[Paper Review] Fluid Stability Below the Neutrinospheres of Supernova Progenitors and the Dominant Role of Lepto-Entropy Fingers

Stephen W. Bruenn, E. A. Raley+1 more|ArXiv.org|Apr 5, 2004

Neutrino Physics Research1 references7 citations

TL;DR

This paper re-evaluates fluid instabilities below the neutrinosphere in core-collapse supernovae using detailed neutrino transport simulations, finding that lepto-entropy fingers—driven by cross-coupling between entropy and lepton fraction perturbations—dominate over neutron fingers. Contrary to prior claims, lepton equilibration is faster than thermal equilibration, making neutron fingers unlikely; instead, lepto-entropy fingers and semiconvection are identified as key instabilities enhancing neutrino emission in proto-neutron stars.

ABSTRACT

We have developed a formalism for analyzing the stability of a fluid in the presence of neutrinos of all flavors and in the presence of a gravitational field. When applied to an extensive two-dimensional grid of core radii and fluid element sizes for each of several time slices of a number of proto-supernovae, we find no evidence for the neutron finger instability as described by the Livermore group. We find, instead, that the rate of lepton equilibration always exceeds that of thermal equilibration. Furthermore, we find that thermal diffusion driven by a lepton fraction difference and lepton diffusion driven by an entropy difference are both nonzero and that the first of these tends to be large in magnitude. An important consequence of this is the presence of a doubly diffusive instability, which we refer to as ``lepto-entropy fingers,'' in an extensive region below the neutrinosphere where the lepton number, $Y_{\ell}$, is small. This instability is driven by a mechanism very different from that giving rise to neutron fingers, and may play an important role in enhancing the neutrino emission. Deep in the core where the entropy is low and the lepton number higher, our analysis indicates a region unstable to another instability which we refer to as ``lepto-entropy semiconvection.'' These instabilities, particularly lepto-entropy fingers, may have already been seen in some multi-dimensional core collapse simulations described in the literature.

Motivation & Objective

• To resolve the long-standing controversy over whether neutron finger instabilities occur below the neutrinosphere in core-collapse supernovae.
• To assess the role of fluid instabilities in enhancing neutrino emission via convective-like motions in proto-supernovae.
• To develop and apply a refined methodology for analyzing doubly diffusive instabilities using detailed neutrino transport simulations.
• To determine the relative rates of thermal and lepton equilibration in dense stellar cores and their impact on instability growth.
• To identify and characterize new instabilities—lepto-entropy fingers and semiconvection—arising from cross-response functions in neutrino-mediated transport.

Proposed method

• Develops a linear stability analysis framework incorporating neutrino-mediated thermal and lepton transport via four response functions derived from detailed neutrino transport simulations.
• Uses both traditional and improved neutrino physics to compute response functions for a two-dimensional grid of core radii and fluid element sizes across multiple post-bounce time slices.
• Applies the response functions to evaluate buoyancy forces and instability growth rates in the presence of gravitational fields and multi-flavor neutrino interactions.
• Compares results against the Livermore group’s neutron finger criteria, which assume thermal equilibration dominates over lepton equilibration.
• Identifies the dominance of cross-response functions—entropy-driven lepton flux and lepton-driven energy flux—as central to the emergence of new instabilities.
• Performs a systematic survey of instability regions across multiple supernova progenitor models using both the Livermore and Lattimer-Swesty equations of state.

Experimental results

Research questions

• RQ1 Does the neutron finger instability, as proposed by the Livermore group, actually occur in proto-supernovae due to rapid thermal equilibration relative to lepton equilibration?
• RQ2 What is the relative rate of neutrino-mediated thermal versus lepton equilibration in the core below the neutrinosphere?
• RQ3 How do cross-coupling response functions between entropy and lepton fraction perturbations influence fluid stability?
• RQ4 What new doubly diffusive instabilities emerge when lepton equilibration exceeds thermal equilibration?
• RQ5 Can lepto-entropy fingers or semiconvection be identified in existing multi-dimensional core-collapse simulations?

Key findings

• Lepton equilibration proceeds significantly faster than thermal equilibration in the core below the neutrinosphere, contradicting the assumption of the Livermore group’s neutron finger model.
• The neutron finger instability does not occur because the required condition of slow lepton equilibration is not met in realistic core-collapse conditions.
• The cross-response function for entropy-driven lepton flux is the largest in magnitude, indicating that entropy differences primarily drive lepton redistribution.
• Lepto-entropy fingers emerge in regions of low lepton fraction and positive entropy gradient, with maximum growth rates at scales ~1/20 the distance from the core center.
• Lepto-entropy semiconvection is identified in unshocked, high-lepton-fraction regions below the Ledoux-unstable zone, favoring small-scale instabilities.
• The presence of lepto-entropy fingers may already be observed in some multi-dimensional core-collapse simulations, suggesting their relevance to the supernova explosion mechanism.