SDSS-IV MaNGA: stellar initial mass function variation inferred from Bayesian analysis of the integral field spectroscopy of early-type galaxies

We analyse the stellar initial mass functions (IMF) of a large sample of early-type galaxies (ETGs) provided by MaNGA (Mapping Nearby Galaxies at Apache Point Observatory). The large number of integral field unit (IFU) spectra of individual galaxies provide high signal-to-noise composite spectra that are essential for constraining IMF and to investigate possible radial gradients of the IMF within individual galaxies. The large sample of ETGs also make it possible to study how the IMF shape depends on various properties of galaxies. We adopt a novel approach to study IMF variations in ETGs, use Bayesian inferences based on full spectrum fitting. The Bayesian method provides a statistically rigorous way to explore potential degeneracy in spectrum fitting and to distinguish different IMFmodels with Bayesian evidence. We find that the IMF slope depends systematically on galaxy velocity dispersion, in that galaxies of higher velocity dispersion prefer amore bottom-heavy IMF, but the dependence is almost entirely due to the change of metallicity, Z, with velocity dispersion. The IMF shape also depends on stellar age, A, but the dependence is completely degenerate with that on metallicity through a combination AZ(-1.42). Using independent age and metallicity estimates we find that the IMF variation is produced by metallicity instead of age. The IMF near the centres of massive ETGs appears more bottom-heavy than that in the outer parts, while a weak opposite trend is seen for low-mass ETGs. Uncertainties produced by star formation history, dust extinction, a-element abundance enhancement, and noise in the spectra are tested.