SPIDER VIII - Constraints on the Stellar Initial Mass Function of
  Early-type Galaxies from a Variety of Spectral Features
  We perform a spectroscopic study to constrain the stellar Initial Mass
Function (IMF) by using a large sample of 24,781 early-type galaxies from the
SDSS-based SPIDER survey. Clear evidence is found of a trend between IMF and
central velocity dispersion, sigma0, evolving from a standard Kroupa/Chabrier
IMF at 100km/s towards a more bottom-heavy IMF with increasing sigma0, becoming
steeper than the Salpeter function at sigma0>220km/s. We analyze a variety of
spectral indices, corrected to solar scale by means of semi-empirical
correlations, and fitted simultaneously with extended MILES (MIUSCAT) stellar
population models. Our analysis suggests that sigma0, rather than [alpha/Fe],
drives the IMF variation. Although our analysis cannot discriminate between a
single power-law (unimodal) and a low-mass (<0.5MSun) tapered (bimodal) IMF, we
can robustly constrain the fraction in low-mass stars at birth, that is found
to increase from 20% at sigma0~100km/s, up to 80% at sigma0~300km/s. Additional
constraints can be provided with stellar mass-to-light (M/L) ratios: unimodal
models predict M/L significantly larger than dynamical M/L, across the whole
sigma0 range, whereas a bimodal IMF is compatible. Our results are robust
against individual abundance variations. No significant variation is found in
Na and Ca in addition to the expected change from the correlation between
[alpha/Fe] and sigma0. [Abridged]
