Further constraints on variations in the IMF from LMXB populations
  We present constraints on variations in the initial mass function (IMF) of
nine local early-type galaxies based on their low mass X-ray binary (LMXB)
populations. Comprised of accreting black holes and neutron stars, these LMXBs
can be used to constrain the important high mass end of the IMF. We consider
the LMXB populations beyond the cores of the galaxies ($>0.2R_{e}$; covering
$75-90\%$ of their stellar light) and find no evidence for systematic
variations of the IMF with velocity dispersion ($\sigma$). We reject IMFs which
become increasingly bottom heavy with $\sigma$, up to steep power-laws
(exponent, $\alpha>2.8$) in massive galaxies ($\sigma>300$km/s), for
galactocentric radii $>1/4\ R_{e}$. Previously proposed IMFs that become
increasingly bottom heavy with $\sigma$ are consistent with these data if only
the number of low mass stars $(<0.5M_{\odot}$) varies. We note that our results
are consistent with some recent work which proposes that extreme IMFs are only
present in the central regions of these galaxies. We also consider IMFs that
become increasingly top-heavy with $\sigma$, resulting in significantly more
LMXBs. Such a model is consistent with these observations, but additional data
are required to significantly distinguish between this and an invariant IMF.
For six of these galaxies, we directly compare with published IMF mismatch
parameters from the Atlas3D survey, $\alpha_{dyn}$. We find good agreement with
the LMXB population if galaxies with higher $\alpha_{dyn}$ have more top-heavy
IMFs -- although we caution that our sample is quite small. Future LMXB
observations can provide further insights into the origin of $\alpha_{dyn}$
variations.
