2023A&A...670A.151Y

The stellar initial mass function (IMF) is commonly interpreted to be a scale-invariant probability density distribution function (PDF) such that many small clusters yield the same IMF as one massive cluster of the same combined number of stars. Observations of the galaxy-wide IMF challenge this as dwarf galaxies do not form as many massive stars as expected. This indicates a highly self-regulated star formation process in which stellar masses are not stochastically sampled from the IMF and are instead related to the environment of star formation. Here, we study the nature of star formation using the relation between the most massive star born in a star cluster and its parental stellar cluster mass (the m_max - M_ecl relation). This relation has been argued to be a statistical effect if stars are sampled randomly from the IMF. By comparing the tightness of the observed m_max - M_ecl distribution with synthetic star clusters with stochastically sampled stellar masses, we find that the expected dispersion of the mock observations is much larger than the observed dispersion. Assuming that m_max and M_ecl uncertainties from the literature are correct, our test rejects the hypothesis that the IMF is a PDF at a more than 4.5σ confidence level. Alternatively, we provide a deterministic stellar mass sampling tool that reproduces the observed m_max - M_ecl distribution and compares well with the luminosities of star-forming molecular clumps. In addition, we find that there is a significant flattening of the m_max - M_ecl relation near m_max = 13 M_⊙. This may suggest strong feedback of stars more massive than about 13 M_⊙, and/or that the ejections of the most massive stars from young clusters in the mass range 63 to 400 M_⊙ are likely important physical processes in forming clusters.