NGC 6517 -8.25 -1.23 1.82 0.185 1.542 10600 590 24.290 24.290 0.309 0.084 8.06636 1.921 0.158 3.38E+05 6.81E+04 3.753 0.148 0.148 -
NGC 6522 -7.65 -1.34 2.50 0.112 2.240 7700 569 23.854 23.854 0.395 0.108 12.37469 1.901 0.156 1.92E+05 3.88E+04 3.874 0.148 0.148 -
NGC 6535 -4.75 -1.79 1.33 0.712 1.681 6800 50 10.340 8.822 0.764 0.254 8.91537 1.868 0.156 1.31E+04 2.64E+03 3.700 0.191 0.186 -
NGC 6539 -8.29 -0.63 1.74 0.862 3.857 7800 296 17.205 17.205 0.127 0.035 16.01500 2.470 0.265 4.50E+05 9.60E+04 3.713 0.152 0.152 -
NGC 6540 -6.35 -1.35 2.50 0.046 1.156 5300 176 13.266 13.266 0.765 0.208 13.30663 1.991 0.168 6.08E+04 1.23E+04 3.578 0.151 0.151 -
NGC 6541 -8.52 -1.81 1.86 0.393 2.313 7500 832 28.844 28.844 0.513 0.139 10.25138 1.869 0.157 4.21E+05 8.53E+04 3.586 0.148 0.148 qLMXB
NGC 6544 -6.94 -1.40 1.63 0.044 1.056 3000 90 9.487 9.487 0.189 0.051 10.29180 1.878 0.154 9.87E+04 1.99E+04 3.684 0.154 0.154 -
NGC 6569 -8.28 -0.76 1.31 1.110 2.537 10900 664 25.768 25.768 0.226 0.062 10.18867 2.242 0.217 4.05E+05 8.43E+04 3.861 0.151 0.151 -
NGC 6584 -7.69 -1.50 1.47 1.021 2.867 13500 486 22.045 22.045 0.499 0.136 11.44562 1.890 0.155 1.98E+05 4.00E+04 3.692 0.148 0.148 -
NGC 6624 -7.49 -0.44 2.50 0.138 1.884 7900 892 29.866 29.866 0.619 0.169 9.60132 2.802 0.326 2.44E+05 5.33E+04 3.770 0.152 0.152 LMXB
NGC 6637 -7.64 -0.64 1.38 0.845 2.150 8800 793 28.160 28.160 0.794 0.224 11.84030 2.419 0.254 2.42E+05 5.14E+04 3.615 0.154 0.154 -
NGC 6638 -7.12 -0.95 1.33 0.602 1.395 9400 450 21.213 21.213 0.498 0.131 10.56374 2.127 0.193 1.32E+05 2.71E+04 3.835 0.146 0.146 -
NGC 6642 -6.66 -1.26 1.99 0.236 1.720 8100 184 13.565 13.565 0.319 0.087 10.53964 1.928 0.158 7.83E+04 1.58E+04 3.867 0.151 0.151 -
NGC 6652 -6.66 -0.81 1.80 0.291 1.396 10000 316 17.776 17.776 0.703 0.191 12.95863 2.151 0.198 8.74E+04 1.80E+04 3.711 0.150 0.150 LMXB
NGC 6656 -8.50 -1.70 1.38 1.238 3.128 3200 671 25.904 25.904 0.342 0.132 8.89052 1.870 0.154 4.14E+05 8.35E+04 3.676 0.189 0.189 qLMXB
NGC 6681 -7.12 -1.62 2.50 0.079 1.859 9000 448 21.166 21.166 0.705 0.192 12.15687 1.886 0.154 1.17E+05 2.36E+04 3.735 0.148 0.148 -
NGC 6712 -7.50 -1.02 1.05 1.525 2.669 6900 296 17.205 17.205 0.221 0.060 12.46119 2.111 0.190 1.86E+05 3.81E+04 3.857 0.150 0.150 LMXB
NGC 6715 -9.98 -1.49 2.04 0.694 6.321 26500 5578 74.686 74.686 0.747 0.139 9.82771 1.876 0.154 1.62E+06 3.27E+05 3.663 0.119 0.119 -
NGC 6717 -5.66 -1.26 2.07 0.165 1.404 7100 108 10.392 10.392 0.506 0.152 8.63129 1.950 0.161 3.15E+04 6.37E+03 3.830 0.163 0.163 -
NGC 6723 -7.83 -1.10 1.11 2.101 3.872 8700 686 26.192 26.192 0.522 0.142 11.10416 2.036 0.176 2.43E+05 4.94E+04 3.733 0.148 0.148 -
NGC 6752 -7.73 -1.54 2.50 0.198 2.222 4000 526 22.935 22.935 0.429 0.117 11.63855 1.878 0.154 2.04E+05 4.12E+04 3.779 0.148 0.148 qLMXB
NGC 6760 -7.84 -0.40 1.65 0.732 2.734 7400 558 23.622 23.622 0.265 0.072 11.63855 2.671 0.304 3.22E+05 6.97E+04 3.816 0.152 0.152 -
NGC 6779 -7.41 -1.98 1.38 1.203 3.008 9400 422 20.543 20.543 0.794 0.238 9.85393 1.878 0.158 1.52E+05 3.08E+04 3.543 0.158 0.158 -
