Modeling a High‐Mass Turn‐Down in the Stellar Initial Mass Function

Abstract

Statistical sampling from the stellar initial mass function (IMF) for all star-forming regions in the Galaxy would lead to the prediction of ~1000 M_☉ stars unless there is a rapid turn-down in the IMF beyond several hundred solar masses. Such a turn-down is not necessary for dense clusters because the number of stars sampled is always too small. Although no upper mass limits to star formation have ever been observed, a theory for the IMF should be able to explain the lack of ~1000 M_☉ stars in normal galaxy disks. Here we explore several mechanisms for an upper mass cutoff, including an exponential decline of the star formation probability after a turbulent crossing time. The results are in good agreement with the observed IMF over the entire stellar mass range, and they give a gradual turn-down compared to the Salpeter function above ~100 M_☉ for the normal thermal Jeans mass, M_J. However, they cannot give both the observed power-law IMF out to the high-mass sampling limit in dense clusters and the observed lack of supermassive stars in whole galaxy disks. The exponential decline is too slow for this. Either there is a sharp upper mass cutoff in the IMF, perhaps from self-limitation, or the IMF is different for dense clusters than for the majority of star formation that occurs at lower density. In the latter case, dense clusters would have to form an overabundance of massive stars relative to the average IMF in a galaxy. Evidence for a difference in the cluster and field IMFs supports this picture, but systematic effects could mimic this evidence even with a universal IMF. Within the framework of the sampling model, the upper mass turn-down should shift toward higher mass when M_J shifts upward, as might be the case in some starburst galaxies, and shift toward lower mass when M_J is lower, as might be the case in ultracold or high-pressure regions. Supermassive stars may therefore be possible in starburst galaxies, while in low surface brightness regions, where ultracold gas might exist at normal pressures, or in galactic cluster cooling flows, where cold gas could have extremely high pressures, a high fraction of the star formation could end up as brown dwarfs.