The Initial Mass Function (IMF) of early-type galaxies (ETGs) has been found to feature systematic variations by both dynamical and spectroscopic studies. In particular, spectral line strengths, based on gravity-sensitive features, suggest an excess
of low-mass stars in massive ETGs, i.e. a bottom-heavy IMF. The physical drivers of IMF variations are currently unknown. The abundance ratio of alpha elements, such as [Mg/Fe], has been suggested as a possible driver of the IMF changes, although dynamical constraints do not support this claim. In this letter, we take advantage of the large SDSS database. Our sample comprises 24,781 high-quality spectra, covering a large range in velocity dispersion (100<sigma0<320 km/s) and abundance ratio (-0.1<[Mg/Fe]<+0.4). The large volume of data allows us to stack the spectra at fixed values of sigma0 and [Mg/Fe]. Our analysis -- based on gravity-sensitive line strengths -- gives a strong correlation with central velocity dispersion and a negligible variation with [Mg/Fe] at fixed sigma0. This result is robust against individual elemental abundance variations, and seems not to raise any apparent inconsistency with the alternative method based on galaxy dynamics.
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 dispers
ion, 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]