NGC 6809 -7.57 -1.94 0.93 2.827 4.445 5400 216 14.697 14.697 0.333 0.341 8.52676 1.868 0.156 1.75E+05 3.55E+04 3.568 0.454 0.454 qLMXB
NGC 6838 -5.61 -0.78 1.15 0.733 1.943 4000 135 11.619 11.619 0.778 0.837 8.65301 2.383 0.247 3.68E+04 7.78E+03 3.674 0.478 0.478 -
NGC 6864 -8.57 -1.29 1.80 0.547 2.797 20900 1051 32.419 32.419 0.453 0.123 11.63855 2.013 0.171 4.75E+05 9.63E+04 3.689 0.148 0.148 -
NGC 6934 -7.45 -1.47 1.53 0.998 3.131 15600 539 23.216 23.216 0.772 0.211 11.63855 1.881 0.154 1.58E+05 3.19E+04 3.645 0.149 0.149 -
NGC 6981 -7.04 -1.42 1.21 2.275 4.599 17000 405 20.125 20.125 0.789 0.214 11.63855 1.912 0.157 1.10E+05 2.22E+04 3.668 0.149 0.149 -
NGC 7006 -7.67 -1.52 1.41 2.037 5.273 41200 761 27.586 27.586 0.909 0.248 11.63855 1.871 0.154 1.93E+05 3.89E+04 3.638 0.148 0.148 -
NGC 7078 -9.19 -2.37 2.29 0.424 3.025 10400 1403 37.457 37.457 0.583 0.159 11.63855 1.925 0.164 8.04E+05 1.63E+05 3.476 0.148 0.148 LMXB
NGC 7089 -9.03 -1.65 1.59 1.070 3.546 11500 1855 43.070 43.070 0.749 0.204 11.63855 1.872 0.154 6.75E+05 1.36E+05 3.565 0.147 0.147 -
NGC 7099 -7.45 -2.27 2.50 0.141 2.427 8100 332 18.221 18.221 0.544 0.322 9.87176 1.903 0.161 1.60E+05 3.24E+04 3.581 0.273 0.273 qLMXB
Palomar 1 -2.52 -0.65 2.57 0.032 1.485 11100 11 5.594 3.978 0.970 0.254 10.00285 2.552 0.281 2.29E+03 4.91E+02 3.695 0.265 0.215 -
Palomar 12 -4.47 -0.85 2.98 0.111 9.506 19000 21 7.183 5.617 0.753 0.250 12.56659 2.168 0.201 1.17E+04 2.42E+03 3.377 0.226 0.206 -
Palomar 15 -5.51 -2.07 0.60 15.743 14.431 45100 128 11.314 11.314 0.813 0.168 16.66471 1.874 0.158 2.64E+04 5.35E+03 3.776 0.131 0.131 -
Palomar 2 -7.97 -1.42 1.53 1.345 3.956 27200 975 31.225 31.225 0.665 0.154 14.02200 1.946 0.161 2.64E+05 5.34E+04 3.744 0.134 0.134 -
Pyxis -5.73 -1.20 1.60 14.899 22.349 39400 83 9.110 9.110 0.569 0.611 11.59449 1.946 0.161 3.36E+04 6.78E+03 3.638 0.477 0.477 -
Ruprecht 106 -6.35 -1.68 0.70 6.167 6.475 21200 126 11.225 11.225 0.730 0.143 13.16012 1.868 0.155 5.70E+04 1.15E+04 3.481 0.128 0.128 -
Terzan 7 -5.01 -0.32 0.93 3.250 5.107 22800 80 8.944 8.944 0.829 0.249 10.37009 2.581 0.287 2.29E+04 4.94E+03 3.624 0.167 0.167 -
Terzan 8 -5.07 -2.16 0.60 7.650 7.268 26300 147 12.124 12.124 0.594 0.347 12.41205 1.885 0.159 1.77E+04 3.59E+03 4.145 0.271 0.271 -
  • Globular cluster absolute magnitude , metallicity [Fe/H], concentration, core radius , half-light radius , and distance are all taken from H10.  is the number of RGB stars along with corresponding upper and lower limits (UL and LL), which are derived using for values and Poisson statistics (Gehrels, 1986) for values .  is the fraction of the total cluster luminosity that was observed in the field of view of the given HST instrument. (fgstars) is the absolute magnitude from foreground stars in the cluster field of view obtained from the Besançon models (Robin et al., 2003). Mass-to-light ratios are taken from Table 8 (column 6) of McLaughlin & van der Marel (2005). Masses were derived by multiplying the by total cluster luminosity derived from . /Mass/ is the normalized number of RGB stars in a cluster.

