Analytical results connecting stellar structure parameters and extended reaction rates

TL;DR

This paper derives analytical expressions linking stellar structure parameters with extended thermonuclear reaction rates using a generalized energy distribution, impacting models of stellar luminosity and neutrino emission.

Contribution

It introduces a new extended reaction rate model based on the pathway distribution, generalizing the Maxwell-Boltzmann distribution for stellar nuclear reactions.

Findings

Derived closed-form expressions for extended reaction rates.

Compared standard and extended thermonuclear functions graphically.

Analyzed the behavior of the new energy distribution.

Abstract

Possible modification in the velocity distribution in the non-resonant reaction rates leads to an extended reaction rate probability integral. The closed form representation for these thermonuclear functions are used to obtain the stellar luminosity and neutrino emission rates. The composite parameter {C} that determines the standard nuclear reaction rate through the Maxwell-Boltzmann energy distribution is extended to {C}^* by the extended reaction rates through a more general distribution than the Maxwell-Boltzmann distribution. The new distribution is obtained by the pathway model introduced by Mathai in 2005 [Linear Algebra and Its Applications, 396, 317-328]. Simple analytic models considered by various authors are utilized for evaluating stellar luminosity and neutrino emission rates and are obtained in generalized special functions such as Meijer's G-function and Fox's H-function. The standard and extended non-resonant thermonuclear functions are compared by plotting them. Behavior of the new energy distribution, more general than Maxwell-Boltzmann is also studied.