The URCA process in convective cores

A Monte Carlo simulation has been carried out for URCA processes in a degenerate convective stellar core, such as would be obtained following degenerate carbon ignition. We find energy loss rates substantially less than obtained by Paczynski in his vibrational approximation for this process. We conclude that the loss rates should be computed by direct integration over the convective core assuming a uniform ratio of the abundances of the URCA pair.     

The URCA process at high temperatures and densities

The URCA neutrino loss rate from a hot stellar environment is investigated. The results indicate that the loss rates for URCA type processes from even mass number nuclei are comparable to the rates from odd mass number nuclei at temperatures above about 10⁹ K. Rates are calculated for some typical odd mass isobar pairs and for the even mass isobar fifty-six for temperatures between 5×10⁸ K to 5×10¹⁰ K.Supported in part by National Science Foundation Grant GP13959.     

The ordinary URCA process in the presence of positrons and large magnetic fields

The effect of positron capture on the ordinary URCA neutrino luminosity in a zero magnetic field is investigated for several values of the degeneracy parameter and the range of temperatures 5×10⁸K–5×10¹⁰K. The rate for this process is then compared with those in large magnetic fields (on the order ofH _c =m ² c ³/eh=4.414×10¹⁰ G). The results indicate that positron capture reduces the effect of large magnetic fields on this process at high temperatures.     

Neutrino luminosity by the ordinary URCA process in an intense magnetic field

The neutrino luminosity by the ordinary URCA process in a strongly magnetized electron gas is computed. General formulae are presented for the URCA energy loss rates for an arbitrary degree of degeneracy. Analytic expressions are derived for a completely degenerate, relativistic electron plasma in the special case of neutron-proton conversion. Numerical results are given for more general cases.The main results are as follows: the URCA energy loss rates are drastically reduced for the regime of great degeneracy by a factor up to 10^–3 for 1, andT ₉10, where =H/H _q ,H _q =m ² c ³/eh=4.414×10¹³ G. In the non-degenerate regime the neutrino luminosity is enhanced approximately linearly with for the temperature range 1T ₉10. Possible applications to white dwarfs and neutron stars are briefly discussed.We have been recently informed that in Gamow home-dialect (Odessa dialect) URCA means thief — (Private communication from Prof. G. Wataghin).     

On convection in the sun

Convective motions driven by a superadiabatic temperature gradient in a viscous thermally conductive medium are considered. Approximate linearized equations governing the perturbation are derived under the following conditions: (i) The ratio of the excess temperature gradient over the adiabatic gradient is small compared with the gradient itself, (ii) The perturbation is of low-frequency type, (iii) The rotation is slow. Only the convective mode is described by these equations (as in the Boussinesq approximation), and the equations are valid for compressible configurations with any ratio between the scale heights of the equilibrium and perturbed quantities. Results of a numerical calculation of unstable perturbations for configurations with a large density stratification are given. They show that under conditions appropriate for the solar convection zone an extremely strong instability is expected to occur if the mixing length is assumed to be equal to 1.5 times the pressure scale height. The horizontal scale of the instability is intermediate between those of granulation and supergranulation. The larger the mixing length, the smaller the growth rate of the instability, and the larger its horizontal scale. Therefore it seems possible to adjust the mixing length to obtain the characteristics corresponding to those of the solar supergranulation. The possible origin of the granulation as an instability in a subsurface zone, where a local increase in the density scale height takes place, is also discussed. To achieve agreement with observations, it seems necessary to assume that the ratio of the mixing length to pressure scale height is an increasing function of the pressure.     

On the interaction between differential rotation and magnetic fields in the Sun

We have performed 3-D numerical simulations of compressible convection under the influence of rotation and magnetic fields in spherical shells. They aim at understanding the subtle coupling between convection, rotation and magnetic fields in the solar convection zone. We show that as the magnetic Reynolds number is increased in the simulations, the magnetic energy saturates via nonlinear dynamo action, to a value smaller but comparable to the kinetic energy contained in the shell, leading to increasingly strong Maxwell stresses that tend to weaken the differential rotation driven by the convection. These simulations also indicate that the mean toroidal and poloidal magnetic fields are small compared to their fluctuating counterparts, most of the magnetic energy being contained in the non-axisymmetric fields. The intermittent nature of the magnetic fields generated by such a turbulent convective dynamo confirms that in the Sun the large-scale ordered dynamo responsible for the 22-year cycle of activity can hardly be located in the solar convective envelope.     

