Compact Remnant Mass Function: Dependence on the Explosion Mechanism and Metallicity

The mass distribution of neutron stars and stellar-mass black holes provides vital clues into the nature of stellar core collapse and the physical engine responsible for supernova explosions. Using recent advances in our understanding of supernova engines, we derive mass distributions of stellar compact remnants. We provide analytical prescriptions for compact object masses for major population synthesis codes. In an accompanying paper, Belczynski et al., we demonstrate that these qualitatively new results for compact objects can explain the observed gap in the remnant mass distribution between ~2-5 solar masses and that they place strong constraints on the nature of the supernova engine. Here, we show that advanced gravitational radiation detectors (like LIGO/VIRGO or the Einstein Telescope) will be able to further test the supernova explosion engine models once double black hole inspirals are detected.

💡 Research Summary

This paper presents a comprehensive theoretical framework for predicting the mass distribution of compact remnants—neutron stars (NSs) and stellar‑mass black holes (BHs)—by incorporating the latest advances in supernova engine physics and stellar metallicity effects. The authors begin by reviewing observational evidence that NS masses cluster around 1.3–1.4 M⊙ but exhibit a broader, possibly bimodal distribution extending up to the maximum NS mass, while BH masses show a wide range up to ~20 M⊙ with a conspicuous paucity of objects between ~2 and ~5 M⊙. Earlier theoretical attempts (e.g., Timmes et al. 1996; Fryer & Kalogera 2001) relied on iron‑core mass proxies or simplistic mass‑loss prescriptions, leading to predictions that conflict with the observed “mass gap.”

The core of the analysis is a three‑stage description of core‑collapse: (i) collapse and bounce, (ii) a convection‑enhanced, neutrino‑driven explosion, and (iii) post‑explosion fallback. The authors adopt the paradigm that the explosion energy is limited by the internal energy stored in the convective region at the moment the shock overcomes the ram pressure of infalling material. They derive analytic expressions for the pressure and energy in this region, showing that typical stored energies are a few ×10⁵¹ erg, consistent with observed supernova energetics.

Two limiting explosion scenarios are explored. In the “fast‑convection” case, the shock revives within ≲250 ms after bounce, the accretion rate has dropped below ~3 M⊙ s⁻¹, and the resulting explosion is relatively energetic (>10⁵¹ erg). Fallback is minimal, so the remnant mass remains close to the proto‑NS mass (≈1.2–1.5 M⊙). In the “delayed‑convection” (SASI‑dominated) case, the shock revival is postponed, the accretion rate stays high for longer, and a substantial amount of material falls back onto the proto‑NS, pushing its mass above the maximum NS limit and leading to direct BH formation.

Metallicity (Z) is incorporated by using modern stellar evolution tracks (e.g., Yoon et al. 2005) that predict stronger line‑driven winds at higher Z. High‑metallicity progenitors lose more mass before collapse, resulting in lighter cores that are easier to explode, thus favoring NS outcomes. Low‑metallicity stars retain more mass, develop heavier cores, and are more prone to delayed explosions and large fallback, producing massive BHs. This metallicity‑dependent explosion/fallback behavior naturally reproduces the observed mass gap: the transition from successful explosions (NS) to failed or weak explosions (BH) occurs over a narrow progenitor mass range, leaving few remnants in the 2–5 M⊙ interval.

The authors translate their detailed calculations into simple analytic prescriptions for the remnant mass as a function of zero‑age main‑sequence mass and metallicity. These formulas are designed for direct implementation in population‑synthesis codes (e.g., StarTrack), enabling rapid generation of synthetic binary populations that reflect the new physics.

Finally, the paper discusses observational tests. Gravitational‑wave detectors such as LIGO, Virgo, and the planned Einstein Telescope will soon provide large samples of binary BH mergers with well‑measured component masses. The predicted mass distribution, especially the location and sharpness of the low‑mass cutoff, is highly sensitive to the assumed explosion delay times and fallback efficiencies. Consequently, statistical analyses of future GW catalogs can discriminate between the fast‑convection and delayed‑convection models, and constrain the role of metallicity in shaping the compact‑object mass function.

In summary, the study (1) refines the physical description of core‑collapse supernovae by focusing on convection‑enhanced neutrino heating, (2) demonstrates how metallicity modulates explosion timing and fallback, (3) provides ready‑to‑use analytic remnant‑mass prescriptions, and (4) outlines a clear pathway for gravitational‑wave observations to test and refine supernova engine theories.