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The Globular Cluster Mass/Low Mass X-Ray Binary Correlation: Implications for Kick Velocity Distributions from Supernovae

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The Globular Cluster Mass/Low Mass X-Ray Binary Correlation: Implications for Kick Velocity Distributions from Supernovae A&A 458, 477–484 (2006) Astronomy DOI: 10.1051/0004-6361:20065298 & c ESO 2006 Astrophysics The globular cluster mass/low mass X-ray binary correlation: implications for kick velocity distributions from supernovae M. Smits1, T. J. Maccarone2,1, A. Kundu3, and S. E. Zepf3 1 Astronomical Institute ‘Anton Pannekoek’, University of Amsterdam, Kruislaan 403, 1098 SJ, Amsterdam, The Netherlands 2 School of Physics and Astronomy, University of Southampton, Southampton, Hampshire SO17 1BJ, UK e-mail: [email protected] 3 Department of Physics and Astronomy, Michigan State University, East Lansing MI, USA Received 28 March 2006 / Accepted 27 July 2006 ABSTRACT Optical and X-ray studies of six nearby galaxies show that the probability a globular cluster will be an X-ray source is consistent with being linearly proportional to its mass. We show that this result is consistent with some recent estimates of the velocity kick distributions for isolated radio pulsars – those which are the sum of two Maxwellians, with the slower distribution at about 100 km s−1 – so long as a large fraction of the retained binaries are in binary systems with other massive stars. We confirm that over a large sample of galaxies, metallicity is clearly a factor in determining whether a globular cluster will contain an X-ray binary, and we estimate the transformations between color and metallicity for a large number of optical filter combinations. We also show that the core interaction rate is roughly linearly proportional to the stellar mass of a globular cluster for the Milky Way when one bins the clusters by mass. Key words. stellar dynamics – binaries: close – globular clusters: general – galaxies: star clusters – X-rays: binaries – galaxies: elliptical and lenticular, cD 1. Introduction optically detected globular clusters, it was found that large frac- tions of the X-ray binaries in elliptical galaxies were in globu- It has long been known that globular clusters contain much larger lar clusters (Sarazin et al. 2001; Angelini et al. 2001 – ALM). numbers of X-ray binaries per unit stellar mass than do field Larger samples of galaxies have shown a trend where the frac- populations of galaxies (Katz 1975; Clark 1975). This overabun- tion of X-ray binaries in globular clusters in a galaxy seems to dance has been ascribed to stellar interactions in globular clus- vary as a function of galaxy type, increasing from spiral galax- / ters which allow neutron stars and or black holes to enter new ies to lenticular to normal ellipticals to cD galaxies (Maccarone binary systems through either tidal capture (Clark 1975; Fabian et al. 2003; Juett 2005; Irwin 2005). et al. 1975) or exchange interactions (Hills 1976) long after the From the observations of elliptical galaxies, with their large supernovae that produce them. In the Chandra era, it has been globular cluster systems, it has been possible to find correla- possible to extend this work to show that the clusters with the tions between cluster properties and the probability that a cluster highest interaction rates are most likely to contain X-ray sources, would contain an X-ray binary which are not statistically signifi- and probably are most likely to contain accreting neutron stars cant in the Milky Way, or which have ambiguous interpretations (Pooley et al. 2003; Heinke et al. 2003; Gendre 2005). in the Milky Way because of the aforementioned correlations While studies of Galactic globular clusters have thus been between different cluster parameters. Specifically, it has been fruitful, the Milky Way’s globular cluster system is rather small shown clearly that metal rich clusters are far more likely to con- (containing only about 150 clusters), so it is not possible to study tain X-ray binaries than metal poor clusters (Kundu et al. 2002), certain phenomena due to lack of statistical significance in a confirming suggestive results from the Milky Way (Grindlay small sample of clusters. Furthermore, some of the Milky Way’s 1993; Bellazzini et al. 1995). These results have been found globular clusters’ parameters, such as metallicity and galacto- again in numerous subsequent papers (see e.g. Jordan et al. 2004; centric radius, are strongly correlated with one another, making Minniti et al. 2004; Xu et al. 2005; Kim et al. 2005). It has also it difficult to isolate the causes of certain effects. As a result, been shown that more luminous clusters are more likely to con- extragalactic globular cluster systems can be invaluable in