Neutrino spectrum from the pair-annihilation process in the hot stellar plasma

M. Misiaszek, A. Odrzywołek, and M. Kutschera

Phys. Rev. D 74, 043006 – Published 23 August 2006

Abstract

A new method of calculating the energy spectrum of neutrinos and antineutrinos produced in the electron-positron annihilation processes in hot stellar plasma is presented. Detection of these neutrinos, produced copiously in the presupernova, which is an evolutionary advanced neutrino-cooled star, may serve in the future as a trigger of a precollapse early warning system. Also, observation of neutrinos will probe final stages of thermonuclear burning in the presupernova. The spectra obtained with the new method are compared to Monte Carlo simulations. To achieve high accuracy in the energy range of interest, determined by neutrino detector thresholds, a differential cross section for production of the antineutrino, previously unknown in an explicit form, is calculated as a function of energy in the plasma rest frame. The neutrino spectrum is obtained as a 3-dimensional integral, computed with the use of the Cuhre algorithm of at least 5% accuracy. Formulas for the mean neutrino energy and its dispersion are given as a combination of Fermi-Dirac integrals. Also, useful analytical approximations of the whole spectrum are shown.

Received 18 November 2005

DOI:https://doi.org/10.1103/PhysRevD.74.043006

Authors & Affiliations

M. Misiaszek and A. Odrzywołek

M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland

M. Kutschera

M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland and The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, 152 Radzikowskiego St, 31-342 Cracow, Poland

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Vol. 74, Iss. 4 — 15 August 2006

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Images

Figure 1
Feynmann diagrams leading to the first-order amplitude for $e^{+} e^{-}$ annihilation into neutrinos. Electron neutrinos are produced via both diagrams, while $μ$ and $τ$ neutrinos only by “ $Z^{0}$ decay.”Reuse & Permissions
Figure 2
Spectrum resulting from the Monte Carlo simulation for $10^{6}$ , $10^{7}$ , $10^{8}$ , $10^{9}$ , $10^{10}$ , and $10^{11}$ loop size (symbols) versus spectrum from (37) computed with the aid of the Cuhre algorithm (solid line, relative accuracy 0.05). We can notice decreasing errors of the Monte Carlo simulation near the maximum and increasing number of events in the high-energy tail. Obviously, the Monte Carlo simulation is unable to reach accuracy of Cuhre methods for $E ≫ 5 MeV$ . This figure clearly justifies efforts to compute the spectrum using the appropriate cross section (31) instead of using Monte Carlo simulation based on the knowledge of the annihilation matrix (11). We would like to point out that a three-dimensional integral (37) may also be computed using advanced Monte Carlo adaptive algorithms, giving similar spectra much faster, but they may fail in some cases, cf. Fig. 3. Spectrum computed for typical situation in stellar center during Si burning with $T = 0.319 MeV$ and $μ = 0.85 + m_{e} MeV$ .Reuse & Permissions
Figure 3
Spectrum of the $μ$ and $τ$ antineutrinos, computed from (37) with the use of the Cuhre algorithm implemented in Cuba library [24] used in our PSNS code [23]. Guaranteed relative accuracy is everywhere better than 3%. This figure explains why the Cuhre deterministic algorithm (solid line), in spite of slow convergence, is recommended to compute the neutrino spectrum. Failure of Monte Carlo algorithms (dashed and dotted line) is apparent. However, these failures do not influence energy moments (mean energy and dispersion of the spectrum) significantly leading to errors smaller than those that the Monte Carlo algorithm produces. Detailed knowledge of the spectrum below 0.1 MeV seems also unimportant from an experimental point of view. Temperature and chemical potential values are as in Fig. 2.Reuse & Permissions
Figure 4
On semilog plot differences between neutrino spectra of electron neutrinos (dashed line), electron antineutrinos (solid line), $μ$ ( $τ$ ) neutrinos (dotted line), and $μ$ ( $τ$ ) antineutrinos (dash-dotted line) are clearly visible. All four spectra are normalized to 1. $T$ and $μ$ are the same as in Fig. 2.Reuse & Permissions
Figure 5
Numerically computed points of the neutrino spectrum (symbols) and the fit (lines). Curves represent spectra for $k T = 1$ , 5, 10 MeV. Even in the worst case considered, $k T = 1 MeV$ ( $\circ$ ), fit (54) is particularly good.Reuse & Permissions

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