Generalized statistics and solar neutrinos

Abstract

In this paper we will show that, because of the long-range microscopic memory of the random force, acting in the solar core, mainly on the electrons and the protons than on the light and heavy ions (or, equally, because of anomalous diffusion of solar core constituents of light mass and of normal diffusion of heavy ions), the equilibrium statistical distribution that these particles must obey, is that of generalized Boltzmann-Gibbs statistics (or the Tsallis non-extensive statistics), the distribution differing very slightly from the usual Maxwellian distribution. Due to the high-energy depleted tail of the distribution, the nuclear rates are reduced and, using earlier results on the standard solar model neutrino fluxes, calculated by Clayton and collaborators, we can evaluate fluxes in good agreement with the experimental data. While proton distribution is only very slightly different from Maxwellian there is a little more difference with electron distribution. We can define one central electron temperature as a few percent higher than the ion central temperature nearly equal to the standard solar model temperature. The difference is related to the different reductions with respect to the standard solar model values needed for B and CN O neutrinos and for Be neutrinos.PACS number(s): 73.40.Hm, 71.30.+h, 96.60.K

Nonextensive distribution and factorization of the joint probability

“…So in the definition of the total system entropy S q = f [p(E i ), q], p(E i ) must be the probability of a microstate of the system and E i can not be replaced by one-body energy e ij . However, in the literature, we find applications of Tsallis' distribution in which E i is systematically replaced by e ij without explanation [6][7][8][9][10][11]. The first examples [6,8] are related to the polytropic model of galaxies and the authors have taken the one-body energy of stars and of solar neutrinos (ǫ = Ψ + v 2 2 ) as E i .…”

“…However, in the literature, we find applications of Tsallis' distribution in which E i is systematically replaced by e ij without explanation [6][7][8][9][10][11]. The first examples [6,8] are related to the polytropic model of galaxies and the authors have taken the one-body energy of stars and of solar neutrinos (ǫ = Ψ + v 2 2 ) as E i . Other examples are the peculiar velocity of galaxy clusters (e ∼ v 2 ) [11] and the electron plasma turbulence where the electron single site density n(r) was taken as system (electron plasma) distribution function and the total energy was calculated with the one-electron potential φ(r) [7,9].…”

Obliquely propagating electron acoustic solitons in magnetized plasmas with nonextensive electrons

“…Nonextensive statistics was successfully applied to a number of astrophysical and cosmological scenarios. Those include stellar polytropes (Plastino and Plastino, 1993), the solar neutrino problem (Kaniadakis et al, 1996), peculiar velocity distributions of galaxies (Lavagno et al, 1998) and systems with long-range interactions and also fractal-like space-times. Cosmological implications were discussed in Torres et al (1997), and plasma oscillations in a collisionless thermal plasmas (which has been recently analysed) were provided from q statistics (Lima et al, 2000).…”

Comparison of Standard Statistical Thermodynamics with Generalized Statistical Thermodynamics Results for Ising Chain

“…On the other hand, this generalization has also been successfully used to overcome the failure of BG statistics in some physical applications such as stellar polytropes [28], the specific heat of the non-ionized hydrogen atom [29], Levy-like anomalous diffusion [30], d = 2 Euler turbulence [31], solar neutrino problem [32] and velocity distribution of galaxy clusters [33].…”