Systematic variation of the stellar Initial Mass Function with velocity
  dispersion in early-type galaxies
  An essential component of galaxy formation theory is the stellar initial mass
function (IMF), that describes the parent distribution of stellar mass in star
forming regions. We present observational evidence in a sample of early-type
galaxies (ETGs) of a tight correlation between central velocity dispersion and
the strength of several absorption features sensitive to the presence of
low-mass stars. Our sample comprises ~40,000 ETGs from the SPIDER survey
(z<0.1). The data, extracted from the Sloan Digital Sky Survey, are combined,
rejecting both noisy data, and spectra with contamination from telluric lines,
resulting in a set of 18 stacked spectra at high signal-to-noise ratio (S/N>
400 per A). A combined analysis of IMF-sensitive line strengths and spectral
fitting is performed with the latest state-of the art population synthesis
models (an extended version of the MILES models). A significant trend is found
between IMF slope and velocity dispersion, towards an excess of low-mass stars
in the most massive galaxies. Although we emphasize that accurate values of the
IMF slope will require a detailed analysis of chemical composition (such as
[a/Fe] or even individual element abundance ratios), the observed trends
suggest that low-mass ETGs are better fit by a Kroupa-like IMF, whereas massive
galaxies require bottom-heavy IMFs, exceeding the Salpeter slope at velocity
dispersions above 200km/s.
