Black Hole Supernovae Outcomes Across a Wide Progenitor Range

This study demonstrates through 23 long-term axisymmetric simulations that black hole supernovae are not limited to the most massive progenitors but occur systematically across a wide range of stellar masses and compactnesses, resulting in diverse explosion energies and black hole masses that cannot be fully predicted by carbon-oxygen core mass alone.

The Gist

Imagine a massive star as a giant, multi-layered onion. For most of its life, it burns fuel in its core, creating an outward pressure that fights against gravity trying to crush it. When the fuel runs out, gravity wins, and the core collapses. Usually, this collapse hits a "brake," bounces back, and sends a shockwave out that blows the whole onion apart in a spectacular supernova, leaving behind a tiny, dense neutron star.

But sometimes, things go differently. This paper explores a specific, dramatic scenario the authors call a Black Hole Supernova (BHSN).

Here is the story of what happens, explained simply:

The "Half-Hearted" Explosion

In a BHSN, the star's core collapses, the shockwave revives, and the explosion starts to happen. It looks like a normal supernova is about to go off. However, the star is so heavy and dense that the "brake" (the proto-neutron star) can't hold on forever.

Think of it like a balloon being inflated. You blow air in, and it starts to expand (the explosion). But if the rubber is too thick and heavy, the balloon doesn't pop; instead, it keeps getting heavier until it suddenly implodes into a black hole.

In these events, the explosion and the black hole formation happen at the same time. The explosion is trying to blow the star apart, but the black hole is forming in the center and starting to eat the star from the inside out.

The "Eating" vs. "Blowing" Battle

The authors ran 23 computer simulations of stars ranging from about 20 to 60 times the mass of our Sun. They found that in 18 of these cases, a black hole formed after the explosion started but before the star was fully blown apart.

• The Battle: The explosion pushes material outward, while the newly forming black hole pulls material inward.
• The Outcome: It's a tug-of-war. Sometimes the explosion wins big, blowing away a huge chunk of the star. Sometimes the black hole wins, swallowing most of the star and only letting a thin layer of the outer skin escape.

The "Onion Layers" Matter

The paper discovered that you can't just look at how heavy a star is to predict what happens. You have to look at its "onion layers" (its internal structure).

• The Compactness: Some stars are "compact," meaning their layers are packed tightly together. These stars tend to form black holes faster.
• The Surprise: Even stars that aren't the heaviest can form black holes if their internal layers are packed just right. The authors found that this "Black Hole Supernova" outcome isn't just for the rare, super-massive stars; it can happen across a wide range of star sizes.

The Aftermath: A Diverse Family of Explosions

Because the battle between the explosion and the black hole plays out differently for each star, the results are all over the map:

1. The Energy: Some explosions are weak (like a firecracker), while others are incredibly powerful (like a nuclear bomb).
2. The Remnant: The black holes left behind range from about 3 to 26 times the mass of our Sun.
   • The "Mass Gap" Stars: Some of the smallest black holes found in these simulations fall into a mysterious "gap" in the universe where we rarely see black holes. This suggests BHSNe might be the reason those "missing" black holes exist.
   • The "Heavy Eaters": The most massive stars ended up with black holes that ate almost the entire star, leaving behind only a tiny puff of the outer hydrogen envelope.

Why This Matters (According to the Paper)

The authors emphasize that for a long time, scientists thought black holes only formed when an explosion failed completely (a "failed supernova"). This paper shows that black holes can form even when an explosion succeeds partially.

They also found that you can't just draw a simple line on a star to say, "Everything inside this line becomes a black hole, and everything outside flies away." The process is messy and lopsided. The explosion blows out in some directions, while the black hole gobbles up material in others.

The "Video Game" Warning

Finally, the authors admit that simulating this is incredibly hard. They found that if their computer models didn't have enough "resolution" (like a pixelated video game), they might get the timing wrong. Just like a low-resolution camera might miss a fast-moving car, a low-resolution simulation might miss the exact moment the star collapses, leading to slightly wrong answers about when the black hole forms.

In short: The universe has a "middle ground" explosion. It's not a total failure, and it's not a total success. It's a chaotic mix where a star tries to explode while simultaneously collapsing into a black hole, creating a diverse family of cosmic events that we are just starting to understand.

Technical Summary

Technical Summary: Black Hole Supernovae Outcomes Across a Wide Progenitor Range

Problem Statement
Black hole supernovae (BHSNe) are defined as core-collapse events where a black hole (BH) forms after shock revival but before the explosion is fully complete. While multidimensional simulations have increasingly identified BHSNe as a natural outcome, they remain one of the least studied channels of core collapse. Previous literature has largely focused on extremely massive ($>40 M_\odot$) and highly compact progenitors, often at low metallicity. It is unclear whether BHSNe are confined to these rare, extreme stars or if they arise systematically across a broader range of progenitor structures. Establishing the progenitor conditions for BHSNe is critical for understanding the resulting black hole and neutron star mass distributions, chemical enrichment, and the role of core-collapse supernovae in galaxy evolution.

