The death of a massive star is a kind of cosmic weather forecast that we still struggle to read. For decades, astronomers have chased the core-collapse supernova as if it were a single switch: either the star explodes, or it quietly collapses into a black hole. But reality is messier. The explosion hinges on a tangle of physics that plays out across the star’s interior and its life history, from the carbon hidden in the core to the way a companion star may have peeled away its outer layers. The neutrino engine that powers many explosions is exquisitely sensitive to the structure just outside the iron core, and the multidimensional turbulence in the collapsing star can tilt the outcome one way or the other. In short, there isn’t a single number you can check and know the ending.
The good news is that a team led by Kiril Maltsev at the Heidelberger Institut für Theoretische Studien and the University of Heidelberg has produced a practical toolkit that translates this complexity into a predictive map you can apply before the star ever blows. The authors stitch together six diagnostic fingerprints of a star’s pre collapse structure, calibrate them against a semi‑analytic model of neutrino-driven explosions, and then show how these fingerprints reliably forecast the final fate across thousands of progenitors, including single stars and binary systems. The work is a collaboration anchored in Heidelberg with partners at Monash University in Australia, OzGrav, KU Leuven, and the Anton Pannekoek Institute in Amsterdam, and the lead authors include K. Maltsev with F. R. N. Schneider, I. Mandel, B. Müller, A. Heger, F. K. Röppe, and E. Laplace. The payoff is not just a prettier chart; it’s a practical recipe for predicting whether a star ends its life as a neutron star, a black hole, or something in between, at a scale needed for population studies and for interpreting the faint whispers of exploding stars we observe across the cosmos.
A multi-variable explodability map
Any one metric to decide a star’s fate falls short. Some workers have focused on a compactness parameter, others on entropy jumps, and a few on the so‑called carbon ignition coordinates. Maltsev and colleagues show that you gain real predictive power only when you stack several diagnostics. They assemble a set of six pre‑SN variables: the inner compactness around 2.5 solar masses, ξ2.5; the central specific entropy s at a particular mass coordinate; the carbon‑oxygen core mass MCO; and two proxies tied to how strongly matter would accrete onto the newborn proto‑neutron star, namely µ4M4 and µ4. Finally, they allow for the influence of metallicity Z and a star’s binary history, which can change the pre‑SN skeleton in important ways. The central idea is simple in spirit: the final fate is carved by several stages of the star’s structure, not by a single hinge.
The team calibrates these proxies against the neutrino‑driven supernova engine codified in a semi‑analytic model known as M16, which compresses the relevant physics into a set of ordinary differential equations for mass advection and neutrino heating. In practice, they went hunting across roughly 3900 one‑D progenitor models that span single stars, binary‑stripped stars, and accretor stars. They then built a predictive scheme—an explodability map—that decides, at the onset of core collapse, whether the star will explode or fail and, in the former case, what kind of compact remnant it will leave behind. The key triumph is that the scheme runs with striking accuracy: it matches the M16 outcomes with about 99.4 percent fidelity across that large catalog. It is a powerful demonstration that a few carefully chosen fingerprints can capture a great deal of the final fate of stars without running three‑dimensional simulations for every case.
Two caveats shape how we should read the maps. First, this explodability framework is built around a particular line of modeling—the M16 semi‑analytic engine and specific 1D progenitor sets—so the exact thresholds can shift if one tunes the underlying physics or uses different progenitor grids. Second, the authors test against a handful of 3D simulations; the 29 models from two groups show overall consistency, but like any frontier science, there are outliers—certain Population III or rapidly rotating progenitors that behave differently in full 3D. The upshot is not a universal law but a robust, testable forecast that scales to population studies and to rapid binary population synthesis, the kind of work that tries to predict the fate of millions of stars across a galaxy.
Why carbon-oxygen core mass matters
One of the most striking discoveries in the paper is that explodability—whether a star will blow apart or collapse into a black hole—displays a bimodal pattern when plotted against the carbon‑oxygen core mass, MCO. The authors report that all the explodability proxies peak and dip twice as MCO climbs from a few solar masses up to around 15 solar masses, with a valley in between where explosions tend to win. In plain terms: the star’s inner furnace and its outer build up conspire to create two “windows” where black holes form by direct collapse, separated by a broad swath where explosions are favored.
Those thresholds are not universal constants; they shift with metallicity Z and with how the hydrogen envelope was removed through binary interactions. At solar metallicity, the three critical CO core masses sit around M(1)CO ≈ 6.6–7.4 M⊙, M(2)CO ≈ 7.1–8.3 M⊙, and M(3)CO ≈ 13–15 M⊙, marking three pivotal boundaries in the fate map. When metallicity drops to Z⊙/10, these numbers slide to smaller values by a modest but meaningful amount, in part because binary mass transfer reduces the helium core and leaves a different carbon stock in the heart of the star. The same pattern appears in both single stars and binary donors, but the exact boundaries drift depending on the donor class—Case C, Case B, Case A—and on the metallicity. The authors emphasize that the same MCO value may map to different outcomes if the star’s binary history changes XC, the carbon fraction at the end of helium burning, which in turn shapes the late‑stage burning and the inner pressure balance of the core.
That two‑peak structure matters for population modeling. If you only tracked MCO and ignored XC or the envelope history, you’d miss the windows where a star is most likely to explode versus collapse. The bimodal pattern is not a quirk of a single proxy; it emerges in ξ2.5, sc, and the two accretion proxies, each carrying information from different layers of the star. The upshot is a coherent narrative: the star’s fate is written in multiple chapters, and the order and emphasis of those chapters can shift with metal content and binarity. This is what makes the mapping to a MCO–Z dependent recipe possible and physically meaningful.
