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An essential component of galaxy formation theory is the stellar initial massfunction (IMF), that describes the parent distribution of stellar mass in starforming regions. We present observational evidence in a sample of early-typegalaxies (ETGs) of a tight correlation between central velocity dispersion andthe strength of several absorption features sensitive to the presence oflow-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 spectralfitting is performed with the latest state-of the art population synthesismodels (an extended version of the MILES models). A significant trend is foundbetween IMF slope and velocity dispersion, towards an excess of low-mass starsin the most massive galaxies. Although we emphasize that accurate values of theIMF slope will require a detailed analysis of chemical composition (such as[a/Fe] or even individual element abundance ratios), the observed trendssuggest that low-mass ETGs are better fit by a Kroupa-like IMF, whereas massivegalaxies require bottom-heavy IMFs, exceeding the Salpeter slope at velocitydispersions above 200km/s.

Systematic variation of the stellar Initial Mass Function with velocity dispersion in early-type galaxies