Table 2: Globular Cluster Parameters and Red Giant Branch Star Values

6 Impact of RGB Stars on Globular Cluster LMXBs

Our sample contains 10 LMXBs in 8 different GCs and 22 GCs with at least one qLMXB. Figure 6 shows that the number density of RGB stars is correlated with the metallicity of a GC. This confirms the prediction of Ivanova et al. (2012) that the number density of RGB stars is larger in metal-rich GCs, and therefore a key contributor to the dynamical formation of LMXBs. However, the correlations and degeneracies between GC parameters and LMXB formation means that RGB star number density is not the only cause of the metallicity effect. To assess the impact of RGB star density on LMXBs we need to identify their properties, such as confirmed optical counterparts and .

6.1 qLMXB Contribution

Unlike LMXBs, qLMXBs are not expected to have red giants as donors (or seeds of formation) because they are not bright persistent sources. While qLMXBs have   erg s, XRB duty cycles in general are not well-known and thus qLMXBs could be in a transition state. Based on the low X-ray luminosities and hence low mass transfer rates, they should have main sequence or white dwarf companions (not ultracompact, i.e. their orbital periods are h). Searches for optical counterparts to qLMXBs have generally only proposed candidates (e.g. Heinke et al., 2005, 2009; Maxwell et al., 2012). This does not rule out the possibility that some have RGB star companions, although this scenario would require a large orbital separation and/or reduced mass loss rates. However, no relationship between qLMXBs and mass nor metallicity in the Galaxy (extragalactic observations are not sensitive enough to detect qLMXBs) has been found (Heinke et al., 2003). Therefore a relationship between qLMXBs and RGB star density is not expected to exist, and as Figures 4 and 5 show the distribution of qLMXB clusters is not metallicity dependent. A KS test of the  parameter for qLMXBs and non-LMXBs yielded a -value of 0.66 and for the RGB star density parameter a -value of 0.68, meaning we cannot reject the null hypothesis of uncorrelated values for either case. This result requires more investigation to analyse the qLMXB frequency in each GC and metallicity. The qLMXBs with the largest RGB star numbers (NGC 5139, NGC 6139, NGC 6352, NGC 6366) and densities (NGC 6093, NGC 6266, NGC 6388) in Figures 4 and 5 are possible transient sources that have previously been in outburst, and thus good candidates for monitoring.

We also analysed the distribution of qLMXBs to study their dependence on metallicity. When we split the qLMXBs into populations based on metallicity at [Fe/H] (the approximate separation of the bimodal [Fe/H] distribution; Bellazzini et al. 1995), we found the fraction of GC-qLMXBs was 14% larger (as a fraction of the total GCs in that population) in the metal-poor (31%) vs. the metal-rich (17%) population. The number of qLMXBs within a GC can vary (see Section 5.3), and so this result is only based on the number of GCs that host at least one qLMXB. In addition, selection effects are a large source of uncertainty because many GCs have not been observed at the  limits for detecting qLMXBs. We have not included statistics for multiple qLMXBs within one GC. More work into the nature of qLMXBs and GC metallicity is needed. As Ivanova et al. (2008) states, an independent correlation (or lack thereof) between qLMXB number and metallicity can help us better understand the metallicity dependence on LMXB formation.

