Formation of Globular Cluster Systems II: Impact of the Cutoff of the Cluster Initial Mass Function

TL;DR

This study models how the exponential cutoff in the cluster initial mass function affects globular cluster system formation, matching observations and revealing the origin of the blue tilt in metallicity-mass relations.

Contribution

It introduces an updated analytic model incorporating the CIMF cutoff, explaining observed GC properties and the origin of the blue tilt in metallicity relations.

Findings

CIMF cutoff masses of 10^{6.5} to 10^{7} solar masses match observed GC scaling relations.

Models with lower cutoff masses fail to reproduce observed metallicity and mass distributions.

The blue tilt arises from formation in low-mass galaxies with limited cold gas, leading to metallicity variations.

Abstract

Observations of young star clusters reveal that the high-mass end of the cluster initial mass function (CIMF) deviates from a pure power-law and instead truncates exponentially. We investigate the effects of this truncation on the formation of globular cluster (GC) systems by updating our analytic model for cluster formation and evolution, which is based on dark matter halo merger trees coupled to empirical galactic scaling relations, and has been shown in previous work to match a wide array of observational data. The cutoff masses of $M_c=10^{6.5} M_{\odot}$ or $10^{7}M_{\odot}$ match many scaling relations: between the GC system mass and host halo mass, between the average metallicity of the GC system and host halo mass, and the distribution of cluster masses. This range of $M_c$ agrees with indirect measurements from extragalactic GC systems. Models with $M_c<10^{6.5}M_{\odot}$ cannot reproduce the observed GC metallicity and mass distributions in massive galaxies. The slope of the mass-metallicity relation for metal-poor clusters (blue tilt) for all $M_c$ models is consistent with observations within their errors, when measured using the same method. We introduce an alternative, more robust fitting method, which reveals a trend of increasing tilt slope for lower $M_c$. In our model the blue tilt arises because the metal-poor clusters form in relatively low-mass galaxies which lack sufficient cold gas to sample the CIMF at highest masses. Massive blue clusters form in progressively more massive galaxies and inherit their higher metallicity. The metal-rich clusters do not exhibit such a tilt because they form in significantly more massive galaxies, which have enough cold gas to fully sample the CIMF.