EVIDENCE FOR A MILD STEEPENING AND BOTTOM-HEAVY INITIAL MASS FUNCTION IN MASSIVE GALAXIES FROM SODIUM AND TITANIUM-OXIDE INDICATORS

Abstract

We measure equivalent widths (EWs)—focusing on two unique features (NaI and TiO 2 ) of low-mass stars (≲ 0.3 M ☉ )—for luminous red galaxy spectra from the Sloan Digital Sky Survey (SDSS) and X-Shooter Lens Survey (XLENS) in order to study the low-mass end of the initial mass function (IMF). We compare these EWs to those derived from simple stellar population models computed with different IMFs, ages, [α/Fe], and elemental abundances. We find that models are able to simultaneously reproduce the observed NaD λ5895 and Na i λ8190 features for lower-mass (∼σ * ) early-type galaxies (ETGs) but deviate increasingly for more massive ETGs, due to strongly mismatching NaD EWs. The TiO 2 λ6230 and the Na i λ8190 features together appear to be a powerful IMF diagnostic, with age and metallicity effects orthogonal to the effect of IMF. We find that both features correlate strongly with galaxy velocity dispersion. The XLENS ETG (SDSS J0912+0029) and an SDSS ETG (SDSS J0041−0914) appear to require both an extreme dwarf-rich IMF and a high sodium enhancement ([Na/Fe] = +0.4). In addition, lensing constraints on the total mass of the XLENS system within its Einstein radius limit a bottom-heavy IMF with a power-law slope to x ⩽ 3.0 at the 90% CL. We conclude that NaI and TiO features, in comparison with state-of-the-art simple stellar population models, suggest a mildly steepening IMF from Salpeter ( dn / dm ∝ m − x with x = 2.35) to x ≈ 3.0 for ETGs in the range σ = 200–335 km s −1 .