Hierarchical Bayesian inference of the Initial Mass Function in Composite Stellar Populations

TL;DR

This paper introduces a hierarchical Bayesian framework for modeling composite stellar populations to accurately infer the variable initial mass function (IMF) in galaxies, overcoming biases from single stellar population assumptions.

Contribution

The paper develops a novel hierarchical Bayesian method to infer the IMF in composite stellar populations, accounting for IMF variability and improving over traditional single population models.

Findings

Using multiple SSPs reduces bias in IMF slope estimation.

Bayesian evidence favors models with more SSPs for fitting CSP spectra.

IMF can be accurately reconstructed at high signal-to-noise ratios.

Abstract

The initial mass function (IMF) is a key ingredient in many studies of galaxy formation and evolution. Although the IMF is often assumed to be universal, there is continuing evidence that it is not universal. Spectroscopic studies that derive the IMF of the unresolved stellar populations of a galaxy often assume that this spectrum can be described by a single stellar population (SSP). To alleviate these limitations, in this paper we have developed a unique hierarchical Bayesian framework for modelling composite stellar populations (CSPs). Within this framework we use a parameterized IMF prior to regulate a direct inference of the IMF. We use this new framework to determine the number of SSPs that is required to fit a set of realistic CSP mock spectra. The CSP mock spectra that we use are based on semi-analytic models and have an IMF that varies as a function of stellar velocity dispersion of the galaxy. Our results suggest that using a single SSP biases the determination of the IMF slope to a higher value than the true slope, although the trend with stellar velocity dispersion is overall recovered. If we include more SSPs in the fit, the Bayesian evidence increases significantly and the inferred IMF slopes of our mock spectra converge, within the errors, to their true values. Most of the bias is already removed by using two SSPs instead of one. We show that we can reconstruct the variable IMF of our mock spectra for signal-to-noise ratios exceeding $\sim$75.