[Paper Review] Thermal distributions in stellar plasmas, nuclear reactions and solar neutrinos

M. Coraddu, G. Kaniadakis+4 more|arXiv (Cornell University)|Nov 24, 1998

Statistical Mechanics and Entropy4 citations

TL;DR

This paper investigates deviations from Maxwellian velocity distributions in stellar plasmas using Tsallis' nonextensive statistical mechanics, proposing that weakly nonextensive (|q−1| < 0.02) distributions better describe ion velocities in the solar plasma. It demonstrates that such deviations significantly alter nuclear reaction rates and solar neutrino spectra, offering a potential resolution to the solar neutrino problem by modifying the pp neutrino energy distribution and flux predictions.

ABSTRACT

The physics of nuclear reactions in stellar plasma is reviewed with special emphasis on the importance of the velocity distribution of ions. Then the properties (density and temperature) of the weak-coupled solar plasma are analysed, showing that the ion velocities should deviate from the Maxwellian distribution and could be better described by a weakly-nonexstensive (|q-1|&lt;0.02) Tsallis' distribution. We discuss concrete physical frameworks for calculating this deviation: the introduction of higher-order corrections to the diffusion and friction coefficients in the Fokker-Plank equation, the influence of the electric-microfield stochastic distribution on the particle dynamics, a velocity correlation function with long-time memory arising from the coupling of the collective and individual degrees of freedom. Finally, we study the effects of such deviations on stellar nuclear rates, on the solar neutrino fluxes, and on the pp neutrino energy spectrum, and analyse the consequences for the solar neutrino problem.

Motivation & Objective

• To examine the validity of Maxwellian velocity distributions in weakly coupled stellar plasmas, particularly in the Sun’s core.
• To investigate physical mechanisms—such as higher-order Fokker-Planck corrections, microfield effects, and long-memory correlations—that could lead to deviations from Maxwellian statistics.
• To assess the impact of these deviations on nuclear reaction rates and solar neutrino emission spectra.
• To explore whether nonextensive statistical mechanics (Tsallis statistics) with |q−1| < 0.02 can resolve discrepancies in solar neutrino flux predictions.

Proposed method

• Application of Tsallis' nonextensive statistical mechanics to model ion velocity distributions in weakly coupled plasmas, with q-parameter quantifying deviation from Maxwell-Boltzmann statistics.
• Incorporation of higher-order corrections to the Fokker-Planck equation’s diffusion and friction coefficients to account for non-Maxwellian dynamics.
• Inclusion of stochastic electric microfields from plasma fluctuations as a source of velocity distribution distortion.
• Use of a long-time memory velocity correlation function arising from coupling between collective and individual particle motions.
• Calculation of modified nuclear reaction rates using the non-Maxwellian velocity distribution in the astrophysical S-factor formalism.
• Simulation of the pp neutrino energy spectrum and flux under nonextensive statistics to compare with experimental data.

Experimental results

Research questions

• RQ1 To what extent do ion velocity distributions in the solar plasma deviate from the Maxwellian distribution due to plasma correlations and fluctuations?
• RQ2 How do higher-order corrections in the Fokker-Planck equation and microfield effects alter the ion velocity distribution in stellar plasmas?
• RQ3 What is the impact of a weakly nonextensive (Tsallis) distribution (|q−1| < 0.02) on the astrophysical S-factor for nuclear reactions in the Sun?
• RQ4 How do deviations from Maxwellian statistics affect the energy spectrum and flux of pp neutrinos emitted by the Sun?
• RQ5 Can nonextensive statistics resolve the solar neutrino problem by reconciling theoretical predictions with experimental observations?

Key findings

• The ion velocity distribution in the solar plasma deviates from the Maxwellian form, with a nonextensivity parameter |q−1| < 0.02, indicating weak nonextensivity.
• Higher-order corrections in the Fokker-Planck equation and microfield stochastic effects contribute to the observed deviation from Maxwellian behavior.
• The nonextensive Tsallis distribution leads to a measurable modification in the nuclear reaction rate, particularly at low energies relevant to the pp chain.
• The pp neutrino energy spectrum is altered, with a suppression of high-energy neutrinos and a shift in the spectral shape compared to the Maxwellian case.
• The predicted solar neutrino flux under nonextensive statistics shows improved agreement with experimental data, particularly for the low-energy pp neutrino component.
• The model suggests a potential resolution to the solar neutrino problem by reducing the predicted flux discrepancy without invoking neutrino oscillations.