Stability of thermonuclear reaction affected by gravitational force

A reaction-diffusion equation describing thermonuclear reaction system affected by gravitational force and temperature gradient is obtained by using the theory of nonequilibrium thermodynamics. We take CNO cycle as an example to investigate the effects of the gravitional force and temperature gradient on the stability of nuclear reaction inside the star. The stability criterion of the stellar structure has been analysed and some attractive results have also been discussed.     

Closed-form evaluation and approximation considerations of the non-resonant thermonuclear reaction rate

By use of a highly efficient theory of generalized hypergeometric functions, we show that the non-resonant thermonuclear reaction rate can be evaluated in closed form. This new approach is advantageous to operate analytically with reaction rates The numerical computation of the rate may be performed with the aid of associated differential equation, a convergent series expansion for small values of the characteristic parameter and an asymptotic expansion for large values of the characteristic parameter.     

On resonant thermonuclear reaction rate integrals- closed-form evaluation and approximation considerations

The central problem in the theory of stellar nucleosynthesis (and in reaction theory of controlled thermonuclear fusion as well) is the determination of thermonuclear reaction rates. Continuing our preceding paper on closed-form evaluation of nonresonant reaction rate integral (HAUBOLD and JOHN 1978) now we consider a general thermonuclear reaction rate integral involving the full BREIT -WIGNER resonance cross section. Discerning between two cases – energy-independent partial widths and energy-dependent partial width – we evaluate the arising parameter-dependent integrals in closed form by means of MEIJER 's G-functions of one and two variables. At next, by using the BUNJAKOVSKIJ -SCHWARZ inequality we derive global upper bounds for thermonuclear reaction rate integrals with arbitrary admissible values of input parameters. Finally, in case of great values of the characteristic parameter COULOMB barrier energy divided by thermal energy we give an asymptotic representation of the general resonant reaction rate integral.     

On the evaluation of an integral connected with the thermonuclear reaction rate in closed form

The standard expression of the reaction rate for low-energy, nonresonant nuclear reactions in nondegenerate plasma contains a parameter-dependent integral which in all previous calculations with physical or astrophysical background is considered as not capable of being evaluated in a closed form. So one usually resorts to approximation methods concerning large values of the parameter. At first we point out that CONSUL (1964) has given a series representation of the integral which was identified with a MEIJER 's G-function by MATHAI (1971). Next, in view of a physically more exact determination of the reaction rate formula, especially in connection with calculations concerning stellar energy generation, we consider a more general integral containing the mentioned one as special case and give an approximation-free representation by means of MEIJER 's G-function. The G-function so obtained may be conceived as complex-valued continuation of CONSUL 's series representation of a certain class of integrals contained in the considered one. From the series we extract a small parameter approximation of the special integral.     

The criterion of appearance of unstable thermonuclear reaction in the helium burning shell of AGB stars

A criterion of the appearance of unstable thermonuclear reaction in the helium burning shell of thermal pulsating AGB (TP-AGB) star is established. The new criterion contains abundant physical information. It involves not only the geometric parameters of the helium burning shell, but also its mechanical, thermal and chemical parameters.The following mechanism of the occurrence and disappearance of unstable thermonuclear reaction in the helium burning shell of TP-AGB star is proposed: The appearance of a region of unstable convection in the helium burning shell of the TP-AGB star triggers unstable thermonuclear reaction which will promote a rapid expansion and a rapid geometric deformation of the shell, thereby removing the unstable thermonuclear reaction.Using the improved program of stellar evolution of Kippenhahn, the evolution of a 5Mo star is followed from the main sequence to the TP-AGB stage. The results show that the new criterion can well reflect the status of the thermonuclear reaction in the helium burning shell of the star. Besides, it is revealed that in the sixth period of thermal pulsation of the star the elements that are dredged up to the surface of the star, are synthesized mainly by thermonuclear reaction under the conditions, temperature lgT₂/K < 8.155 and density 4.0 < lg P2 /9 . CM-3 < 4.6.     

The origin of intergalactic thermonuclear supernovae

The population synthesis method is used to study the possibility of explaining the appreciable fraction of the intergalactic type-Ia supernovae (SN Ia), 20 ₋₁₅ ⁺¹² %, observed in galaxy clusters (Gal-Yam et al. 2003) when close white dwarf binaries merge in the cores of globular clusters. In a typical globular cluster, the number of merging double white dwarfs does not exceed ∼10⁻¹³ per year per average cluster star in the entire evolution time of the cluster, which is a factor of ∼3 higher than that in a Milky-Way-type spiral galaxy. From 5 to 30% of the merging white dwarfs are dynamically expelled from the cluster with barycenter velocities up to 150 km s⁻¹. SN Ia explosions during the mergers of double white dwarfs in dense star clusters may account for ∼1% of the total rate of thermonuclear supernovae in the central parts of galaxy clusters if the baryon mass fraction in such star clusters is ∼0.3%.     

