Re-examination of constraints on the Maxwell-Boltzmann distribution by Helioseismology

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 (MBD). Strong constraints on such deviations were made previously with the detailed helioseismic information of the solar structure. With a small deviation parameterized with a factor exp[-δ (E/kT)²], it was shown δ restricted between -0.005 and +0.002. These constraints have been carefully re-examined in the present work. We find that a normalization factor was missed in the previous modified MBD. In this work, the normalization factor c is calculated as a function of δ. It shows the factor c is almost unity within the range 0< δ ≤0.002, which supports the previous conclusion. However, it demonstrates that δ cannot take a negative value from the normalization point of view. As a result, a stronger constraint on δ is defined as 0≤ δ ≤0.002. The astrophysical implication on the solar neutrino fluxes is simply discussed based on a positive δ value of 0.003. The reduction of the ⁷Be and ⁸B neutrino fluxes expected from the modified MBD can possibly shed alternative light on the solar neutrino problem. In addition, the resonant reaction rates for the ¹⁴N(p, γ)¹⁵O reaction are calculated with a standard MBD and a modified MBD, respectively. It shows that the rates are quite sensitive even to a very small δ. This work demonstrates the importance and necessity of experimental verification or testing of the well-known MBD at high temperatures.