Such work has shown that, as the mass of a galaxy increases, the strength of the giant sensitive Ca ii triplet decreases (Saglia et al., 2002 Cenarro et al., 2003) while the strength of dwarf sensitive features such as Na i and the Wing-Ford molecular FeH band increases (van Dokkum & Conroy, 2010, 2011 Smith et al., 2012 Spiniello et al., 2012 Ferreras et al., 2013 Spiniello et al., 2014 Smith et al., 2015 La Barbera et al., 2016). Of particular importance are IMF-sensitive spectral features, which can probe the ratio of low- to high-mass stars (Cohen, 1978 Faber & French, 1980 Carter et al., 1986 Couture & Hardy, 1993). The IMF of unresolved stellar populations can be inferred from modeling the integrated emission. Future LMXB observations can provide further insights into the origin of α d y n variations. We find good agreement with the LMXB population if galaxies with higher α d y n have more top-heavy IMFs – although we caution that our sample is quite small. For six of these galaxies, we directly compare with published “IMF mismatch" parameters from the Atlas3D survey, α d y n. Such a model is consistent with these observations, but additional data are required to significantly distinguish between this and an invariant IMF. We also consider IMFs that become increasingly top-heavy with σ, resulting in significantly more LMXBs. 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. Previously proposed IMFs that become increasingly bottom heavy with σ are consistent with these data if only the number of low mass stars ( < 0.5 M ⊙) varies.
We reject IMFs which become increasingly bottom heavy with σ, up to steep power-laws (exponent, α > 2.8) in massive galaxies ( σ > 300 k m s − 1), for galactocentric radii > 1 / 4 R e. We consider the LMXB populations beyond the cores of the galaxies ( > 0.2 R e covering 75 − 90 % of their stellar light) and find no evidence for systematic variations of the IMF with velocity dispersion ( σ). Comprised of accreting black holes and neutron stars, these LMXBs can be used to constrain the important high mass end of the IMF. 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.