Black Hole Formation in Failing Core-Collapse Supernovae

Abstract: We present results of a systematic study of failing core-collapse supernovae and the formation of stellar-mass black holes (BHs). Using our open-source general-relativistic 1.5D code GR1D equipped with a three-species neutrino leakage/heating scheme and over 100 presupernova models, we study the effects of the choice of nuclear equation of state (EOS), zero-age main sequence (ZAMS) mass and metallicity, rotation, and mass-loss prescription on BH formation. We find that the outcome, for a given EOS, can be estimated, to first order, by a single parameter, the compactness of the stellar core at bounce. By comparing protoneutron star (PNS) structure at the onset of gravitational instability with solutions of the Tolman-Oppenheimer-Volkof equations, we find that thermal pressure support in the outer PNS core is responsible for raising the maximum PNS mass by up to 25% above the cold NS value. By artificially increasing neutrino heating, we find the critical neutrino heating efficiency required for exploding a given progenitor structure and connect these findings with ZAMS conditions, establishing, albeit approximately, for the first time based on actual collapse simulations, the mapping between ZAMS parameters and the outcome of core collapse. We also study the effect of progenitor rotation and find that the dimensionless spin of nascent BHs may be robustly limited below a^* = Jc/GM^2 = 1 by the appearance of nonaxisymmetric rotational instabilities.

• The paper demonstrates that progenitor core compactness (ξ2.5) is a key predictor, with higher values indicating quicker black hole formation.
• It uses the GR1D code to simulate over 100 presupernova models, showing how EOS softness and thermal pressure affect protoneutron star stability.
• Introducing rotation alters collapse dynamics via centrifugal support, though nonaxisymmetric instabilities limit the resulting extreme spin in black holes.

Overview of "Black Hole Formation in Failing Core-Collapse Supernovae"

This paper, authored by Evan O'Connor and Christian D. Ott, presents a comprehensive study of black hole (BH) formation from failing core-collapse supernovae (CCSNe). Emphasizing the role of the stellar mass, equation of state (EOS), and angular momentum, the paper details the results of systematic simulations using the GR1D code, thereby providing a rich dataset for analyzing core-collapse outcomes and BH properties.

Study Design and Methods

The authors utilize the GR1D framework, a general-relativistic 1.5D code, to model a wide variety of initial stellar conditions. The code features a three-species neutrino leakage/heating scheme that, despite its simplifications, allows for extensive parameter sweeps across different EOS, stellar masses, and rotation regimes. The study explores over 100 presupernova models with varying zero-age main sequence (ZAMS) masses, metallicities, and rotational states, enabling a thorough examination of BH formation scenarios.

Key to the analysis is the concept of progenitor core compactness at bounce, denoted as $\xi_{2.5}$, which serves as a primary predictive parameter for the postbounce dynamics and potential for BH formation. This parameter quantifies the density structure of the progenitor core, influencing whether the supernova mechanism might succeed or fail.

Results and Systematic Trends

1. EOS and Thermodynamics: The properties of the nuclear EOS significantly affect the maximum mass that a protoneutron star (PNS) can support. The paper demonstrates that thermal pressure in the hot outer layers of a PNS can augment the maximum stable mass by up to 25% above the cold neutron star value. Models with softer EOS show more pronounced thermal effects compared to stiffer ones.
2. Influence of Core Compactness: The study identifies a crucial relationship between $\xi_{2.5}$ and the delay before BH formation. Higher compactness values generally predict faster BH formation and therefore less time for a successful explosion, implying that such stars are more likely to collapse directly into BHs.
3. Role of Rotation: Introducing rotation can significantly alter the collapse dynamics through centrifugal support, which may stabilize a PNS long enough to alter the core-collapse outcome. However, when evaluating potential BH birth spins, this study suggests a strong limiting effect by nonaxisymmetric instabilities, which prevent extreme rotations.
4. Neutrino Mechanism Exploration: Using a parametrized neutrino heating framework, the authors estimate the critical conditions required to revive shocks and induce explosions in failing CCSNe. Their findings suggest that higher compactness progenitors require significantly greater neutrino heating efficiency to avoid BH formation.

Implications and Future Directions

The implications of this research are substantial for understanding both the distribution of stellar remnants and the nature of failed supernovae. By mapping core-collapse outcomes back to ZAMS conditions, the study highlights the critical influence of metallicity and mass loss prescriptions—factors that remain highly uncertain in stellar evolution.

Practically, these results could better inform population synthesis models of BHs in the universe, potentially aiding in the interpretation of observational data from gravitational wave detectors and neutrino observatories. The study also raises pertinent questions regarding the limitations of current EOS models and the need for more sophisticated multidimensional simulations to capture the full complexity of core-collapse dynamics.

In conclusion, while the paper addresses a vast parameter space with a high degree of sophistication, continued advancements in computational techniques and more nuanced physical models, including full transport schemes and multidimensional dynamics, will be necessary to further refine predictions of supernova outcomes and BH birth characteristics.