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. There is little observational evidence for variation of the IMF in our Galaxy (Bastian et al. 2010 ARA&A 48 339). 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 (e.g., Bate 2012 MNRAS 419 3115), and such simulations show that the form of the IMF does not vary greatly, even when the metallicity of star-forming gas is varied between 1/100 and 3 times solar metallicity (Myers et al. 2011 ApJ 735 49; Bate 2014 MNRAS 442 285; Bate 2019 MNRAS 484 2341).

The strongest observational evidence for variation of the IMF is from stellar populations that formed much earlier in the Universe (Smith 2020 ARA&A 58 577). Recently, following a preliminary DiRAC study of star formation at redshift z = 5 (Bate 2023 MNRAS 519 688), DiRAC has been used to perform a study of how the low-mass end of the IMF may vary between redshifts z = 0 – 10 and metallicities ranging from 1/100 to 3 times the solar value (Bate 2025 MNRAS 537 752). The main result from this study is that although the IMF does not vary significantly with metallicity for present-day star formation (z = 0), as the redshift is increased the IMF becomes increasingly `bottom-light’, in which low-mass stars are much rarer than for present-day star formation (Fig. 1a), and the magnitude of this effect increases with increasing metallicity. This is a result of the warmer cosmic microwave background radiation at higher redshift preventing high-metallicity gas from cooling as effectively as it can at low redshift, resulting in less fragmentation and larger typical stellar masses. The numerical IMFs have been fit by analytic functions (Fig. 1b) that allow the form of the IMF to be varied continuously with redshift and metallicity so that, for example, the functions could be used to vary the stellar IMF in simulations of galaxy formation.

Figure 1: Left: Α subset of the initial mass functions (IMFs) obtained from radiation hydrodynamical simulations of star cluster formation at redshifts z = 0 – 10 and metallicities 1/100 to 3 times the solar metallicity (Z = 0.01 − 3 Z_⊙).  As the redshift and/or metallicity are increased the IMFs become increasingly bottom-light IMF (i.e., there is a deficit of brown dwarfs and low-mass stars).  Right-panel: Analytic functions (solid lines) describing the behaviour of the median stellar mass, μ, with redshift, z, and metallicity, Z, that is obtained from the simulations (points).