Simple interpolation functions for the galaxy-wide stellar initial mass function and its effects in early-type galaxies

TL;DR

This paper explores how the galaxy-wide stellar initial mass function (IGIMF) varies with galaxy luminosity and star formation rate in early-type galaxies, providing simple functions to describe these dependencies and their impact on stellar mass estimates.

Contribution

It introduces simple interpolation functions for the IGIMF's dependence on galaxy luminosity, linking star formation rate effects to observable properties in early-type galaxies.

Findings

Stellar masses in less luminous ETGs are slightly lower than canonical IMF predictions.

In the most luminous ETGs, stellar masses may be up to twice as high as canonical IMF estimates.

The paper provides convenient functions to relate IGIMF variations to galaxy luminosity in different passbands.

Abstract

The galaxy-wide stellar initial mass function (IGIMF) of a galaxy is thought to depend on its star formation rate (SFR). Using a catalogue of observational properties of early-type galaxies (ETGs) and a relation that correlates the formation timescales of ETGs with their stellar masses, the dependencies of the IGIMF on the SFR are translated into dependencies on more intuitive parameters like present-day luminosities in different passbands. It is found that up to a luminosity of approximately $10^9 \ {\rm L}_{\odot}$ (quite independent of the considered passband), the total masses of the stellar populations of ETGs are slightly lower than expected from the canonical stellar initial mass function. However, the actual mass of the stellar populations of the most luminous ETGs may be up to two times higher than expected from an SSP-model with the canonical IMF. The variation of the IGIMF with the mass of ETGs are presented here also as convenient functions of the luminosity in various passbands.