Methodology
The authors performed 23 long-term, axisymmetric (2D) core-collapse simulations using the FLASH code (v4). The study utilized a progenitor suite from Sukhbold et al. (2018) spanning Zero-Age Main Sequence (ZAMS) masses of 19.51–60 $M_\odot$, corresponding to compactness parameters ($\xi_{2.5}$) ranging from 0.31 to 0.63.

The simulations were conducted in two stages:

1. Pre-BH Formation: Evolution from core bounce to BH formation (occurring between $\sim0.65$ s and $\sim4.35$ s post-bounce). The simulations employed Newtonian hydrodynamics with an effective relativistic gravitational potential (Case A), the SFHo nuclear equation of state (EOS) at high densities, and the Ye-based Helmholtz EOS at low densities. Neutrino transport was modeled using the analytic M1 approximation with energy-dependent transport across 12 logarithmic bins for three neutrino species.
2. Post-BH Formation: Upon BH formation, an excision mask was applied to the central region to allow continued evolution of the explosion and accretion for at least 5,000 s. The gravitational mass of the remnant was calculated by subtracting neutrino mass-energy losses from the baryonic mass. Passive particles were used to track the fate of mass shells (accretion vs. ejection).

The study also included a comparison between a 2D axisymmetric model and a 3D model of a stripped 39 $M_\odot$ progenitor to assess geometric effects.

Key Results

• Prevalence of BHSNe: BHSN outcomes were found across nearly the full ZAMS mass range studied (19.51–60 $M_\odot$), specifically for progenitors with compactness $0.40 \lesssim \xi_{2.5} \lesssim 0.63$. Of the 23 models, 18 resulted in BH formation after shock revival.
• Formation Timescales: BH formation occurred between $\sim0.7$ s and $\sim4.4$ s after bounce. While higher compactness generally correlated with earlier BH formation, the relationship was not monotonic due to the complex dependence on the progenitor's inner mass-radius structure.
• Remnant Masses: Final BH gravitational masses ranged from $\sim3 M_\odot$ to $\sim26 M_\odot$. The remnant mass generally increased with ZAMS mass, primarily reflecting the growth of the carbon-oxygen (CO) core. Notably, the lowest-mass BHSN progenitors produced BHs within the "lower mass gap" ($\sim3.9 M_\odot$ and $\sim2.8 M_\odot$).
• Explosion Energies: Final explosion energies spanned a wide range, from $\sim2 \times 10^{49}$ erg to $\sim3 \times 10^{51}$ erg. The evolution of diagnostic explosion energy ($E_{\text{diag}}$) showed distinct regimes:
  • High-mass progenitors ($\ge 51 M_\odot$) experienced a massive decline in $E_{\text{diag}}$ post-BH formation as thermal energy was drained to overcome the large overburden, resulting in weak explosions that only unbound the hydrogen envelope.
  • Low-mass progenitors ($\le 27 M_\odot$) maintained relatively constant $E_{\text{diag}}$ post-BH formation, as their shocks were already near the CO core edge, allowing neutrino-heated bubbles to survive.
• Mass Partitioning: Except for the most massive models ($\ge 51 M_\odot$), no single spherical mass coordinate cleanly separated ejecta from remnant material. For progenitors below $\sim51 M_\odot$, the partition was highly aspherical, with a fraction of every mass shell outside the BH contributing to the ejecta. The CO-core mass was found to be a better predictor of remnant mass than the He-core mass for intermediate-mass models, though it was still imperfect.
• 2D vs. 3D Comparison: A comparison of a 39 $M_\odot$ stripped progenitor in 2D and 3D revealed that while early evolution (bounce, shock revival) was similar, the 2D model collapsed to a BH earlier ($\sim620$ ms) than the 3D model ($\sim1$ s). The 3D PNS contracted more gradually and remained stable longer, suggesting that 2D axisymmetry may accelerate BH formation in certain regimes.

Significance and Claims
The paper claims that BHSNe are not restricted to the most extreme, massive stars but are a viable and potentially common outcome for a broad range of compact massive stars. The study demonstrates that:

1. Distinctiveness: BHSNe are dynamically and measurably distinct from fallback supernovae, characterized by accretion directly from the infalling star on timescales of seconds rather than hours, and substantial impacts on explosion dynamics.
2. Complexity of Progenitor Structure: While compactness is a useful diagnostic, the detailed inner mass-radius structure of the progenitor is essential for predicting the specific path to BH formation, the explosion energy, and the final remnant mass. The CO-core mass alone is an inadequate proxy for the final BH mass, particularly at the low- and high-mass ends of the distribution.
3. Astrophysical Impact: If realized in nature, BHSNe could populate the stellar-mass black hole distribution across a broad mass range, including the lower mass gap. They would produce a diverse class of transients with varying explosion energies and ejecta masses, distinct from both standard successful supernovae and failed explosions.
4. Numerical Challenges: The study highlights that late-time resolution in multidimensional simulations is critical. Insufficient resolution can under-resolve steep density gradients at the proto-neutron star (PNS) surface, leading to inaccurate central density evolution and potentially biased BH formation times.

The authors conclude that while BHSNe represent a distinct theoretical outcome, fully three-dimensional simulations and future work coupling these models to radiative transfer and nucleosynthesis are necessary to robustly determine their observational signatures and contribution to chemical enrichment.