6.2 GC-LMXB Metallicity Relation

While qLMXBs are not known to be dependent on GC metalliticity, LMXB formation is. However, metallicity is known to be related to many other GC parameters, such as mass and density. Despite this, the metallicity effect has been shown to be independent of other factors. Kim et al. (2013) showed that for a sample of 408 extragalactic GC-LMXBs, the mass-metallicity relation was negligible (15%) compared to the factor of 3 difference in LMXB production between metal-rich and metal-poor GCs. Kim et al. (2013) also found that for extragalactic LMXBs, the metallicity dependence not only hold for all bright LMXBs, but that the effect is independent of X-ray luminosity ( erg s), stellar age, dynamical properties (e.g. stellar encounter rate, Galactocentric distance), and selection effects. This makes the prediction that RGB star density causes the LMXB-metallicity dependence more intriguing, since the remaining GC parameters have been separated from the metallicity dependence (there is no known mass-metallicity relationship for Milky Way GCs). The results of our study are only physically relevant if the initial conjecture is true: that LMXB companions should be RGB stars. Therefore we need to identify what fraction, if any, of the LMXBs in our sample are actually known to have RGB star counterparts.

6.3 Milky Way GC-LMXB Counterparts

An issue with work of this nature is that it is incredibly difficult to definitively determine the companions of LMXBs in GCs because the stellar density is so high. Verbunt & Lewin (2006) summarized potential candidates for a number of GC-LMXBs in the literature, with most being classified as a ‘faint star’ or having no clear counterpart. The LMXB in NGC 6624 could be a white dwarf or stripped core of an evolved main sequence star. NGC 7078 (M15) has 2 LMXBs, where X-1 is thought to have a red giant companion and X-2 a blue star as its companion. The orbital period of an LMXB was often used as an indicator of the type of companion, with orbital periods h meaning degenerate stars, 3 h h indicating main sequence stars, and h for giants. While these studies have suggested a number of LMXB companions are main sequence stars, this is based on the identification of a blue optical counterpart near/at the position of the X-ray source. The accretion disc of an LMXB is known to emit in the UV, which further complicates optical counterpart identification. With no confirmation of counterparts for any LMXBs, we cannot say with any certainty that RGB stars are or are not companions. Population synthesis models (e.g. Ivanova et al., 2008) have predicted that the LMXB formation rate is highest for neutron stars with main sequence donors. However, the mass transfer rates and thus X-ray luminosities of these systems are low ( erg s). Therefore red giant companions are thought to compose the brightest LMXBs because they provide the necessary mass transfer rates to drive higher  (Fragos et al., 2008, 2009). Only three of the bright GC-LMXBs in the Milky Way have X-ray luminosities erg s, the sources in NGC 6441, NGC 6624, and Liller 1 (Liu et al., 2007), where Liller 1 is not part of our sample. From these candidates and their  values we can infer that 2 of the 10 LMXBs in different clusters from our sample possibly have RGB star companions.

6.4 LMXB Compact Object Type

We still have not addressed the impact that the accretor in the LMXB has on our interpretation. If the compact object in a GC-LMXB is a black hole, those with luminosities erg s don’t require RGB star companions. In any case, the compact objects in bright Milky Way GC-LMXBs are all neutron stars. Only 4 black hole candidates have been identified to date, with two detected in radio and not X-ray (Strader et al., 2012), and two with X-ray luminosities erg s (Chomiuk et al., 2013; Miller-Jones et al., 2015). Nonetheless, Ivanova et al. (2010) found that RGB stars have a similar effect on the production of black hole LMXBs indirectly by increasing the formation rates of the seeds (LMXBs with red giant donors) of black hole-white dwarf binaries.

6.5 RGB Star Proxies and Metallicity

Our study attempted to address why metal-rich GCs produce more LMXBs than metal-poor GCs by investigating the relationship between the number density of RGB stars in a GC and GC metallicity. Even if our sample of GC-LMXBs does not have RGB star donors, we are still probing the relationship between the number density of RGB stars and metallicity of all GCs and not just those with an LMXB. If all metal-rich GCs had much higher RGB star densities than metal-poor ones, it would be evidence to support the impact of GC metallicity on LMXB formation (we point out that N13 did find a trend of increasing number counts on the RGB bump with increasing metallicity). In Figure 5, the RGB star number density does appear to be larger for metal-rich LMXBs compared to the best-fitting relation, and the overall distribution is correlated with [Fe/H] based on Spearman and Kendall Rank tests. However, we caution that the explicit dependence of volume on , which is correlated with both LMXB formation and metallicity, biases this result. As we stated above, the correlation of  with [Fe/H] is purely dynamical as a result of Galactocentric distance effects from tidal interactions. When investigating the effect of RGB star density on GC metallicity, it is difficult to remove the correlation that density (through ) has on metallicity.

