Finite size source effects and the correlation of neutrino transition probabilities through supernova turbulence

TL;DR

This paper investigates how the finite size of a supernova neutrino source affects the correlation of neutrino transition probabilities in turbulent supernova environments, revealing that turbulence can obscure spectral features depending on anisotropy.

Contribution

It introduces a model for analyzing the correlation of neutrino transition probabilities considering finite source size and turbulence anisotropy in supernovae.

Findings

High-density resonance features can be obscured by turbulence due to finite source size.

Low-density and non-resonant channels may retain spectral features despite turbulence.

Turbulence anisotropy influences the persistence of spectral features.

Abstract

(Abridged) The transition probabilities describing the evolution of a neutrino with a given energy along some ray through a turbulent supernova are random variates unique to each ray. If the source of the neutrinos were a point then all neutrinos of a given energy and emitted at the same time which were detected in some far off location would have seen the same turbulent profile therefore their transition probabilities would be exactly correlated. But if the source has a finite size then the profiles seen by neutrinos emitted from different points at the source will have seen different turbulence and the correlation of the transition probabilities will be reduced. In this paper we study the correlation of the neutrino transition probabilities through turbulent supernova profiles as a function of the separation between the emission points using an isotropic and an anisotropic power spectrum for the random field used to model the turbulence. The spectral features in the high density resonance mixing channel of the next Galactic supernova neutrino burst may be strongly obscured by large amplitude turbulence when it enters the signal due to the finite size of the source while the presence of features in the low density and non resonant mixing channels may persist, the exact amount depending upon the degree of anisotropy of the turbulence.