Empirical mapping between τ and progenitor-core structure metrics (compactness ξ_M and Ertl’s M4–μ4)

Calibrate an empirical mapping τ = f(ξ_M, M4, μ4) that links the spectral parameter τ derived from neutrino observations to pre-collapse progenitor metrics—compactness ξ_M and Ertl’s two-parameter criterion (M4, μ4)—by assembling a sample or simulations that jointly constrain these core metrics and post-explosion observables.

Background

The τ parameter is an observationally derived descriptor of the supernova neutrino spectrum that encodes aspects of the explosion’s energetics and transport efficiency. Theoretical progenitor metrics—compactness ξ_M and Ertl’s M4–μ4 criterion—quantify the pre-collapse core structure and are used to predict explodability and post-bounce dynamics.

The authors point out that their current dataset lacks objects with independently constrained ξ_M and (M4, μ4), and that quantitatively calibrating τ against these metrics would require matched samples or simulations. They explicitly defer this empirical mapping to future work, highlighting it as an unresolved task.