To exclude the intrinsic dependence of density on metallicity, we can use the  parameter. While  only represents the number of RGB stars per M and not a volume density, it is independent of mass and density, which both influence LMXB formation. Therefore  can be used as an independent probe of whether the number of RGB stars in a GC varies with metallicity, explaining the enhanced production of LMXBs in metal-rich GCs. From Figure 4, we found no dependence between the  parameter and metallicity. Although we cannot reject the null hypothesis based on a Spearman’s Rank test, this does not mean that  and [Fe/H] are not correlated. The shallow slope from the least squares fit and large uncertainties on  are an indication that further analysis with improved measurements would lead to a more robust result. As a result we cannot claim there is an independent relationship between RGB star number density and metallicity.

6.6 Degeneracy of GC Parameters Affecting LMXB Formation

Our goal was to determine the underlying physical cause for the metallicity dependence of GC-LMXBs. Both the number of RGB stars and the density of RGB stars are related to the GC mass (Figure 3) and  (Section 5.3) respectively. These parameters (GC mass and ) are already known to be indicators of whether a GC hosts an LMXB. Therefore the argument invokes parameters that are known to affect LMXB formation to explain the metallicity dependence. Given that there is no mass-metallicity relation in the Galaxy, we have removed GC mass from our correlation by normalizing for it. However, the dependence of  on metallicity is confounding because it is instead attributed to a dependence of  on Galactocentric distance. The purely dynamical origin for this relationship (i.e. tidal interactions/stripping) is telling since dynamical interactions promote LMXB formation. If metal-rich GCs are more likely to have an active dynamical history, possibly due to a highly inclined orbit about the disc in a galaxy or the surrounding environment, they will preferentially form LMXBs. Kim et al. (2006) showed that GCs closer to the centres of galaxies are more likely to harbour LMXBs than those in the outskirts, due to Galactic tidal forces that cause GCs to have smaller core radii (higher central densities). However, a study of NGC 1399 by Paolillo et al. (2011) found that GC-LMXBs follow the radial distribution of their parent GC population and argued against any external dynamical effects from the galaxy influencing LMXB formation in GCs. Tidal stripping from GCs usually occurs in galaxy centres and has not been confirmed at larger Galactocentric distances, while the metallicity effect for LMXBs holds at all Galactocentric distances (Kim et al., 2013; Mineo et al., 2014). If external dynamics do contribute to the GC-LMXB metallicity effect, the dynamical formation/evolution of metal-rich and metal-poor GCs would have to be different throughout a galaxy. Therefore, while we confirmed the prediction from Ivanova et al. (2012) that the number density of RGB stars is larger in metal-rich GCs, we cannot claim that it is the (sole) underlying cause of the metallicity effect on LMXB formation.

7 Improvements and Future Work

To improve our analysis a number of developments need to take place. Firstly, the uncertainties on measurements of GC distances and luminosities need to be improved. The end-of-mission GAIA data will improve distance measurements for GCs, which is currently one of the dominant sources of uncertainty in all GC studies. Higher spatial resolution data using JWST that covers the entire GC population will improve both number statistics and consistency between GCs. Specifically, observing the complete extent of each GC will reduce the large uncertainties associated with luminosity correction. The ratios we used can be inaccurate but are internally consistent, only resulting in a systematic error in GC mass. However, our largest source of uncertainty in  comes from the modelled ratios used to determine masses, which limits the both the interpretation and significance of our results. Follow-up work to localize LMXBs with Chandra and analyse the optical counterparts in HST images in the X-ray error ellipse can yield further insight on companions.

Future endeavours will need to reduce the uncertainty on GC parameters in order to obtain more robust results. The GCs in M31 might appear to be ideal targets for many reasons. First, each GC is at the same distance and data is available for the entire cluster, eliminating two of the largest uncertainties in our work. The recently completed Panchromatic Hubble Andromeda Treasury survey obtained 6-filter photometry in the UV to NIR for one-third of M31’s disc, and is complete for the bright-end of the RGB in the field. However, the central stellar density in M31’s GCs is too high to count RGB stars with current observations. Therefore our analysis remains restricted to our Galaxy and improving measurements such as . As Ivanova et al. (2012) stated, a population synthesis study that includes red giants will also advance our understanding of their effect while controlling for GC parameters such as the affect has on RGB star density. This could be accomplished using models with the same over a wide range of metallicity at fixed mass and Galactocentric distance. The second part of the prediction from Ivanova et al. (2012) stated that the average masses of RGB stars should be larger in metal-rich GCs. This could be investigated observationally using estimates of stellar masses from isochrone-fitting across the red giant branch or spectral analysis. Lastly, with the upcoming launch of eROSITA, which will detect all XRBs in our galaxy down to erg s, it will be possible to survey qLMXBs in GCs and determine any relationship between their formation or luminosity distribution and GC parameters such as metallicity.

