2021ApJ...920...93L

The complexity of constraining the stellar initial mass function (IMF) in early-type galaxies cannot be overstated, given the necessity of very high signal-to-noise ratio (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 near-IR 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 Å spectral region and allow us to study the radial variation of the stellar population properties out to 1R_e. Carrying out parallel simulations that mimic the retrieval of all of 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 to retrieve accurate estimates not only of the age and metallicity but also of all of 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. and Vazdekis et al. EMILES stellar population models. We find agreement with both a parallel full spectral fitting of the same data and literature results.