A model for the minimum mass of bound stellar clusters and its dependence on the galactic environment

Abstract

We present a simple physical model for the minimum mass of bound stellar clusters as a function of the galactic environment. The model evaluates which parts of a hierarchicallyclustered star-forming region remain bound given the time-scales for gravitational collapse, star formation, and stellar feedback. We predict the initial cluster mass functions (ICMFs) for a variety of galaxies and we show that these predictions are consistent with observations of the solar neighbourhood and nearby galaxies, including the Large Magellanic Cloud and M31. In these galaxies, the low minimum cluster mass of ∼ 10 2 M is caused by sampling statistics, representing the lowest mass at which massive (feedback-generating) stars are expected to form. At the high gas density and shear found in the Milky Way's Central Molecular Zone and the nucleus of M82, the model predicts that a mass > 10 2 M must collapse into a single cluster prior to feedback-driven dispersal, resulting in narrow ICMFs with elevated characteristic masses. We find that the minimum cluster mass is a sensitive probe of star formation physics due to its steep dependence on the star formation efficiency per free-fall time. Finally, we provide predictions for globular cluster (GC) populations, finding a narrow ICMF for dwarf galaxy progenitors at high redshift, which can explain the high specific frequency of GCs at low metallicities observed in Local Group dwarfs like Fornax and WLM. The predicted ICMFs in high-redshift galaxies constitute a critical test of the model, ideally-suited for the upcoming generation of telescopes.

The Strikingly Metal-rich Halo of the Sombrero Galaxy*

“…An increase of M min implies a smaller percentage of star clusters that have dissolved completely at the present time, thus increasing S N . Recent studies indicate that sufficiently high values of S N result for M min 10 3 M , which is expected for high-pressure starbursting environments with turbulent velocities σ = 10 − 100 km s −1 and gas surface densities Σ ISM ∼ 10 2 M pc −2 (Goudfrooij 2018;Trujillo-Gomez et al 2019), as seen in vigorously star-forming galaxies at high redshift (e.g., Tacconi et al 2013). Future studies of lensed high-redshift galaxies with the James Webb Space Telescope and future 30-m-class ground-based telescopes will be able to provide significantly improved constraints to S N and the low-mass regime of the CMF in such objects, and hence allow this scenario to be tested.…”

Star Clusters Near and Far

“…Recently, Trujillo-Gomez et al (2019) have extended the Reina-Campos and Kruijssen (2017) model to investigate the effect of feedback on the formation of low mass clusters, hence the intrinsic shape of the cluster mass function at the low mass end. The model evaluates which parts of the star-forming region remain bound given the time-scales for gravitational collapse, star formation, and stellar feedback that also determine the upper mass distribution.…”

A model for the formation of stellar associations and clusters from giant molecular clouds

“…But even with infinite mass resolution, addressing this question properly in numerical simulations will require some treatment of the granularity of stars, for both realistic stellar feedback and stellar dynamics. The IMF sampling effect proposed in Trujillo-Gomez et al (2019) is not captured by a feedback treatment adopting IMFaveraged feedback rates, and either requires some sampling scheme (e.g. Sormani et al 2017;Su et al 2018), or individually resolved stars.…”