SCYON Abstract

Received on September 06 2011

On the reliability of proxies for globular cluster collision rates

Authors	Thomas J. Maccarone (¹) and Mark B. Peacock (²)
Affiliation	(¹) University of Southampton (²) Michigan State University
Accepted by	Monthly Notices of the Royal Astronomical Society
Contact
URL	http://adsabs.harvard.edu/abs/2011MNRAS.415.1875M
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Abstract

A variety of different proxies for the stellar collision rates in globular clusters is used in the literature, depending on the quality of data available. We present com- parisons between these proxies and the full integrated collision rate for different King models. The most commonly used proxy, Γ, defined to be ρ₀³/2r_c², where ρ₀ is the central cluster density, and r_c is the core radius based on the 1966 King model, is an accurate representation of the collision rate from the King model to within about 25% for all but the least concentrated globular clusters. By integrating over King models with a range of parameters, we show that Γ_h, defined to be ρ_h³/2r_h², where ρ_h is the average density within the half-light radius, and r_h is the half-light radius, is only marginally better correlated with the full King model collision rate than is the cluster luminosity. The two galaxies where results of King model fitting have been reported in detail show a dearth of core-collapsed clusters relative to that seen in the Milky Way, indicating that the core radii of the most concentrated clusters are probably slightly overestimated, even with excellent data. Recent work has suggested that shallower than linear relations exist between proxies for Γ and the probability that a cluster will contain an X-ray source; we show that there is a similarly shallower than linear relationship between Γ and Γ_h that can explain the relationship where Γ_h is used; we also show that reasonable measurement errors are likely to produce a shallower than linear relationship even when Γ itself is used. We thus conclude that the existing evidence is all consistent with the idea that X-ray binary formation rates are linearly proportional to cluster collision rates. We also find, through comparison with Gunn- Griffin models (sometimes referred to as multi-mass King models) suggestive evidence that the retention fractions of neutron stars in globular clusters may be related to the present day concentration parameters, which would imply that the most concentrated clusters today were the most concentrated clusters at the time of their supernovae.