From pre-SN maps to rapid population synthesis
Population synthesis aims to predict the demographics of stellar remnants across entire galaxies, but decompressing the physics of core collapse into a few centuries‑old stellar models is a computational bottleneck. The authors address this by turning their pre‑SN explodability criteria into a practical CCSN recipe that can be used in rapid population synthesis codes. The essential move is to parameterize the CO core thresholds as a function of metallicity and mass transfer history, then connect CO to a simple decision rule for explosion versus failure. They introduce an explicit form for the Z dependence: each critical boundary M(i)CO(Z) is modeled as a linear function of log Z, calibrated using the Z = Z⊙ and Z = Z⊙/10 data for each MT class. In short, they turn a high‑dimensional physics problem into a compact, transferable recipe that fits neatly into existing population synthesis frameworks.
Another practical twist is how the remnants are handled when a star does explode. The semi‑analytic engine M16 not only predicts success or failure but also whether a neutron star or a black hole will result, depending on the explosion energy and how much mass falls back onto the compact remnant. The authors present two approaches to fallback: a deterministic criterion tied to Edelay and Eexpl that signals a fallback BH if the explosion loses a large fraction of its initial energy, and a probabilistic fallback model B that assigns a 10 percent chance of fallback BH formation within the intermediate MCO window. The deterministic version achieves near perfect NS vs BH discrimination on a wide set of progenitors, while the probabilistic variant captures the reality that turbulence and stochasticities in collapse can blur the lines. Taken together, these refinements produce a CCSN recipe that is both physically grounded and pragmatically usable in population studies.
In their cross‑checks, Maltsev and coauthors compare their MCO–based recipe against several established recipes that have guided population synthesis for years. The standout contrast is that their framework tends to be more optimistic about explosions, guaranteeing successful supernovae over a broad MCO range (roughly 8.4 to 12.4 M⊙ for solar metallicity, with continuity to higher MCO under certain MT histories). They also reproduce a plausible neutron star–black hole landscape that is consistent with observed binary black hole mergers, while leaving room for the existence of a low mass gap in some channels. The practical upshot is that the new recipe can sit alongside or replace older recipes in binary population synthesis codes, potentially recalibrating predicted rates for different remnant populations and the formation of merging black holes that detectors like LIGO and Virgo see today.
Linking theory to observations and the red supergiant puzzle
One of the paper’s most tangible tests is its dialogue with real stars we have watched end their lives in the sky. The authors connect MCO to observable pre‑SN luminosities of Type IIP progenitors through a scaling relation that ties TACCB, the terminal age core carbon luminosity, to MCO. Using this bridge, they estimate CO core masses for several well‑studied progenitors, including SN 2012ec, SN 2009kr, and SN 2009hd, as well as a couple of candidate failed SNe. The comparison is nuanced: their CCSN recipe can accommodate the most luminous Type IIP progenitors and partially address the missing red supergiant problem by suggesting that a slice of RSGs may end life as failed SNe or direct BHs. But it does not solve the problem outright; the missing red supergiants still pose a challenge that invites additional physics or alternative explanations beyond the scope of the present framework.
Beyond red supergiants, the authors touch on a broader cast of transients. Type IIb and Ib supernovae, Type Ic events such as the luminous SN 2011bm, and the enigmatic Type IIn SN2010jl each provide fresh data points on which the MCO–based recipe is tested. Some transients with bright pre‑SN luminosities imply higher MCO values and are only partially compatible with the most conservative versions of explosive scenarios. The overarching message is not a single yes or no for each event but a structured dialogue: the observed diversity in supernovae is broadly compatible with a framework in which the CO core mass, metallicity, and binary history sculpt the final fate, but the exact details depend on the star’s internal physics and its life story before collapse.
On a grand scale, the work hints at a more self‑consistent picture of stellar death and cosmic black hole births. Because the model distinguishes single stars from binary stripped stars and explicitly encodes how metallicity shifts the fate map, it provides a route to predict how often neutron stars versus black holes should emerge in different galactic environments, and how the binary pathways connect to the population of merging compact objects we observe with gravitational waves. It also underscores how much our understanding of the final act depends on the star’s interior choreography long before the collapse begins. The authors’ practical CCSN recipe promises to sharpen our cosmic forecasts, even as it invites further tests with future 3D simulations and a broader set of observed transients.
Takeaway: this work reframes the explosion verdict as a chorus of pre‑collapse fingerprints rather than a single whistle. By weaving together ξ2.5, sc, MCO, µ4M4, µ4, Z, and a star’s binary history, Maltsev and colleagues provide a usable map from which astronomers can forecast the fate of tens of thousands of stars. It is not a final law of stellar death, but a practical compass that aligns deep theory with the growing library of observed supernovae and the evolving census of compact remnants in the universe. The result is a step toward turning the messy physics of core collapse into a workable science of cosmic fates.
Closing thoughts
This collaborative effort—rooted in the Heidelberg ecosystem and extended through Monash, KU Leuven, Amsterdam, and beyond—bridges the gap between detailed simulations and big‑picture population studies. It highlights how modern astrophysics often advances by stitching together multiple lines of evidence into a coherent predictive framework rather than chasing a single, universal threshold. As computational power grows and 3D models grow more diverse, the explodability map will be stress‑tested and refined. Yet the core message remains clear: stars die in ways that are patterned and predictable when you listen to the right chorus of pre‑collapse cues. The universe, it seems, keeps score in more than one way, and this new scorecard helps us finally read it with more than a rough approximations.
