Does the finite size of the proto-neutron star preclude supernova neutrino flavor scintillation due to turbulence?

Abstract

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 and would not form a representative sample of the underlying parent transition probability distributions. 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 δx between the emission points using an isotropic and an anisotropic power spectrum for the random field used to model the turbulence. We find that if we use an isotropic power spectrum for the random field, the correlation of the high (H) density resonance mixing channel transition probability is significant, greater than 0.5, for emission separations of δx = 10 km, typical of proto neutron star radii, only when the turbulence amplitude is less than C⋆ ∼ 10%; at larger amplitudes the correlation in this channel drops close to zero for this same separation of δx = 10 km. In contrast, there is significant correlation in the low (L) density resonant and non-resonant channels even for turbulence amplitudes as high as 50%. Switching to anisotropic spectra requires the introduction of an 'isotropy' parameter kI whose inverse defines the scale below which the field is isotropic. We find the correlation of all transition probabilities, especially the H resonance channel, strongly depends upon the choice of kI relative to the long wavelength radial cutoff k⋆. The spectral features in the H 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 L and non resonant mixing channels may persist, the exact amount depending upon the degree of anisotropy of the turbulence.

Turbulence patterns and neutrino flavor transitions in high-resolution supernova models

“…Finally, it should be noted that, since the neutrinosphere source has a finite size, the neutrinos emitted from different points propagate through somewhat different (but correlated) density profiles. In this context, it might also JCAP11(2014)030 be interesting to study the correlation of the transition probabilities along relatively close trajectories, as proposed in [56].…”

SNEWPY: A Data Pipeline from Supernova Simulations to Neutrino Signals

“…of 1/ √ 3. This case is relevant when there are large amounts of turbulence in the vicinity of the H resonance no matter the mass ordering-see Kneller & Mauney (2013). With this structure for the S m and Sm matrices we obtain…”

“…The TwoFlavorDecoherence transformation is relevant when there is 10% amount of turbulence in the vicinity of the H resonance-see Kneller (2010); Kneller & Mauney (2013). This prescription models 50% mixing between the matter states which participate in the H resonance.…”

What can be learned from a future supernova neutrino detection?

“…But perhaps an even more significant effect from the asphericity of the explosion is the turbulence generated in the fluid. Turbulence is known to affect neutrino evolution [250,259,260,261,262,263,264,257,265,266,267,268]. In order to study the turbulence effects upon the neutrinos the ideal would be to take density profiles from multi-dimensional simulations of supernovae, construct the charged-current potential V CC from them, insert the potential into the Schrödinger equation, and solve it.…”