8 Summary

One of the unanswered questions in GC-LMXB studies is the origin of the metallicity effect. Why are there times more LMXBs in metal-rich GCs compared to metal-poor ones? In this work we investigated this relationship using the hypothesis that the RGB star number density is correlated with metallicity, and thus is the underlying physical cause of the correlation. We used HST data from the ACS and WFPC2 instruments for 109 unique Milky Way GCs to calculate the number of RGB stars, . We made corrections for the fraction of cluster light observed and foreground star contamination. Normalizing by GC mass we found no correlation between  (number of RGB stars per M) and metallicity. Because RGB stars are likely mass-segregated, many will be located within the half-light radius of a GC. We normalized  by the GC volume at the half-light radius to find the number density of RGB stars. The RGB star number density was correlated with metallicity [Fe/H], indicating the underlying cause of the LMXB preference for metal-rich GCs. Spearman and Kendall Rank tests gave -values of 0.00016 and 0.00021 and coefficients and respectively.

However, we caution that this result is inherently biased by the half-light radius , which affects LMXB formation rate and is possibly negatively correlated with GC metallicity. The dynamical origin of the -metallicity correlation (tidal stripping) suggests that metal-rich GCs may have had more active dynamical histories, which would promote LMXB formation. In addition, not all LMXBs have RGB star companions, but this does not preclude a relationship between RGB star density and [Fe/H]. No correlation between qLMXBs (number or RGB star parameters) and GC metallicity was found, although a qLMXB census in Galactic GCs is needed to further this analysis. Follow-up observations of Milky Way GCs with JWST that cover the entire cluster extent will reduce uncertainties, as will updated distance measurements with GAIA. Even next generation space-based optical telescopes will not have the capability to study promising extragalactic GCs in e.g. M31, where a more consistent, relevant, and robust analysis would be possible. An investigation of the average masses of RGB stars in relation to Milky Way GC metallicity would provide further insight into this intriguing problem.

acknowledgements

We thank the referee for helpful comments that improved the manuscript. We thank David M. Nataf for helpful comments on the methodology and Bill Harris for comments on the manuscript. Support for this work was provided by Discovery Grants from the Natural Sciences and Engineering Research Council of Canada and by Ontario Early Researcher Awards. NV acknowledges support from Ontario Graduate Scholarships. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET:www.sharcnet.ca) and Compute/Calcul Canada. We acknowledge the following archives: the Hubble Legacy Archive (hla.stsci.edu).
Facilities: HST (ACS, WFC, WFPC2)

