Reexamination of constrains on the Maxwell-Boltzmann distribution by Helioseismology

TL;DR

This paper reexamines constraints on deviations from the Maxwell-Boltzmann distribution in stellar nuclear reactions using helioseismic data, finding a narrower allowed deviation range and emphasizing the importance of experimental verification.

Contribution

It corrects previous analyses by including a normalization factor, tightening constraints on deviations from the Maxwell-Boltzmann distribution in stellar environments.

Findings

Normalized factor c is near unity for 0<δ≤0.002

δ cannot be negative based on normalization

Modified δ affects solar neutrino fluxes and reaction rates

Abstract

Nuclear reactions in stars occur between nuclei in the high-energy tail of the energy distribution and are sensitive to possible deviations from the standard equilibrium thermal-energy distribution, the well-known Maxwell-Boltzmann Distribution (\textsf{MBD}). In a previous paper published in Physics Letters 441B(1998)291, Degl'Innocenti {\it et al}. made strong constrains on such deviations with the detailed helioseismic information of the solar structure. With a small deviation parameterized with a factor exp$[{-\delta (E/kT)^2}]$, it was shown $\delta$ restricted between -0.005 and +0.002. These constrains have been carefully reexamined in the present work. We find that a normalization factor was missed in the previous modified \textsf{MBD}. In this work, the normalization factor $c$ is calculated as a function of $\delta$. It shows the factor $c$ is almost unity within the range 0$< \delta \leq$0.002, which supports the previous conclusion. However, it demonstrates that $\delta$ cannot take a negative value from the normalization point of view. As a result, a stronger constraint on $\delta$ is defined as 0$\leq \delta \leq$0.002. The astrophysical implication on the solar neutrino fluxes is simply discussed based on a positive $\delta$ value of 0.003. The reduction of the $^7$Be and $^8$B neutrino fluxes expected from the modified \textsf{MBD} can possibly shed alternative light on the solar neutrino problem. In addition, the resonant reaction rates for the $^{14}$N($p$,$\gamma$)$^{15}$O reaction are calculated with a standard \textsf{MBD} and a modified \textsf{MBD}, respectively. It shows that the rates are quite sensitive even to a very small $\delta$. This work demonstrates the importance and necessity of experimental verification or test of the well-known \textsf{MBD} at high temperatures.