{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"3d4a3aa0e53e259cd4136b762824a03ce5ee6d9221e504603a56acdad01b6165","created":"2026-10-03T07:17:54Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"7cf6e9f06881c10d2263481a261dfb85a8acc22e20121e5294e8c0c83c8612d9","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"astro.compact-binary-origins.pair-instability-gap","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"Very massive stars should explode completely, because light in their cores turns into electron-positron pairs, leaving no black holes between roughly 50 and 130 solar masses; yet black holes in that range are seen merging.","posed_since":"","precise":"Pair-instability and pulsational pair-instability supernovae predict no black holes from single-star collapse between $M_{\\mathrm{low}} \\sim 45 \\text{ to } 65\\,M_{\\mathrm{sun}}$ and $M_{\\mathrm{high}} \\sim 120 \\text{ to } 130\\,M_{\\mathrm{sun}}$, with $M_{\\mathrm{low}}$ sensitive to the $12\\mathrm{C}(\\alpha,\\gamma)16\\mathrm{O}$ rate and rotation. Determine M_low and whether gap events (GW190521; GW231123 with components $\\sim 100 \\text{ to } 140\\,M_{\\mathrm{sun}}$ and spins $\\sim 0.8 \\text{ to } 0.9$) are hierarchical mergers, stellar-merger products, or evidence of a higher gap edge. Answer: inferred $M_{\\mathrm{low}}$ and a classification of gap events.","problem_ref":null,"references":"","settled_by":"A population-level detection of the drop in the mass function together with spin signatures that separate hierarchical from first-generation black holes.","status_note":"2025: GW231123, with total mass about $190\\ \\text{to}\\ 265\\,M_{\\mathrm{sun}}$ and high spins, has components in or near the gap; analyses favor hierarchical mergers.","title":"Where is the lower edge of the pair-instability mass 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