Explodability criteria for the neutrino-driven supernova mechanism

¹ Heidelberger Institut für Theoretische Studien, Schloss-Wolfsbrunnenweg 35, D-69118 Heidelberg, Germany
² Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Philosophenweg 12, D-69120 Heidelberg, Germany
³ Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut, Mönchhofstr. 12-14, D-69120 Heidelberg, Germany
⁴ School of Physics and Astronomy, Monash University, Clayton, Australia
⁵ OzGrav: The ARC Center of Excellence for Gravitational Wave Discovery, Australia
⁶ Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium
⁷ Anton Pannekoek Institute of Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands

^⋆ Corresponding author: kiril.maltsev@protonmail.com

Received: 1 April 2025
Accepted: 20 May 2025

Abstract

Massive stars undergoing iron core-collapse at the end of their evolution terminate their lives either as successful or failed supernovae (SNe). The physics of core-collapse supernovae (CCSNe) is complex and understanding it requires computationally expensive simulations. Therefore, using these simulations to predict CCSN outcomes over large, densely sampled parameter spaces of SN progenitors (as is needed, e.g., for population synthesis studies) is not feasible. To remedy this situation, we present a set of explodability criteria that allow us to predict the final fates of stars by evaluating multiple stellar structure variables at the onset of core collapse. These criteria are calibrated to predictions made using a semi-analytical SN model, when evaluated over a set of ∼3900 heterogeneous stellar progenitors (comprised of single stars, binary-stripped and accretor stars). Over these, the explodability criteria achieve a > 99% agreement with the semi-analytical model. We test these criteria on 29 state-of-the-art 3D CCSN simulation outcomes from two different groups. Furthermore, we find that all explodability proxies needed for our pre-SN structure-based criteria have two distinct peaks and intervening valleys as a function of the carbon-oxygen (CO) core mass, M_CO, coinciding with failed and successful SNe, respectively. The CO core masses of explodability peaks shift systematically with metallicity, Z, as well as with the timing of the hydrogen-rich envelope removal via binary mass transfer. Using the criteria and the systematic shifts, we identify critical values in M_CO that define windows over which black holes form by direct collapse. With these findings, we formulate a CCSN recipe based on M_CO and Z that is applicable for rapid binary population synthesis and other studies. Our explodability formalism is consistent with observations of Type IIP, IIb, Ib and Ic SN progenitors and it partially addresses the missing red supergiant problem by direct black hole formation.