Matthew Bate (University of Exeter)

The distribution of stellar masses, known as the initial mass function (IMF), is of central importance in astrophysics, due to the fact that the radiative, chemical and mechanical feedback from a star depends strongly on its mass. Despite many observational studies, there is little evidence for variation of the IMF in our Galaxy (Bastian et al. 2010 ARA&A 48 339). During the past decade, radiation hydrodynamical simulations of star cluster formation have been able to produce stellar populations that match the typical stellar properties of Galactic stellar populations quite well (Bate 2012 MNRAS 419 3115). In agreement with observations, they have found that the distributions of stellar masses produced by present-day Galactic star formation are surprisingly invariable. For example, star cluster formation calculations have shown that varying the metallicity of star-forming gas between 1/100 and 3 times solar metallicity has little effect on stellar properties for present-day star formation (Myers et al. 2011 ApJ 735 49; Bate 2014 MNRAS 442 285; Bate 2019 MNRAS 484 2341).  The only effect of metallicity for present-day star formation that has yet been identified is on the frequency of close binary systems – a triumph of the simulations of (Bate 2014, 2019), performed using DiRAC, is that they do produce the recently observed anti-correlation of close binary frequency with metallicity (Badenes et al. 2018 ApJ 854 147; El-Badry & Rix 2019 482 L139; Moe, Kratter & Badenes 2019 ApJ 875 61). 

The strongest evidence for variation of the IMF is from stellar populations that formed much earlier in the Universe (Smith 2020 ARA&A 58 577). Recently, DiRAC has been used to perform the first radiation hydrodynamical simulations of star cluster formation at high redshift: z = 5 (Bate 2023 MNRAS 519 688). The main result from this study is that although the IMF does not depend significantly on metallicity for present-day star formation (z = 0), it does depend on metallicity at redshift z = 5: high metallicity gives a `bottom-light’ IMF in which low-mass stars are much rarer than in present-day star formation (Fig. 1). The difference at high-redshift is that the cosmic microwave background radiation is much warmer. High-metallicity gas is unable to cool to as lower temperatures at z = 5 as at z = 0, resulting in less fragmentation and larger typical stellar masses.

Figure 1: The cumulative stellar initial mass functions (IMFs) obtained from radiation hydrodynamical simulations of star cluster formation performed at redshifts z = 0 (left; Bate 2019) and z = 5 (right; Bate 2023). The IMFs at z = 0 are quite insensitive to the metallicity of the molecular gas (ranging from Z = 0.01 − 3 Z_⊙), but at redshift z = 5 the IMFs become metallicity dependent, with high metallicity gas producing a bottom-light IMF.