Nonequilibrium Theory In Solar Nuclear Reaction Systems

The missing solar neutrino puzzle has been an unsolved theory problem nearly for about thirty years, and the research on the core nuclear reaction systems of the Sun is one of vital ways in our quest to understand this celebrated basic problem. According to recent status of investigation on the solar neutrino problem, in this thesis we extend the theory of nonequilibrium system into interior nuclear reaction systems of the Sun to investigate the influence of irreversible processes on the solar interior and the production rates of solar neutrinos.We first apply and extend nonequilibrium dynamics to the interior nuclear reaction systems of stars so as to obtain the dynamical evolution equations suitable for describing stellar interiors being the irreversible processes such as nuclear reaction, diffusion, convection etc and under the influence of inhomogeneous pressure, gravitation and temperature gradient etc. We make the nonequilibrium dynamical investigation, separately, on the stellar CNO cycle, the solar core p-pI chain and the core 3α reactions of a red giant star. We explain in a new point of view the long stability for stars in the main sequence and the helium "flash" instability appearing in a red giant star at the ignition of helium combustion, and show a breaking effect of the gravitation and temperature gradient (g-T) on the stability of stellar nuclear reactions, which in a red giant star is 107 times of the value in the core of the solar star and so might be related immediately to the dynamical instability taking place in stars after the main sequence.We further develop a new dynamical approach to investigate the nonequilibrium dynamical behaviors driven by ~3He of the solar nuclear reaction systems when convective motions disturb the core region, related problem to which was first proposed by Dilke and Gough (1972) and it has been still paid close attention up to now, for concerning the understanding of the solar neutrino problem. We use our new theoretical approach to obtain the instability criterion for the nuclear reaction systems, which relates closely to the gravitational acceleration and temperature gradient in the solar interior. It is showed with calculations in solar model that p-pI nuclear reaction system driven by ~3He is unstable for convection in the layer extending from 0.2R_☉ to 0.4 R_☉, where ~3He player was predicted to become overstable.Because of the remarkable space inhomogeneity of fluctuation in stellar interior, we develop and apply nonequilobrium statistical theory in stellar nuclear reaction-diffusion systems so as to describe space-time correlation in the fluctuation and derive a generalized master equation that includes diffusion processes, convective processes, inhomogeneous pressure, gravitation and temperature gradient etc. We investigate the density fluctuation in stellar p-pI nuclear reaction system. It is showed that there is a series of fluctuation waves inside stars to propagate in space, they present the propagation processes of local distortion of the probability distribution function, the growing and the decaying of waves determine the stability of stellar interior, and g-T effect is an important factor leading to the growingfluctuation waves.When the inhomogeneous pressure drives particles to flow from one region with high pressure to another with low pressure, the pressure effect introduces the spatial correlation of density fluctuation as well. In order to investigate the fluctuation behavior in the nuclear reaction-diffusion system affected by pressure, we extend the phenomenological theory to statistical theory and so obtain a new master equation, which can be used to analyze nonlinear density fluctuation in the above system. It is showed that the pressure can produce oscillations to lead a supercritical time structure, it influences the bifurcation characteristic not only of the mean density waves but also of the high orders of fluctuation waves, and especially near the critical point the phase velocity of fluctuation waves is higher than the speed of sound.Many researchers believed that the discrepancy between predicted and measured solar neutrino fluxes might simply come from our lack of understanding of the solar interior. 3He might destabilize g modes in the Sun so that the core might become unstable to overturning motions and core mixing could reduce the flux of solar neutrinos from that predicted by standard solar models to the observed low level, it has not been convincingly demonstrated, but nor has it been ruled out. We notice the effect of chemical fluctuation on the interior and solar neutrino production, one seemingly very important problem but having been ignored for long, and investigate the fluctuation behavior driven by 3He in the solar core that is disturbed by convective motions. It is showed that there is a series of growing fluctuation waves in the layer extending from 0.2Rs to 0.4R?, and the convective effect changes the spectrum and phase velocity of the original fluctuation waves. These growing fluctuation waves are driven by 3He and excited by the convective disturbance. They are placed in the so-called overstable region and produce such instability as oscillations in the solar core.We deal with oscillations and nonlinear behaviors in the core p-pl nuclear reaction system and their effect on the production rates of solar neutrinos. It is showed that a supercritical time oscillation can be excited in the solar core if a flow field disturbs the p-pl system and the particle number density of 3He oscillates periodically when it is produced and destroyed in the nuclear reactions. We obtain the characteristic oscillation with periodic of 5 min near the peak of energy generating rate for 3He reaction, the solar gravity field in the convection is mainly responsible for driving this instability. The density oscillation for 3He can lead to the oscillation of solar energy production, which may contain tow branch of oscillation with the period of 5 min and 2.5 min separately, so that it makes the changes of the solar core temperature and therefore modify the predicted B and 7Be neutrino fluxes.We investigate the nonlinear bifurcation in the core 3He nuclear reaction-diffusion system. It is showed that the system jumps to a new state of supercritical bifurcation where density of 3He is enhanced. In this state transformation the total amount of 3He is not conserved. This nonlinear effect gives the system an ability to enhance the amount of 3He production and a noticeable property of regulation, alters the original birth competition between p-pl and p-pll + p-pIII chains and thereby suppresses the production rates of both the 8B and 7Be neutrinos, which is mathematically in agreement on the inference byCumming and Haxton (1996). The energy-generating rate of 3He reaction increases due to the nonlinear density enhancement of 3He, in principle allowing a locally extreme heat region with a heightened rate of energy generation. This is corresponding to the guess of Grandpierre (1996).