The galaxy-wide stellar initial mass function in the presence of cluster-to-cluster IMF variations

TL;DR

This paper models how variations in the initial mass function (IMF) within star clusters influence the integrated galactic initial mass function (IGIMF), revealing that IMF variability significantly impacts galaxy-wide stellar mass distributions and can explain observed differences in galaxy types.

Contribution

It introduces a model incorporating Gaussian-distributed IMF variations into IGIMF calculations, highlighting their dominant effect on the characteristic mass and overall shape of the stellar mass function.

Findings

Increasing IMF parameter dispersions flattens the IGIMF at mass ends.

Higher characteristic mass dispersion shifts the IGIMF peak to lower masses.

IMF variations are essential to reproduce the stellar mass functions of ultra-faint dwarf galaxies.

Abstract

We calculate the integrated galactic initial stellar mass function (IGIMF) in the presence of IMF variations in clusters. IMF Variations for a population of clusters are taken into account in the form of Gaussian distributions of the IMF parameters. For the tapered power law function used here, these are the slopes at the high and low mass ends, $\Gamma$ and $\gamma$, and the characteristic mass $M_{ch}$. Variations are modeled by varying the width of the Gaussian distributions. The reference values are the standard deviations of the parameters observed for young clusters in the present-day Milky Way $\sigma_{\Gamma}=0.6$, $\sigma_{\gamma}=0.25$, and $\sigma_{M_{ch}}=0.27$ M$_{\odot}$. Increasing the dispersions of $\gamma$ and $\Gamma$ moderately flattens the IGIMF at the low and high mass ends. Increasing $\sigma_{M_{ch}}$ shifts the peak of the IGIMF to lower masses, rendering the IGIMF more bottom heavy. This can explain the bottom heavy stellar mass function of Early-type galaxies as they are the result of the merger of disk galaxies where the physical conditions of the star forming gas vary significantly both in time and space. The effect of IMF variations is compared to that due to other effects such as variations in the shape of the initial cluster mass function, metallicity, and galactic SFR. We find that the effect of IMF variations is a dominant factor that always affects the characteristic mass of the IGIMF. We compare our results to a sample of ultra-faint dwarf satellite galaxies (UFDs). Their present-day stellar mass function is an analog to their IGIMF at the time their stellar populations have formed. We show that the slope of the IGIMF of the UFDs can only be reproduced when IMF variations of the same order as those measured in the present-day Milky Way are included. (Abridged)