2014ApJ...784..162P

A number of recent studies have proposed that the stellar initial mass function (IMF) of early type galaxies varies systematically as a function of galaxy mass, with higher mass galaxies having bottom-heavy IMFs. These bottom-heavy IMFs have more low-mass stars relative to the number of high mass stars, and therefore naturally result in proportionally fewer neutron stars (NSs) and black holes (BHs). In this paper, we specifically predict the variation in the number of BHs and NSs based on the power-law IMF variation required to reproduce the observed mass-to-light ratio trends with galaxy mass. We then test whether such variations are observed by studying the field low-mass X-ray binary (LMXB) populations of nearby early-type galaxies. In these binaries, an NS or BH accretes matter from a low-mass donor star. Their number is therefore expected to scale with the number of BHs and NSs present in a galaxy. We find that the number of LMXBs per K-band light is similar among the galaxies in our sample. These data therefore demonstrate the uniformity of the slope of the IMF from massive stars down to those now dominating the K-band light and are consistent with an invariant IMF. Our results are inconsistent with an IMF which varies from a Kroupa/Chabrier like IMF for low-mass galaxies to a steep power-law IMF (with slopex= 2.8) for high mass galaxies. We discuss how these observations constrain the possible forms of the IMF variations and how future Chandra observations can enable sharper tests of the IMF.