com- tain X-ray binaries than less luminous clusters (see e.g. ALM; plementing the Galactic globular clusters for producing the best KMZ). We refer the reader also to reviews by Verbunt & Lewin possible data on how globular cluster parameters affect X-ray (2006) and Fabbiano (2006) for a broader overview of the liter- binary production. ature. While ROSAT was able to observe globular cluster X-ray Other results have been suggested by the data, but are not sources in M 31 (see e.g. Supper et al. 1997), it was not until as clearly significant. While in the Milky Way, it is clear that the advent of the Chandra X-ray Observatory that there was suf- denser globular clusters are more likely to contain large numbers ficient angular resolution to resolve apart the sources in more of X-ray sources per unit stellar mass (Pooley et al. 2003; Heinke distant galaxies, or to obtain sufficiently accurate positions that et al. 2003; Gendre 2005), the extragalactic clusters have core comparisons could be made with optical counterparts. Early radii which have not been sufficiently well resolved spatially as on, by comparing the positions of X-ray sources with those of to establish this effect clearly. KMZ found an anti-correlation Article published by EDP Sciences and available at http://www.edpsciences.org/aa or http://dx.doi.org/10.1051/0004-6361:20065298 478 M. Smits et al.: Globular cluster LMXBs and kicks Table 1. The color–metallicity relations for 10 different colors. Color N Relation V − I 65 [Fe/H] = −5.79 + 4.68 (V − I) U − B 72 [Fe/H] = −1.91 + 3.22 (U − I) B − V 78 [Fe/H] = −4.83 + 4.91 (B − V) V − R 55 [Fe/H] = −5.93 + 9.82 (V − R) U − V 72 [Fe/H] = −3.15 + 2.05 (U − V) B − R 55 [Fe/H] = −5.49 + 3.58 (B − R) B − I 65 [Fe/H] = −5.87 + 2.75 (B − I) U − R 55 [Fe/H] = −3.61 + 1.71 (U − R) U − I 64 [Fe/H] = −4.19 + 1.57 (U − I) R − I 54 [Fe/H] = −4.41 + 6.39 (R − I) catalogs will be presented in future work (Kundu et al., in prep.) In all, our sample includes 98 X-ray sources in 2276 globular clusters. These data points are plotted in Fig. 1. Because the data are taken in different filter sets (B − I for Fig. 1. The globular clusters analyzed in this data set. Small dots rep- NGC 1399 and V−I for the rest of the galaxies), we must develop resent optically detected globular clusters, while the larger open circles an algorithm to convert from magnitudes to cluster masses and surround the clusters with X-ray sources. metallicities. The I-band magnitudes are used to estimate the cluster masses, while the colors are used to estimate the cluster metallicities. Following the procedure of Kundu & Whitmore (1998), we determine the color-to-metallicity conversions for all between cluster half-light radius and LMXB hosting probabil- commonly used sets of photometric filters. We take all globular ity in NGC 4472, but noted that it was statistically insignif- clusters from the Harris (1996) catalogue for which there are icant. Jordan et al. (2004) estimated King model parameters data in a given pair of filters, for which there is a spectroscopic of globular clusters in M 87. They then inferred stellar colli- − < . Γ metallicity measurement, and for which E(B V) 0 4. We sion rates ( ) from the model fits, and found that the collision then de-redden the data, using the E(B − V) versus extinction rates were strongly correlated with the likelihood that a clus- relations from Cardelli et al. (1989), and fit [Fe/H] as a function ter would contain an X-ray binary, but that this correlation was of color and vice versa, and take the bisector of the two fits. only marginally better than the correlation with cluster lumi- This typically produces a color-metallicity relation with a scatter nosity. The absence of strong signatures of cluster concentra- of about 0.2 dex in [Fe/H]. The fact that the scatter is typically tion should not be taken as evidence that cluster concentration so small (i.e. about the same size as what would be expected is uncorrelated with X-ray binary production. Half-light radius from measurement errors) indicates that linear color-metallicity is not expected to be very well correlated with core concentra- relations are adequate for most purposes. The results are given tion, making the null result of KMZ unsurprising. Because the in Table 1. core radii of globular clusters in the Virgo Cluster are typically a small fraction of a pixel on the Advanced Camera for Surveys aboard the Hubble Space Telescope, neither is it surprising that 3. Analysis Jordan et al. (2004) were unable to find a strong signature of cluster concentration. Assuming that the probability that a globular cluster contains an In this paper, we analyze a sample of six galaxies for which LMXB can be described as a power law function of the clus- there is good optical and X-ray data.
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