Given a flurry of recent claims for systematic variations in the stellar initial mass function (IMF), we carry out the first inventory of the observational evidence using different approaches. This includes literature results, as well as our own new findings from combined stellar population synthesis (SPS) and Jeans dynamical analyses of data on ~4500 early-type galaxies (ETGs) from the SPIDER project. We focus on the mass-to-light ratio mismatch relative to the Milky Way IMF, δIMF, correlated against the central stellar velocity dispersion, σsstarf. We find a strong correlation between δIMF and σsstarf, for a wide set of dark matter (DM) model profiles. These results are robust if a uniform halo response to baryons is adopted across the sample. The overall normalization of δIMF and the detailed DM profile are less certain, but the data are consistent with standard cold DM halos and a central DM fraction that is roughly constant with σsstarf. For a variety of related studies in the literature, using SPS, dynamics, and gravitational lensing, similar results are found. Studies based solely on spectroscopic line diagnostics agree on a Salpeter-like IMF at high σsstarf but differ at low σsstarf. Overall, we find that multiple independent lines of evidence appear to be converging on a systematic variation in the IMF, such that high-σsstarf ETGs have an excess of low-mass stars relative to spirals and low-σsstarf ETGs. Robust verification of super-Salpeter IMFs in the highest-σsstarf galaxies will require additional scrutiny of scatter and systematic uncertainties. The implications for the distribution of DM are still inconclusive.
C. Tortora, Aaron J. Romanowsky, and N. R. Napolitano. "An inventory of the stellar initial mass function in early-type galaxies" Astrophysical Journal (2013). https://doi.org/10.1088/0004-637X/765/1/8