Explosion Mechanisms and Multidimensional Instabilities

Multidimensional flow can help a stalled supernova shock by increasing the residence time of matter in the neutrino-heated gain region and by adding nonradial stress behind the shock. Convection and the standing accretion shock instability (SASI) can both participate, while rapid rotation and magnetic fields define a distinct route for a restricted progenitor class. Which effect dominates, and whether a particular star explodes, remain unresolved. This comparison includes evidence available through 2026-08-18.

Helpful background. Stress–Energy and Conservation supplies energy budgets; the Einstein equations supply relativistic gravity; Relativistic Matter and Compact Objects supplies transport and dense-matter closure; Black-Hole Dynamics supplies generic collapse geometry; Computational Relativity supplies multidimensional validation; and Black-Hole Perturbation Theory supplies instability language.

A multidimensional critical condition

In spherical steady-flow models, the critical electron-flavor neutrino luminosity is a surface

$$L_{\nu,\mathrm{crit}} =L_{\nu,\mathrm{crit}}(\dot M,M_{\rm PNS},R_{\rm PNS}, \langle\epsilon_\nu^2\rangle,\text{microphysics}),$$

not one universal number. A common diagnostic compares gain-layer advection and heating times,

$$\frac{\tau_{\rm adv}}{\tau_{\rm heat}} \sim \frac{M_g/\dot M}{|E_{\rm bind,g}|/\dot Q_g}.$$

Nonradial motion can enlarge $M_g$, slow radial advection, and supply turbulent Reynolds stress that supports a larger shock radius. These effects tend to lower the critical luminosity relative to a matched spherical model. Janka develops the critical-luminosity and multidimensional timescale arguments in Janka 2012, §§IV.C.3–IV.C.5, Eqs. (9)–(11).

The comparison must be matched. Progenitor density and interface structure, finite-temperature equation of state, opacity and reaction set, gravity or full-GR treatment, transport closure, spatial dimension, angular and radial resolution, perturbation seed, and simulated post-bounce runtime can each move the shock trajectory. A result that changes several axes at once does not measure a “dimensionality effect”.

Convection and SASI occupy different regimes

Neutrino-driven convection grows from negative entropy gradients in the gain region. A useful linear indicator is the Foglizzo parameter

$$\chi=\int_{r_g}^{r_s}\frac{\sqrt{\max(0,-N^2)}}{|v_r|}\,dr ,$$

where $N^2\gt0$ denotes stable buoyancy and $N^2\lt0$ local convective instability. Only unstable layers contribute to this growth integral; using $|N|$ in a stably stratified layer would count oscillations as growth. Large $\chi$ allows an advected small perturbation enough time for multiple e-foldings, whereas finite-amplitude progenitor perturbations can seed convection even outside the idealized linear criterion. Convection mixes heated matter outward and newly accreted matter inward, broadening the distribution of residence times.

The SASI is instead associated with a feedback cycle of shock deformation, advected entropy–vorticity perturbations, and acoustic or pressure feedback. It can produce sloshing or spiral shock motion, modulate accretion, and create periods of enhanced heating. Rapid advection and a compact gain region can favor SASI activity, whereas sustained buoyant convection can disrupt its coherent cycle. Burrows reviews convection, SASI, and the broader mechanism debate in Burrows 2013, §§IV.A.1–IV.A.5.

Evidence for either instability is not evidence that it alone caused an explosion. A SASI oscillation can coexist with a failing shock; convection can be vigorous without making the total ejecta energy positive. The credible positions are therefore “neutrino heating aided by different flow instabilities in different parameter regimes”, not mutually exclusive labels for every model.

Comparison of mechanism claims

The following dated evidence matrix states what each position explains and what would count against overgeneralizing it. Its date is the page cutoff, 2026-08-18.

Position	Evidence for the mechanism	Contrary evidence or limitation	Comparison controls
Neutrino-driven convection and turbulence	Multidimensional gain flow can increase residence time, shock radius, and nonradial pressure support; successful model suites connect those effects to sustained heating.	Success is sensitive to progenitor compactness and interfaces, opacity set, gravity, resolution, and duration; transient shock expansion is not sufficient.	Match progenitor, EOS, weak rates, transport and closure, GR approximation, grid, perturbations, and runtime.
SASI-aided neutrino heating	Coherent sloshing or spiral cycles can enlarge the shock episodically and redistribute angular momentum and accretion flow.	SASI can saturate without explosion and may be weak when buoyant convection dominates; observed oscillation power does not establish causation.	Compare cycle frequency, gain advection time, perturbation spectrum, dimensionality, and shock/heating budgets.
Magnetorotational explosion	A rapidly rotating core with sufficiently amplified ordered field can extract rotational energy and drive bipolar outflow.	Many stellar-evolution progenitors rotate too slowly for this to dominate; magnetic amplification and reconnection can be under-resolved.	State precollapse angular momentum and field geometry, nonideal assumptions, GR, 3D resolution, and rotational-energy budget.
Acoustic assistance	Proto-neutron-star motion can launch sound that deposits energy in some formulations.	The required large coherent oscillations and dominant acoustic power were not broadly reproduced as a generic engine; neutrino heating usually remains entangled.	Report mode excitation, acoustic flux, numerical viscosity, boundary treatment, and comparison with neutrino power.

