The Pinching Floor

Neutrinos from a core-collapse supernova carry ~99% of the gravitational binding energy released when the stellar core collapses. Their energy spectrum isn’t thermal — it’s “pinched,” meaning narrower than a blackbody distribution at the same mean energy. The pinching parameter quantifies this narrowing: values above 2 indicate anti-pinching (broader than thermal), while values below 2 indicate pinching.

Analysis of 25 three-dimensional supernova simulations spanning progenitor masses from 8.1 to 100 solar masses (arXiv:2603.11272) reveals that the anti-electron neutrino pinching parameter reaches a floor of approximately 1.92. This floor is lower than one-dimensional predictions because convection in the proto-neutron star mixes the emission region, homogenizing the conditions that produce the neutrinos and narrowing the spectrum beyond what a static stratified atmosphere would produce.

The diagnostic power comes from failures. Models that form black holes — failed explosions where the proto-neutron star collapses further — show distinctive anti-pinching behavior beginning about 0.5 seconds after core bounce. The spectrum broadens rather than narrows, because the collapsing material creates extreme temperature gradients that the convection can’t homogenize. Anti-pinching at the right time is a black hole signature.

For long-running successful explosions, the flavor hierarchy itself shifts: after five seconds of cooling, the leptonic neutrino flavors carry about 40% of the radiated energy rather than the initially dominant electron neutrinos. And viewing angle introduces spectral variations of 0.8-1.5 in the pinching parameter — meaning the direction you observe from changes the spectral shape as much as the underlying physics.