References

  • Agar & Barmby (2013) Agar J. R. R., Barmby P., 2013, AJ, 146, 135
  • Bahramian et al. (2013) Bahramian A., Heinke C. O., Sivakoff G. R., Gladstone J. C., 2013, ApJ, 766, 136
  • Bahramian et al. (2014) Bahramian A., et al., 2014, ApJ, 780, 127
  • Bailin & Harris (2009) Bailin J., Harris W. E., 2009, ApJ, 695, 1082
  • Barmby et al. (2000) Barmby P., Huchra J. P., Brodie J. P., Forbes D. A., Schroder L. L., Grillmair C. J., 2000, AJ, 119, 727
  • Barmby et al. (2007) Barmby P., McLaughlin D. E., Harris W. E., Harris G. L. H., Forbes D. A., 2007, AJ, 133, 2764
  • Bellazzini et al. (1995) Bellazzini M., Pasquali A., Federici L., Ferraro F. R., Pecci F. F., 1995, ApJ, 439, 687
  • Bregman et al. (2006) Bregman J. N., Irwin J. A., Seitzer P., Flores M., 2006, ApJ, 640, 282
  • Bruzual & Charlot (2003) Bruzual G., Charlot S., 2003, MNRAS, 344, 1000
  • Cardelli et al. (1989) Cardelli J. A., Clayton G. C., Mathis J. S., 1989, ApJ, 345, 245
  • Carretta et al. (2009) Carretta E., Bragaglia A., Gratton R., D’Orazi V., Lucatello S., 2009, A&A, 508, 695
  • Chabrier (2003) Chabrier G., 2003, PASP, 115, 763
  • Chomiuk et al. (2013) Chomiuk L., Strader J., Maccarone T. J., Miller-Jones J. C. A., Heinke C., Noyola E., Seth A. C., Ransom S., 2013, ApJ, 777, 69
  • Clark (1975) Clark G. W., 1975, ApJ, 199, L143
  • Dotter et al. (2007) Dotter A., Chaboyer B., Jevremović D., Baron E., Ferguson J. W., Sarajedini A., Anderson J., 2007, AJ, 134, 376
  • Dotter et al. (2008) Dotter A., Chaboyer B., Jevremović D., Kostov V., Baron E., Ferguson J. W., 2008, ApJS, 178, 89
  • Dotter et al. (2010) Dotter A., et al., 2010, ApJ, 708, 698
  • Fabian et al. (1975) Fabian A. C., Pringle J. E., Rees M. J., 1975, MNRAS, 172, 15P
  • Fragos et al. (2008) Fragos T., et al., 2008, ApJ, 683, 346
  • Fragos et al. (2009) Fragos T., et al., 2009, ApJ, 702, L143
  • Gehrels (1986) Gehrels N., 1986, ApJ, 303, 336
  • Goldsbury et al. (2013) Goldsbury R., Heyl J., Richer H., 2013, ApJ, 778, 57
  • Grindlay (1993) Grindlay J. E., 1993, in Smith G. H., Brodie J. P., eds, Astronomical Society of the Pacific Conference Series Vol. 48, The Globular Cluster-Galaxy Connection. p. 156
  • Harris (1996) Harris W. E., 1996, AJ, 112, 1487
  • Harris (2009) Harris W. E., 2009, ApJ, 703, 939
  • Harris et al. (2006) Harris W. E., Whitmore B. C., Karakla D., Okoń W., Baum W. A., Hanes D. A., Kavelaars J. J., 2006, ApJ, 636, 90
  • Heinke et al. (2003) Heinke C. O., Grindlay J. E., Lugger P. M., Cohn H. N., Edmonds P. D., Lloyd D. A., Cool A. M., 2003, ApJ, 598, 501
  • Heinke et al. (2005) Heinke C. O., Grindlay J. E., Edmonds P. D., Cohn H. N., Lugger P. M., Camilo F., Bogdanov S., Freire P. C., 2005, ApJ, 625, 796
  • Heinke et al. (2009) Heinke C. O., Cohn H. N., Lugger P. M., 2009, ApJ, 692, 584
  • Humphrey & Buote (2008) Humphrey P. J., Buote D. A., 2008, ApJ, 689, 983
  • Ivanova & Kalogera (2006) Ivanova N., Kalogera V., 2006, ApJ, 636, 985
  • Ivanova et al. (2008) Ivanova N., Heinke C. O., Rasio F. A., Belczynski K., Fregeau J. M., 2008, MNRAS, 386, 553
  • Ivanova et al. (2010) Ivanova N., Chaichenets S., Fregeau J., Heinke C. O., Lombardi Jr. J. C., Woods T. E., 2010, ApJ, 717, 948
  • Ivanova et al. (2012) Ivanova N., et al., 2012, ApJ, 760, L24
  • Jordán (2004) Jordán A., 2004, ApJ, 613, L117
  • Jordán et al. (2004) Jordán A., et al., 2004, ApJ, 613, 279
  • Jordán et al. (2005) Jordán A., et al., 2005, ApJ, 634, 1002
  • Katz (1975) Katz J. I., 1975, Nature, 253, 698
  • Kavelaars & Hanes (1997) Kavelaars J. J., Hanes D. A., 1997, MNRAS, 285, L31
  • Kim et al. (2006) Kim E., Kim D.-W., Fabbiano G., Lee M. G., Park H. S., Geisler D., Dirsch B., 2006, ApJ, 647, 276
