The optimally-sampled galaxy-wide stellar initial mass function - Observational tests and the publicly available GalIMF code

TL;DR

This paper introduces a deterministic optimal sampling method for the galaxy-wide initial mass function (IGIMF), compares it with observations, and provides a Python tool for calculating the IGIMF and related models based on galaxy properties.

Contribution

It presents a new optimal sampling approach for the IGIMF, demonstrating its consistency with empirical relations and providing a publicly available Python module for practical applications.

Findings

IGIMF aligns with observed cluster and galaxy relations

GalIMF code enables calculation of IGIMF and OSGIMF

Predictions about supernova occurrence based on SFR

Abstract

Here we present a full description of the integrated galaxy-wide initial mass function (IGIMF) theory in terms of the optimal sampling and compare it with available observations. Optimal sampling is the method we use to discretize the IMF into stellar masses deterministically. Evidence has been indicating that nature may be closer to deterministic sampling as observations suggest a smaller scatter of various relevant observables than random sampling would give, which may result from a high level of self-regulation during the star formation process. The variation of the IGIMFs under various assumptions are documented. The results of the IGIMF theory are consistent with the empirical relation between the total mass of a star cluster and the mass of its most massive star, and the empirical relation between a galaxy's star formation rate (SFR) and the mass of its most massive cluster. Particularly, we note a natural agreement with the empirical relation between the IMF's power-law index and a galaxy's SFR. The IGIMF also results in a relation between the galaxy's SFR and the mass of its most massive star such that, if there were no binaries, galaxies with SFR $<10^{-4}$ M$_\odot$/yr should host no Type II supernova events. In addition, a specific list of initial stellar masses can be useful in numerical simulations of stellar systems. For the first time, we show optimally-sampled galaxy-wide IMFs (OSGIMF) which mimics the IGIMF with an additional serrated feature. Finally, A Python module, GalIMF, is provided allowing the calculation of the IGIMF and OSGIMF in dependence on the galaxy-wide SFR and metallicity.