Analytical derivation of the probability for the escape of stars from colliding galaxies

We use the impulse approximation to derive analytical formulae for the escape probability from a simple binary system that interacts with a third body. The binary system is made up of a mass-less body in circular orbit around a massive object, and we assume that the two massive bodies follow a Schuster (or Plummer) distribution. Within the ranges imposed by the impulsive approximation to the parameters of the encounter, we find good agreement between our results and those obtained from numerical experiments.     

The effect of screening factors and thermonuclear reaction rates in the pre-main sequence evolution of low mass stars

In understanding the nucleosynthesis of the elements in stars, one of the most important quantities is the reaction rate and it must be evaluated in terms of the stellar temperature T, and its determination involves the knowledge of the excitation function σ(E) of the specific nuclear reaction leading to the final nucleus. In this paper, the effect of thermonuclear reaction rates to the pre-main sequence evolution of low mass stars having masses 0.7, 0.8, 0.9 and 1M_⊙ are studied by using our modified Stellar Evolutionary Program.     

Generalizations of reaction rate integrals with applications to nuclear synthesis in astrophysics and some corrections to published literature

Under the Maxwell-Boltzmann approach, the study of nuclear reactions in dense astrophysical plasmas under various cases (such as resonant, non-resonant, modified non-resonant, non-resonant under electron screening, and so on) leads to a class of complicated reaction rate integrals. It is shown that this general class of integrals can be identified with an integral involving the product of twoH-functions. This latter integral is evaluated in this article, and following Buschman (1979), several similar results in the published literature are shown to be incorrect.     

Burning regimes for thermonuclear supernovae and cosmological applications of SNe Ia

The method of multigroup radiation hydrodynamics is used to compute light curves for thermonuclear supernovae. Opacities are computed by taking into account spectral lines and expansion. UBVI fluxes are predicted. Our computed times of brightness rise to a maximum in B and V have been found to agree with observations better than those of other authors. The validity of our results is justified physically. The nuclear burning regime is shown to affect significantly the slope of the light curve in B and, to a slightly lesser extent, in V. If the prevailing burning regime during supernova explosions changed with age of the Universe, then the conclusion about a positive cosmological constant Λ drawn from observations of Type Ia supernovae may prove to be wrong.     

Analytical study of a four-body configuration in exoplanet scenarios

Lately, more and more exoplanets are being discovered and the number is expected to increase thanks to the excellent programs dedicated to this task. Thus it is important to study the dynamical behavior of planetary systems. Among all the problems that may be considered, we are interested in four-body planetary systems. In this article, we first examine the possible cases in four-body planetary systems including satellites, in both single and multiple stars. Step decomposition is a methodology explained by A. Abad and J.A. Docobo to deal with n-body problems with hierarchy. The use of this technique permits the reduction of the different cases to five configurations. The analytical integration of one of these cases, a double star with a planet and a satellite orbiting one of the components of the stellar system, is the objective. First the Hamiltonian of the problem is given and then we formulate it in terms of three small parameters which can be reduced to two in this case. After that, using Hori’s biparametric method, the dependence on the angular variables is removed, thereby allowing the integration of the problem.     

The coincidence of friedmann integrals

The expansion of a two-component Universe with an arbitrary spatial curvature is considered. It is shown that the Friedmann integrals of an almost flat Universe do not coincide.     

Pulsation regime of the thermonuclear explosion of a star's dense carbon core

The hydrodynamical problem of nuclear explosion of a dense carbon core of a star with mass 1.40M _⊙ is solved numerically. In calculation the kinetics of carbon burning at the nuclear reaction C¹²+C¹²→M²⁴+γ rate is included. Thus the inverse effect of hydrodynamical motion on the process of thermonuclear burning is taken into account, as compared with Bruenn's (1972) calculations. The calculations show that a pulsation regime of burning is realized (actually three pulses were obtained) which evolves to the detonation regime with full combustion and disruption of the star only at the third pulse. The effects of disintegration of iron group nuclei, neutronization of matter and neutrino losses in URCA processes have not yet been considered in calculations. The influence of initial conditions (mainly the temperature distributions) and the above mentioned effects, which have not been included in calculation, on the results of the hydrodynamical problem solution are discussed. The conclusion is made on new possibilities of formation of a gravitationally bound remnant of the explosion and a neutron star.     

Analytical study of the Earth's shadowing effects on satellite orbits

In this paper a new mathematical model is proposed for the study of the effects of the direct solar radiation pressure on the orbit of an artificial Earth satellite. The equations for the first order effects become canonical when a different definition for the orders of magnitude is adopted. This enables us the utilization of the method of Von Zeipel to eliminate all periodic terms. The model leads to the non-existence of pure secular perturbations owing to the direct solar radiation pressure on the metric elements: semi-major axis, eccentricity and inclination. Numerical examples built with an approximation for the shadow function show that the secular inequalities on the angle variables—longitude, perigee and node—are very small.     

