{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"865ef13d7832987872fd3862cdf0c7001b1f12b18228598b2382fea136c6ca7e","created":"2026-10-03T07:17:55Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"87abe4b802f1f69db6aaa12ec2cc7aff7735b61eb6918f5153fa06fa92d6c056","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"astro.star-formation-imf.imf-peak","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"The most common birth mass of stars is about a fifth of the Sun's mass, and this peak is found almost everywhere we look. Why nature prefers this mass, and whether it changes in very different environments, is not explained.","posed_since":"","precise":"The initial mass function $dN/d\\operatorname{log} m$ peaks at $m_c \\sim 0.2-0.3\\,M_{\\mathrm{sun}}$ and falls as dN/dlog m ~ m^-1.35 (Salpeter slope, 2.35 in $dN/dm$) above $\\sim 1\\,M_{\\mathrm{sun}}$. Derive $m_c$ from first principles, distinguishing between the thermal Jeans mass at the transition to dust-dominated cooling, the mass of the first hydrostatic core, protostellar radiative heating, and turbulent fragmentation, and predict how $m_c$ scales with metallicity, gas pressure and radiation field.","problem_ref":null,"references":"","settled_by":"Simulations converged in resolution that predict $m_c$ and its environmental scaling, tested against measured IMFs in clusters of different metallicity and density.","status_note":"The 2024 review by Hennebelle and Grudic argues that dust opacity and the first hydrostatic core set the peak, which is not yet confirmed by tests across environments.","title":"What sets the typical stellar mass near 0.2 solar 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