On large-scale solar convection

We examine the effects of rotation about a vertical axis on thermal convection with a simple model in which an inviscid, incompressible fluid of zero thermal conductivity and electrical resistivity is contained in a thin annulus of rectangular cross-section. The initial steady state assumed is one of no motion relative to the rotating frame with constant (unstable) vertical temperature gradient and uniform toroidal magnetic field. Small periodic disturbances are then introduced and the linearized perturbation equations solved. We also determine the second-order mean circulations and magnetic fields that are forced by non-zero Reynolds and thermal stresses and magnetic field transports.The solutions have several properties which are relevant to large-scale solar phenomena if giant long-lived convection cells exist on the sun. In particular, the convective cells are tilted in latitude in the same sense as bipolar magnetic regions, and induce vertical magnetic fields with the same tilt. They transport momentum across latitude circles through Reynolds stresses and induced meridional circulations thus setting up a differential rotation. Cells which grow slowly compared to the rotation rate and have comparable dimensions in latitude and longitude transport momentum toward the equator. The cells also form a poloidal magnetic field from initial toroidal field, in a manner similar to that put forth by Parker.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On efficiency of convection of Öpik's cellular convection theory

The physical meaning of the convection efficiency parameter of Öpik's theory is clarified by relating it to that of the mixing-length theory. A compact comparison of both theories is presented to explain the earlier findings of Gough and Weiss (1976), that Öpik's theory becomes indistinguishable from the mixing-length theory when the value of Öpik's cell depth is taken as being equal to 2.44 times the local pressure scale height for the solar convective envelope.     

On the initial phase of interaction between expanding stellar envelopes and surrounding medium

The initial stages of deceleration in the circumstellar medium of a stellar envelope, thrown off by a shock wave, are investigated. The equations of spherical-symmetric adiabatic hydrodynamics are shown to have a similarity solution in the case of the density of the expanding envelope being approximated by a reasonable power law. The overall flow pattern has such a form that the stellar material is decelerated in the internal shock wave while another shock propagates through the circumstellar matter. Between the shocks there is a contact discontinuity separating the circumstellar and stellar matter. The characteristics of the similarity solution are calculated for various exponents in the density laws of an expanding envelope and circumstellar matter and for two values of the adiabatic index (=5/3, 4/3). Some parts of the flow exhibit Rayleigh-Taylor instability.Special attention is paid to the validity of the hydrodynamics. In full agreement with D'yachenkoet al. (1969), we conclude that the kinetic and collisionless processes are of great importance if the initial stages of stellar envelope deceleration are to be properly monitored.The results obtained can also be employed to describe the interaction between the exploding core of a red giant star and its rarefied envelope. This is of interest for explosive nucleosynthesis.The similarity solution is applied to the envelopes expelled both by type-II supernovae and by rapid novae. In particular, the thermalization time-scale of circumstellar plasma is estimated. For SNii this time-scale proves to be of the order of 60 yr. This confirms with the observational data on the moment of the maximum radio-emission of young SNRs. In the case of rapid novae, this time is less by a factor of 10. Therefore, the peak radio and X-ray (2 keV) lumnosity may occur several years after the rapid nova outburst. The explosion of a degenerate carbon core is found to result in the heating of the hydrogen-helium envelope of a red giant star up to 3×10⁶ K.     

On the interaction between a strong stellar wind and a surrounding disk nebula

The interaction between a strong stellar wind carrying no intrinsic angular momentum and a surrounding disk nebula is investigated. We analyze the shape and stability of the wind-nebula interface, the strength and direction of the ensuing mass motions and the time scales for nebular disruption. The resultant time scale is given by Equation (44). The dominant physical process is one of nebular accretion onto the central star due to turbulent viscosity in the disk. The turbulence will be driven in the upper layers of the disk by the wind. We note that if the accretion supplies mass for the wind (after the absorption of stellar energy), then the particle fluxes may undergo a runaway increase until the energy or momentum flux in the wind is limited by the total stellar luminosity. This may explain the origin of strong, pre-Main-Sequence winds.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

On the nonradiative magnetized accretion flows with convection

In this paper, we explore the radial structure of radiatively inefficient accretion flows (RIAFs) in the presence of an ordered magnetic field and convection. We assume the magnetic field has the toroidal and vertical components. We apply the influences of convection on equations of angular momentum and energy. The convective instability can transport the angular momentum inward or outward. We establish two cases for consideration of the effects of convection parameter on magnetized RIAFs. In the first case, we assume the convection parameter as a free parameter and in the other case we calculate convection parameter through use of mixing length theory. In both cases, the solutions show that a magnetized RIAF is very sensitive to the convection parameter and transport direction of angular momentum due to convection. Moreover, we show that the convection strength strongly depends on magnetic field and viscosity.     