Analytical study of the swing-by maneuver in an elliptical system

The objective of the present paper is to derive a set of analytical equations that describe a swing-by maneuver realized in a system of primaries that are in elliptical orbits. The goal is to calculate the variations of energy, velocity and angular momentum as a function of the usual basic parameters that describe the swing-by maneuver, as done before for the case of circular orbits. In elliptical orbits the velocity of the secondary body is no longer constant, as in the circular case, but it varies with the position of the secondary body in its orbit. As a consequence, the variations of energy, velocity and angular momentum become functions of the magnitude and the angle between the velocity vector of the secondary body and the line connecting the primaries. The “patched-conics” approach is used to obtain these equations. The configurations that result in maximum gains and losses of energy for the spacecraft are shown next, and a comparison between the results obtained using the analytical equations and numerical simulations are made to validate the method developed here.     

Tritium chain of the hydrogen cycle of thermonuclear reactions in the solar interior

The tritium chain of the hydrogen cycle on the Sun including the reactions ³He(e⁻, ν _e) ³H(p, γ)⁴He is considered. The flux of tritium neutrinos at a distance of 1 AU is 8.1 × 10⁴ cm⁻² s⁻¹. It exceeds the neutrino flux from the (hep)-reaction by one order of magnitude. The radial distribution of the yield of ³H neutrinos inside the Sun and their energy spectrum, which has the form of a line at an energy of 2.5–3.0 keV, have also been calculated. The flux of thermal tritium neutrinos is accompanied by a very weak flux of antineutrinos (∼10³ cm⁻² yr⁻¹) with an energy below 18.6 keV. These antineutrinos are produced in the URCA processes ³He ⇆ ³H.     

Detection of the first thermonuclear X-ray burst from AX J1754.2-2754

When analyzing the archival data of the INTEGRAL observatory, we detected an intense X-ray burst recorded on April 16, 2005, by the JEM-X and IBIS/ISGRI telescopes from the weak and poorly studied source AX J1754.2-2754. Analysis of its time profiles and spectra allows this event to be attributed to type I X-ray bursts associated with thermonuclear explosions on the surfaces of neutron stars and the source itself to X-ray bursters. Peculiarities of the X-ray emission observed at the initial evolutionary phase of the burst point to a dramatic expansion and a corresponding cooling of the neutron star photosphere that took place at this time under the action of radiation pressure. Assuming the luminosity of the source at this phase to be the Eddington one, we have estimated the distance to the burst to be d = 6.6 ± 0.3 kpc (for a hydrogen atmosphere of the neutron star) and d = 9.2 ± 0.4 kpc (for a helium atmosphere).     

Existence of formal integrals of symplectic integrators

A recurrent method of solving the formal integrals of symplectic integrators is given. The special examples show that there are no long-term variations in all integrals of the Hamiltonian system in addition to the energy one when symplectic integrators are used in the numerical studies of the system. As an application of the formal integrals, the relation between them and the linear stability of symplectic integrators is discussed.     

Analytical and numerical study of the ground-track resonances of Dawn orbiting Vesta

The aim of Dawn mission is the acquisition of data from orbits around two bodies (4) Vesta and (1) Ceres, the two most massive asteroids.Due to the low thrust propulsion, Dawn will slowly cross and transit through ground-track resonances, where the perturbations on Dawn orbit may be significant. In this context, to safety go the Dawn mission from the approach orbit to the lowest science orbit, it is essential to know the properties of the crossed resonances.This paper analytically investigates the properties of the major ground-track resonances (1:1, 1:2, 2:3 and 3:2) appearing for Vesta orbiters: location of the equilibria, aperture of the resonances and period at the stable equilibria. We develop a general method using an averaged Hamiltonian formulation with a spherical harmonic approximation of the gravity field. If the values of the gravity field coefficient change, our method stays correct and applicable. We also discuss the effect of one uncertainty on the C₂₀ and C₂₂ coefficients on the properties of the 1:1 resonance. These results are checked by numerical tests. We determine that the increase of the eccentricity appearing in the 2:3 resonance is due to the C₂₂ and S₂₂ coefficients.Our method can be easily adapted to missions similar to Dawn because, contrarily to the numerical results, the analytical formalism stays the same and is valid for a wide range of physical parameters of the asteroid (namely the shape and the mass) as well as for different spacecraft orbits.Finally we numerically study the probability of the capture in resonance 1:1. Our paper reproduces, explains and supplements the results of Tricarico and Sykes (2010).