Stellar Centre Research Articles

Generating potentials via difference equations

The condition for pressure isotropy, for spherically symmetric gravitational fields with charged and uncharged matter, is reduced to a recurrence equation with variable, rational coefficients. This difference equation is solved in general using mathematical induction leading to an exact solution to the Einstein field equations which extends the isotropic model of John and Maharaj. The metric functions, energy density and pressure are well behaved which suggests that this model could be used to describe a relativistic sphere. The model admits a barotropic equation of state which approximates a polytrope close to the stellar centre.

Variability of the H2O maser associated with U Orionis

H2O line observations at =1 :35 cm of the Mira Ceti-type variable star U Ori are reported. The ob- servations cover the time interval from March, 1980, to September, 1999. Variations of the integral flux and ve- locity centroid of the H2O line are analysed. The flux in general correlates with the visual light curve, following it with some phase delay ' 0:2 0:4P (P is the period of the star). The maser emission is generated in a quasi- stationary layer of gas and dust at a distance of about 10 14 cm from the stellar centre. The maser variability is explained by the action of periodic shocks, driven by stel- lar pulsation and arriving to the maser in each stellar cy- cle. The shocks provide the maser pumping, whereas the sink of the waste energy is controlled by the dust, period- ically heated by the stellar radiation near the light maxi- mum; this accounts for the correlation of the maser radi- ation maximum with the descending branch of the light curve. Temporary weakness of the maser emission may be due to decay of the quasi-stationary layer, which is then rebuilt by a powerful shock, carrying away from the star a portion of the lost mass, once per a few stellar periods { the \superperiod. In its turn, the superperiod may re- flect multiperiodic pulsation of the star or the presence of a long-term activity cycle, connected with restructuring of the stellar magnetic eld, which is known to be strong in U Ori.

Diffusion process produced by random internal waves

The aim of the paper is to present a new transport process which is likely to have great importance for understanding the internal constitution of the stars.In order to set the problem in context, we first give a short presentation of the physical properties of the Sun and stars, described usually under the names Standard Solar Model or Standard Stellar Models (SSM). Next we show that an important shortcoming of SSM is that they do not explain the age dependence of the lithium deficiency of stars of known age: stars of galactic clusters and the Sun. It was suggested a long time ago that the presence of a macroscopic diffusion process in the radiative zone should be assumed, below the surface convective zone of solar-like stars. It is then possible for the lithium present in the convective zone to be carried to the thermonuclear burning level below the convective zone. The first assumption was that differential rotation generates turbulence and therefore that a turbulent diffusion process takes place. However, this model predicts a lithium abundance which is strongly rotation dependent, contrary to the observations. Furthermore, as the diffusion coefficient is large all over the radiative zone, it prevents the possibility of gravitational separation by diffusion and consequently leads to the impossibility of explaining the difference in helium abundance between the surface and the centre of the Sun. The consequence is obviously that we need to take into account another physical process.Stars having a mass M < 1.3M[odot ] have a convective zone which begins close to the stellar surface and extends down to a depth which is an appreciable fraction of the stellar radius. In the convective zone, strong stochastic motions carry, at least partially, heat transfer. These motions do not vanish at the lower boundary and generate internal waves into the radiative zone. These random internal waves are at the origin of a diffusion process which can be considered as responsible for the diffusive transport of lithium down to the lithium burning level. This is certainly not the only physical process responsible for lithium deficiency in main sequence stars, but its properties open the way to a completely consistent analysis of lithium deficiency.The model of generation of gravity waves is based on a model of heat transport in the convective zone by diving plumes. The horizontal component of the turbulent motion at the boundary of the convective zone is assumed to generate the horizontal motion of internal waves. The result is a large horizontal component of the diffusion coefficient, which produces in a short time an horizontally uniform chemical composition. It is known that gravity waves, in the absence of any dissipative process, cannot generate vertical mixing. Therefore, the vertical component of the diffusion coefficient is entirely dependent on radiative damping. It decreases quickly in the radiative zone, but is large enough to be responsible for lithium burning.Owing to the radial dependence of velocity amplitude, the diffusion coefficient increases when approaching the stellar centre. However, very close to the centre, nonlinear dissipative and radiative damping of internal waves become large and the diffusion coefficient vanishes at the very centre.

