Supernovae: an example of complexity in the physics of compressible fluids

TL;DR

This paper models supernovae as complex fluid phenomena using catastrophe theory, revealing new self-similar solutions with dominant gravity forces that differ from traditional models, and analyzing their collapse and post-collapse dynamics.

Contribution

It introduces a new self-similar solution assuming dominant gravity forces, contrasting with previous models, and provides detailed analysis of collapse and post-collapse behavior.

Findings

Loss of equilibrium described by Painlevé I equation

Velocity field diverges at collapse time, differing from previous models

New self-similar solution matches numerical results globally

Abstract

The supernovae are typical complex phenomena in fluid mechanics with very different time scales. We describe them in the light of catastrophe theory, assuming that successive equilibria between pressure and gravity present a saddle-node bifurcation. In the early stage we show that the loss of equilibrium may be described by a generic equation of the Painlev\'e I form. In the final stage of the collapse, just before the divergence of the central density, we show that the existence of a self-similar collapsing solution compatible with the numerical observations imposes that the gravity forces are stronger than the pressure ones. This situation differs drastically in its principle from the one generally admitted where pressure and gravity forces are assumed to be of the same order. Our new self-similar solution (based on the hypothesis of dominant gravity forces) which matches the smooth solution of the outer core solution, agrees globally well with our numerical results. Whereas some differences with the earlier self-similar solutions are minor, others are very important. For example, we find that the velocity field becomes singular at the collapse time, diverging at the center, and decreasing slowly outside the core, whereas previous works described a finite velocity field in the core which tends to a supersonic constant value at large distances. This discrepancy should be important for explaining the emission of remnants in the post-collapse regime. Finally we describe the post-collapse dynamics, when mass begins to accumulate in the center, also within the hypothesis that gravity forces are dominant.