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 ( > 0.2 R _ { 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 ^ { -1 } } ) , 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 ( < 0.5 \hbox { $ \thinspace M _ { \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 .