On the origin of the metallicity dependence in dynamically formed extragalactic low-mass X-ray binaries

Globular clusters (GCs) effectively produce dynamically-formed low-mass X-ray binaries (LMXBs). Observers detect ~100 times more LMXBs per stellar mass in GCs compared to stars in the fields of galaxies. It has also been observationally established that metal-rich GCs are about 3 times more likely to contain an X-ray source than their metal-poor counterparts. Recent observations have shown that this ratio holds in extragalactic GCs for all bright X-ray sources with Lx between 2X10^{37} and 5X10^{38} erg/s. In this Letter, we propose that the observed metallicity dependence of LMXBs in extragalactic GCs can be explained by the differences in the number densities and average masses of red giants in populations of different metallicities. Red giants serve as seeds for the dynamical production of bright LMXBs via two channels - binary exchanges and physical collisions - and the increase of the number densities and masses of red giants boost LMXB production, leading to the observed difference. We also discuss a possible effect of the age difference in stellar populations of different metallicities.