SPIDER VIII – constraints on the stellar initial mass function of early-type galaxies from a variety of spectral features

Abstract

We perform a spectroscopic study to constrain the stellar Initial Mass\nFunction (IMF) by using a large sample of 24,781 early-type galaxies from the\nSDSS-based SPIDER survey. Clear evidence is found of a trend between IMF and\ncentral velocity dispersion, sigma0, evolving from a standard Kroupa/Chabrier\nIMF at 100km/s towards a more bottom-heavy IMF with increasing sigma0, becoming\nsteeper than the Salpeter function at sigma0>220km/s. We analyze a variety of\nspectral indices, corrected to solar scale by means of semi-empirical\ncorrelations, and fitted simultaneously with extended MILES (MIUSCAT) stellar\npopulation models. Our analysis suggests that sigma0, rather than [alpha/Fe],\ndrives the IMF variation. Although our analysis cannot discriminate between a\nsingle power-law (unimodal) and a low-mass (<0.5MSun) tapered (bimodal) IMF, we\ncan robustly constrain the fraction in low-mass stars at birth, that is found\nto increase from 20% at sigma0~100km/s, up to 80% at sigma0~300km/s. Additional\nconstraints can be provided with stellar mass-to-light (M/L) ratios: unimodal\nmodels predict M/L significantly larger than dynamical M/L, across the whole\nsigma0 range, whereas a bimodal IMF is compatible. Our results are robust\nagainst individual abundance variations. No significant variation is found in\nNa and Ca in addition to the expected change from the correlation between\n[alpha/Fe] and sigma0. [Abridged]\n