On the cooling of the moon by solid convection

If a molten, or partially molten, lunar core exists at present, constraints would be placed on the viscosity of the solid mantle and the distribution of radioactive heat sources. Models in which the heat sources have been concentrated near the surface would rapidly solidify if the effective viscosity was equal to, or less than, 10²² cm² s⁻¹. Retention of most of the heat sources throughout the mantle would permit present day solid convection to occur without cooling the core.     

On the stability of mean-field models of the solar convection zone

The stability of the solutions of the mean-field theories of turbulent media is questioned. It is done here for the model equations for the solar convection zone which have been used, in particular, to explain the differential rotation. We present an approximation valid for axisymmetric, short-wave disturbances. A critical local Rayleigh number can be defined - involving eddy diffusivities - above which the stratification becomes unstable. For mixing-length models of the solar convection zone we always find sub-critical Rayleigh numbers. One must be careful, however, with other theoretical models. Those we have considered do not reach sufficiently high surface pressure values so that there the associated Rayleigh numbers exceed their critical limits. In the outermost layers in such models, therefore, the solutions could really be unstable.     

Nonlinear coupling between pulsation and convection in late type stars

A simple idealized nonlinear model applicable to long period variable stars has been formulated that assumes the convective envelope ofM giants is composed of giant convection cells, which are comparable in size to the stellar radius. The simplicity of this model essentially constitutes a physical analog to the strong dynamic coupling that occurs if the convective envelope of the star undergoes both modes of motion. As shown implicitly in the time scales associated with these motions, the coupling produces asymmetrical fluctuations of the entire star, the mean velocity of which is comparable to the escape velocity of the star at particular values of the ratio of the pulsation and convection time scales. It is suggested that this can account for the mass loss from late type stars, and the circumstellar dust shells that are associated extensively with long period variables.For critical values of the pulsation and convection time scales, the solutions correspond to the rapid expansion of the entire convective envelope, and is the basis of a new mechanism that simulates the manner in which pulsating stars ballistically accelerate their convective shells to form planetary nebulae.     

The effect of convection on the process of carbon burning in a degenerate core

The results of a numerical investigation of the hydrostatic carbon burning in a degenerate carbon core withM=1.4M are presented. Convective heat transfer has been taken into account according to the mixing length formalism. It is shown that for small convection the effective (10^–3) computational results are in agreement with the assumption of a hydrostatic evolution of the core. At 10^–2 the burning times in successive mass zones become less than the hydrodynamic time for the core. In this case carbon burning starts with a rapidly propagating thermal instability. The connection between the convective and neutrino mechanisms of burning propagation is discussed.     

Effects of convection electric field on the thermal plasma flow between the ionosphere and the protonosphere

Dynamic behavior of the coupled ionosphere-protonosphere system in the magnetospheric convection electric field has been theoretically studied for two plasmasphere models. In the first model, it is assumed that the whole plasmasphere is in equilibrium with the underlying ionosphere in a diurnal average sense. The result for this model shows that the plasma flow between the ionosphere and the protonosphere is strongly affected by the convection electric field as a result of changes in the volume of magnetic flux tubes associated with the convective cross-L motion. Since the convection electric field is assumed to be directed from dawn to dusk, magnetic flux tubes expand on the dusk side and contract on the dawn side when rotating around the earth. The expansion of magnetic flux tubes on the dusk side causes the enhancement of the upward H⁺ flow, whereas the contraction on the dawn side causes the enhancement of the downward H⁺ flow. Consequently, the H⁺ density decreases on the dusk side and increases on the dawn side. It is also found that significant latitudinal variations in the ionospheric structures result from the L-dependency of these effects. In particular, the H⁺ density at 1000 km level becomes very low in the region of the plasmasphere bulge on the dusk side. In the second model, it is assumed that the outer portion of the plasmasphere is in the recovery state after depletions during geomagnetically disturbed periods. The result for this model shows that the upward H⁺ flux increases with latitude and consequently the H⁺ density decreases with latitude in the region of the outer plasmasphere. In summary, the present theoretical study provides a basis for comparison between the equatorial plasmapause and the trough features in the topside ionosphere.