Analytical Results Connecting Stellar Structure Parameters and Extended Reaction Rates

Abstract

Possible modification in the velocity distribution in the nonresonant reaction rates leads to an extended reaction rate probability integral. The closed form representation for these thermonuclear functions is 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 (2005). 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 nonresonant thermonuclear functions are compared by plotting them. Behaviour of the new energy distribution, which is more general than the Maxwell-Boltzmann, is also studied.