The Stellar Initial Mass Function and Population Properties of M89 from Optical and NIR Spectroscopy: Addressing Biases in Spectral Index Analysis

Abstract: The complexity of constraining the stellar initial mass function (IMF) in early-type galaxies cannot be overstated, given the necessity of both very high signal-to-noise (S/N) data and the difficulty of breaking the strong degeneracies that occur among several stellar population parameters including age, metallicity and elemental abundances. With this paper, the second in a series, we present a detailed analysis of the biases that can occur when retrieving the IMF shape by exploiting both optical and NIR IMF sensitive spectral indices. As a test case, here we analyze data for the nearby galaxy M89, for which we have high S/N spectroscopic data that cover the 3500-9000{\AA} spectral region and allow us to study the radial variation of the stellar population properties out to 1 R_e. Carrying out parallel simulations that mimic the retrieval of all the explored stellar parameters from a known input model, we quantify the amount of bias at each step of our analysis. From more general simulations we conclude that to accurately retrieve the IMF, it is necessary not only to retrieve accurate estimates of the age and metallicity, but also of all the elemental abundances that the spectral index fits are sensitive to. With our analysis technique applied to M89, we find consistency with a bottom-heavy IMF with a negative gradient from the center to half R_e when using the Conroy et al. 2018 as well as Vazdekis et al. 2016 EMILES stellar population models. We find agreement both with a parallel full spectral fitting of the same data and with literature results.