A new method for deriving the stellar birth function of resolved stellar populations

TL;DR

This paper introduces a novel statistical method based on Poisson Point Processes to derive the stellar birth function from resolved stellar populations, effectively handling measurement errors, incompleteness, and complex parameter correlations.

Contribution

The new approach models the entire likelihood without binning, enabling simultaneous estimation of the IMF, SFH, and MDF, including nuisance parameters, using simulated data for validation.

Findings

Method accurately recovers input parameters in simulations.

Handles measurement errors and incompleteness effectively.

Allows simultaneous estimation of multiple population parameters.

Abstract

We present a new method for deriving the stellar birth function (SBF) of resolved stellar populations. The SBF (stars born per unit mass, time, and metallicity) is the combination of the initial mass function (IMF), the star-formation history (SFH), and the metallicity distribution function (MDF). The framework of our analysis is that of Poisson Point Processes (PPPs), a class of statistical models suitable when dealing with points (stars) in a multidimensional space (the measurement space of multiple photometric bands). The theory of PPPs easily accommodates the modeling of measurement errors as well as that of incompleteness. Compared to most of the tools used to study resolved stellar populations, our method avoids binning stars in the color-magnitude diagram and uses the entirety of the information (i.e., the whole likelihood function) for each data point; the proper combination of the individual likelihoods allows the computation of the posterior probability for the global population parameters. This includes unknowns such as the IMF slope and combination of SFH and MDF, which are rarely solved for simultaneously in the literature, however entangled and correlated they might be. Our method also allows proper inclusion of nuisance parameters, such as distance and extinction distributions. The aim of this paper, is to assess the validity of this new approach under a range of assumptions, using only simulated data. Forthcoming work will show applications to real data. Although it has a broad scope of possible applications, we have developed this method to study multi-band HST observations of the Milky Way Bulge. Therefore we will focus on simulations with characteristics similar to those of the Galactic Bulge.