A hierarchical Bayesian approach for reconstructing the Initial Mass Function of Single Stellar Populations

TL;DR

This paper introduces a hierarchical Bayesian method with a new SPS code to reconstruct the initial mass function of stellar populations, allowing for flexible deviations from parametric models and assessing uncertainties.

Contribution

The authors develop a novel hierarchical Bayesian approach with a regularized, flexible IMF inference method, enhancing the accuracy of IMF reconstruction from stellar population data.

Findings

Successfully reconstructs input parameters in mock populations.

Systematic uncertainties can bias IMF estimates.

Bayesian framework facilitates model ingredient comparisons.

Abstract

Recent studies based on the integrated light of distant galaxies suggest that the initial mass function (IMF) might not be universal. Variations of the IMF with galaxy type and/or formation time may have important consequences for our understanding of galaxy evolution. We have developed a new stellar population synthesis (SPS) code specifically designed to reconstruct the IMF. We implement a novel approach combining regularization with hierarchical Bayesian inference. Within this approach we use a parametrized IMF prior to regulate a direct inference of the IMF. This direct inference gives more freedom to the IMF and allows the model to deviate from parametrized models when demanded by the data. We use Markov Chain Monte Carlo sampling techniques to reconstruct the best parameters for the IMF prior, the age, and the metallicity of a single stellar population. We present our code and apply our model to a number of mock single stellar populations with different ages, metallicities, and IMFs. When systematic uncertainties are not significant, we are able to reconstruct the input parameters that were used to create the mock populations. Our results show that if systematic uncertainties do play a role, this may introduce a bias on the results. Therefore, it is important to objectively compare different ingredients of SPS models. Through its Bayesian framework, our model is well-suited for this.