The inner structure of an accretion disc around a magnetic neutron star

Abstract The effect of a magnetic binary neutron star on the inner structure of its accretion disc is considered. The stellar field penetrates the disc and toroidal field is created as a result of the vertical shearing motions, its magnitude being diffusion limited. If the disc’s magnetic diffusivity, ν. is treated as a function of ω, the distance from the stellar centre, with a radial length scale of ∼ω w, a self-consistent solution can be found for the inner region. In the orbital plane, the magnetic force has a small effect on the radial momentum, so the angular velocity is Keplerian. The vertical equilibrium is a balance between the gradients in azimuthal magnetic pressure and thermal pressure, while the inflow is caused by the transfer of angular momentum from the disc to the star, via magnetic stresses. Vertical equilibrium breaks down as the inflow speed becomes a significant fraction of the Keplerian speed, this occurring in the region of the Alfven radius based on radial free-fall. However, if ν ...

Phenomenological theory of gravitational vacuum

An idea is developed that the vacuum in the gravitational field acquires properties of an elastic medium described by a definite tension τ ik . The vacuum is stated to also participate in the formation of the space-time metric, together with the usual matter. So, the matter, vacuum and metric form a complex unity determined by the solution of the field equations. The vacuum may prove to play an essential role in the extremely strong fields existing in superdense celestial bodies. The tensor τ ik is not to be identified with the pseudo-tensor of the energy-momentum of the gravitational field the idea of which is preserved. The problem of vacuum is investigated in the case of the central symmetry static field. A number of properties of the tensor τ ik is found using the symmetry of the field and comparison with the post-Newton limit. The external and internal problems, as well as the procedure of joining the solutions on the surface of a celestial body, have been formulated. The stellar surface is determined in the usual way:P(r) = 0 whereP is the matter pressure. The theory includes three dimensionless parametersa=p/ɛ,b=p ⊥/ɛ (ɛ,p, p ⊥ are the density of the vacuum energy and of its pressures in the radial and transverse directions) and ω determining the vacuum elastic properties. Generally speaking, they depend on the valueP/ρc2 in the stellar centre where ϱ is the mass density. From general physical considerations it is shown that 0 ≤ ω ≤ 1 + lim P→∞ (l/q). The field equations are solved for the simple version of the theoryb=−a. There are solutions corresponding to superdense celestial bodies with masses considerably exceeding that of the Sun.

Stellar winds and breezes

Steady stellar winds are generally divided into two classes: (i) the winds proper, for which the energy flux per unit solid angle, E ∞ , is non-zero, and (ii) the breezes, for which E oo = 0. The breezes may be distinguished from one another by the value of the ratio, g , of kinetic to thermal energy of the particles in the limit of large distance, r , from the stellar centre, or more precisely by g=lim mv 2 r->∞ — kT ' where v ( r ) is breeze velocity, T ( r ) is temperature, m is mean particle mass, and k is the Boltzmann constant. Solutions have previously been obtained for values of g in the range 0 < g < 1, in which the breezes are subsonic everywhere with respect to the isothermal speed of sound. It is demonstrated here that two distinct solutions exist as g -> 5/3, namely (in an obvious notation) the g = 5/3 — and the g = 5/3 + possibilities. It is shown that, if g > 5/3 ( g < 5/3) the solutions are everywhere supersonic (subsonic) with respect to the adiabatic speed of sound. If 1 < g < 5/3, they possess a critical point, at which the isothermal speed of sound and the flow speed coincide. The winds are examined in the limit E ∞ -> 0, and the relation with the breezes is studied. In particular, it is shown that, for r < 0 ( E ∞ -2/5 ), the winds satisfy the stellar breeze equations to leading order, and possess a critical point at r = 0 (1). For r > 0 ( E ∞ -2/5 ), the solutions do not obey the breeze equations. They ultimately follow the Durney asymptotic law [T = 0 ( r -4/3 ), for r -> ∞] for the winds. This demonstration of how the winds merge continuously into the breezes as E ∞ -> 0 is new. The question of how the particle density ( N 0 ) and temperature ( T 0 ) at the base of the stellar corona determine the type of solution realized outside the star is examined. Even when the flow speed, v 0 , at the base of the corona is subsonic, non-uniqueness can occur. In one domain of the ( N 0 , T 0 ) plane, two distinct types of breeze are possible; in another these, together with a wind (E∞ =f= 0), are permissible. Elsewhere (large N 0 , moderate T 0 ) only a unique breeze exists or (small N 0 and/or T 0 ) a unique wind. In some domains (large T 0 ) no steady solution exists, unless the requirement that the corona is subsonic is relaxed. In this case, however, the problems of non-uniqueness are severely aggravated.