Testing the Universality of the Stellar IMF with Chandra and HST

The stellar initial mass function (IMF), which is often assumed to be universal across unresolved stellar populations, has recently been suggested to be bottom-heavy for massive ellipticals. In these galaxies, the prevalence of gravity-sensitive absorption lines (e.g. Na I and Ca II) in their near-IR spectra implies an excess of low-mass ($m <= 0.5$ $M_odot$) stars over that expected from a canonical IMF observed in low-mass ellipticals. A direct extrapolation of such a bottom-heavy IMF to high stellar masses ($m >= 8$ $M_odot$) would lead to a corresponding deficit of neutron stars and black holes, and therefore of low-mass X-ray binaries (LMXBs), per unit near-IR luminosity in these galaxies. Peacock et al. (2014) searched for evidence of this trend and found that the observed number of LMXBs per unit $K$-band luminosity ($N/L_K$) was nearly constant. We extend this work using new and archival Chandra X-ray Observatory (Chandra) and Hubble Space Telescope (HST) observations of seven low-mass ellipticals where $N/L_K$ is expected to be the largest and compare these data with a variety of IMF models to test which are consistent with the observed $N/L_K$. We reproduce the result of Peacock et al. (2014), strengthening the constraint that the slope of the IMF at $m >= 8$ $M_odot$ must be consistent with a Kroupa-like IMF. We construct an IMF model that is a linear combination of a Milky Way-like IMF and a broken power-law IMF, with a steep slope ($alpha_1=$ $3.84$) for stars < 0.5 $M_odot$ (as suggested by near-IR indices), and that flattens out ($alpha_2=$ $2.14$) for stars > 0.5 $M_odot$, and discuss its wider ramifications and limitations.