  • Kim et al. (2009) Kim D.-W., et al., 2009, ApJ, 703, 829
  • Kim et al. (2013) Kim D.-W., Fabbiano G., Ivanova N., Fragos T., Jordán A., Sivakoff G. R., Voss R., 2013, ApJ, 764, 98
  • Kundu & Whitmore (1998) Kundu A., Whitmore B. C., 1998, AJ, 116, 2841
  • Kundu et al. (2002) Kundu A., Maccarone T. J., Zepf S. E., 2002, ApJ, 574, L5
  • Kundu et al. (2007) Kundu A., Maccarone T. J., Zepf S. E., 2007, ApJ, 662, 525
  • Larsen et al. (2001) Larsen S. S., Brodie J. P., Huchra J. P., Forbes D. A., Grillmair C. J., 2001, AJ, 121, 2974
  • Liu et al. (2007) Liu Q. Z., van Paradijs J., van den Heuvel E. P. J., 2007, VizieR Online Data Catalog, 346, 90807
  • Maccarone et al. (2004) Maccarone T. J., Kundu A., Zepf S. E., 2004, ApJ, 606, 430
  • Mamajek (2012) Mamajek E. E., 2012, ApJ, 754, L20
  • Maxwell et al. (2012) Maxwell J. E., Lugger P. M., Cohn H. N., Heinke C. O., Grindlay J. E., Budac S. A., Drukier G. A., Bailyn C. D., 2012, ApJ, 756, 147
  • McLaughlin & van der Marel (2005) McLaughlin D. E., van der Marel R. P., 2005, ApJS, 161, 304
  • Mieske et al. (2006) Mieske S., et al., 2006, ApJ, 653, 193
  • Miller-Jones et al. (2015) Miller-Jones J. C. A., et al., 2015, MNRAS, 453, 3919
  • Mineo et al. (2014) Mineo S., et al., 2014, ApJ, 780, 132
  • Miocchi et al. (2013) Miocchi P., et al., 2013, ApJ, 774, 151
  • Nataf et al. (2013) Nataf D. M., Gould A. P., Pinsonneault M. H., Udalski A., 2013, ApJ, 766, 77
  • Paolillo et al. (2011) Paolillo M., Puzia T. H., Goudfrooij P., Zepf S. E., Maccarone T. J., Kundu A., Fabbiano G., Angelini L., 2011, ApJ, 736, 90
  • Peacock et al. (2010) Peacock M. B., Maccarone T. J., Kundu A., Zepf S. E., 2010, MNRAS, 407, 2611
  • Peng et al. (2006) Peng E. W., et al., 2006, ApJ, 639, 95
  • Piotto et al. (2002) Piotto G., et al., 2002, A&A, 391, 945
  • Pooley et al. (2003) Pooley D., et al., 2003, ApJ, 591, L131
  • Robin et al. (2003) Robin A. C., Reylé C., Derrière S., Picaud S., 2003, A&A, 409, 523
  • Sarajedini et al. (2007) Sarajedini A., et al., 2007, AJ, 133, 1658
  • Sarazin et al. (2003) Sarazin C. L., Kundu A., Irwin J. A., Sivakoff G. R., Blanton E. L., Randall S. W., 2003, ApJ, 595, 743
  • Schlafly & Finkbeiner (2011) Schlafly E. F., Finkbeiner D. P., 2011, ApJ, 737, 103
  • Sivakoff et al. (2007) Sivakoff G. R., et al., 2007, ApJ, 660, 1246
  • Strader & Smith (2008) Strader J., Smith G. H., 2008, AJ, 136, 1828
  • Strader et al. (2006) Strader J., Brodie J. P., Spitler L., Beasley M. A., 2006, AJ, 132, 2333
  • Strader et al. (2012) Strader J., Chomiuk L., Maccarone T. J., Miller-Jones J. C. A., Seth A. C., 2012, Nature, 490, 71
  • Trudolyubov & Priedhorsky (2004) Trudolyubov S., Priedhorsky W., 2004, ApJ, 616, 821
  • VandenBerg & Clem (2003) VandenBerg D. A., Clem J. L., 2003, AJ, 126, 778
  • Vanderbeke et al. (2015) Vanderbeke J., De Propris R., De Rijcke S., Baes M., West M. J., Blakeslee J. P., 2015, MNRAS, 450, 2692
  • Verbunt & Lewin (2006) Verbunt F., Lewin W. H. G., 2006, Globular cluster X-ray sources. Cambridge: Cambridge Univ. Press, pp 341–379
  • Vulic et al. (2014) Vulic N., Gallagher S. C., Barmby P., 2014, ApJ, 790, 136

Appendix A Colour-Magnitude Diagrams For ACS Globular Clusters

Figure 7: Colour-magnitude diagrams as in Figure 1 for the ACS survey GCs.
Figure 8:
Figure 9:
Figure 10:
Figure 11:
Figure 12:

Appendix B Colour-Magnitude Diagrams For WFPC2 Globular Clusters

Figure 13: Colour-magnitude diagrams as in Figure 1 but for the WFPC2 survey GCs in the Johnson plane.
Figure 14:
Figure 15:
Figure 16:
Figure 17:
Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
218403
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description