The two-dimensional and three-dimensional turbulence cascades are also different. Axisymmetry promotes large coherent structures through an inverse cascade and forbids nonaxisymmetric spiral degrees of freedom; three dimensions permit a forward cascade to smaller scales. Neither is automatically “more explosive” at finite resolution. Numerical viscosity can move energy between scales, so an apparent 2D–3D ordering without a resolution study is not a continuum conclusion. Mezzacappa and collaborators emphasize the linked transport and computational challenges in Mezzacappa et al. 2020, §§6.5–6.7.

A modern primary comparison sharpens that caution. Boccioli and collaborators analyzed 1D+, 2D, and 3D suites from GR1D, FLASH, and FORNAX and found a strong connection between progenitor compactness and gain-region neutrino heating in Boccioli et al. 2025, §3, Figures 2–3, and Appendix C. Their multidimensional sample includes SFHo models with multi-energy M1 transport, but it is not a fully matched code experiment: some progenitors, equations of state, opacities, transport frames, inelastic-scattering treatments, spatial dimensions, and grids differ across the assembled suites, and gravity uses relativistic corrections rather than one shared full-GR formulation. The study is evidence against a simple “high compactness always fails” rule and evidence for a heating–compactness trend within its model classes; its stated mismatches prevent using it to isolate a universal 2D–3D effect or an opacity-independent explosion boundary.

What counts as an explosion

A robust verdict requires sustained shock expansion, positive outward mass flux, and an energy budget that trends toward positive asymptotic ejecta energy after accounting for nuclear recombination and the binding of unmodeled overburden. The diagnostic energy at a finite time is not automatically the final kinetic energy. Simulations should also close baryon, total-energy, and lepton-number budgets and show that the verdict survives grid refinement, transport changes, and a longer runtime.

This standard explains why credible groups can reach different conclusions: they may use different progenitors, opacity revisions, equations of state, gravity, dimensionality, closures, resolution, or stopping times. Competing results should first be mapped onto those formulation axes. A matched code-comparison with identical continuum inputs is more discriminating than counting explosions across unmatched suites.

The open question is not whether neutrino heating, convection, or SASI exists; it is which combination produces a converged explosion and nucleosynthetic outcome across the relevant progenitor population. A concrete re-review trigger is a coordinated matched-code comparison, a converged three-dimensional multi-energy transport calculation, a revised progenitor or opacity calibration, or multimessenger data that distinguish a rapidly rotating magnetic engine from neutrino-dominated dynamics.

Check a mechanism comparison

Run A is axisymmetric, uses progenitor P, multi-group transport closure C, and fine grid spacing; it explodes. Run B is three-dimensional, uses progenitor Q, gray leakage, and coarse spacing; it fails. Does this establish that 2D is more explodable than 3D, and what comparison would answer the narrower question?

Solution

No. Progenitor, transport fidelity, closure, dimension, and resolution all changed, so the causal variable is unidentified. The narrower test holds P, the equation of state, opacity set, gravity, closure C, radial and effective angular resolution, perturbation amplitude, and runtime fixed, then compares 2D and 3D while monitoring heating, gain mass, turbulence spectra, shock trajectory, conservation residuals, and asymptotic-energy trend. Repeating at two or more resolutions tests whether the ordering survives toward the continuum limit.

References

• Boccioli, Luca, David Vartanyan, Evan P. O’Connor, and Daniel Kasen. “Neutrino Heating in 1D, 2D, and 3D Core-Collapse Supernovae: Characterizing the Explosion of High-Compactness Stars.” Monthly Notices of the Royal Astronomical Society 540 (2025): 3885–3905. DOI.
• Burrows, Adam. “Colloquium: Perspectives on Core-Collapse Supernova Theory.” Reviews of Modern Physics 85 (2013): 245–261. DOI.
• Janka, Hans-Thomas. “Explosion Mechanisms of Core-Collapse Supernovae.” Annual Review of Nuclear and Particle Science 62 (2012): 407–451. arXiv.
• Mezzacappa, Anthony, Eirik Endeve, O. E. Bronson Messer, and Stephen W. Bruenn. “Physical, Numerical, and Computational Challenges of Modeling Neutrino Transport in Core-Collapse Supernovae.” Living Reviews in Computational Astrophysics 6 (2020): 4. DOI.