IMF and [Na/Fe] abundance ratios from optical and NIR spectral features in early-type galaxies

We present a joint analysis of the four most prominent sodium-sensitive features (Na D, Na i ...8190A, Na i ...1.14 ...m, and Na i ...2.21 ...m), in the optical and near-infrared spectral ranges, of two nearby, massive (... ~ 300 km s super( -1)), early-type galaxies (named XSG1 and XSG2). Our analysis relies on deep Very Large Telescope/X-Shooter long-slit spectra, along with newly developed stellar population models, allowing for [Na/Fe] variations, up to ~1.2 dex, over a wide range of age, total metallicity, and initial mass function (IMF) slope. The new models show that the response of the Na-dependent spectral indices to [Na/Fe] is stronger when the IMF is bottom heavier. For the first time, we are able to match all four Na features in the central regions of massive early-type galaxies finding an overabundance of [Na/Fe] in the range 0.5-0.7 dex and a bottom-heavy IMF. Therefore, individual abundance variations cannot be fully responsible for the trends of gravity-sensitive indices, strengthening the case towards a non-universal IMF. Given current limitations of theoretical atmosphere models, our [Na/Fe] estimates should be taken as upper limits. For XSG1, where line strengths are measured out to ~0.8 R sub( e), the radial trend of [Na/Fe] is similar to [.../Fe] and [C/Fe], being constant out to ~0.5 R sub( e), and decreasing by ~0.2-0.3 dex at ~0.8 R sub( e), without any clear correlation with local metallicity. Such a result seems to be in contrast to the predicted increase of Na nucleosynthetic yields from asymptotic giant branch stars and Type II supernovae. For XSG1, the Na-inferred IMF radial profile is consistent, within the errors, with that derived from TiO features and the Wing-Ford band presented in a recent paper. (ProQuest: ... denotes formulae/symbols omitted.)