A method of computing the gravitational field of an axially symmetric flat galaxy

A method has been developed for computing the gravitational force field of an axially symmetric flat galaxy from its surface mass density. The method is simple to program, fast, and accurate. An inversion formula is derived that allows computation of surface density from rotation curves by use of any method that converts density to force. The method is compared with a method of Clutton-Brock that utilizes Hankel transforms of Laguerre functions.     

Instability of a gravitating partially-ionized plasma

The effect of Hall currents and collision with neutrals on the instability of a horizontal layer of a self-gravitating partially-ionized plasma of varying density have been studied. It is assumed that the plasma is permeated by a variable horizontal magnetic field stratified vertically. A variational principle is shown to characterize the problem. By making use of the existence of the variational principle, proper solutions have been obtained for a semi-infinite plasma in which density has a one-dimensional (exponential) vertical stratification. The dispersion relation has been derived and solved numerically. It is found that the collisions with neutrals have a stabilizing influence while Hall currents have a destabilizing influence.     

Finite Larmor radius effects on the Rayleigh-Taylor instability of a rotating plasma of variable density

The Rayleigh-Taylor instability in a rotating plasma of variable density has been investigated to include simultaneously the effects of viscosity and the finiteness of the ion Larmor radius. It is shown that, for a plasma in which the density is stratified along the vertical, the solution is characterized by a variational principle. Making use of this, proper solutions have been otained for a semiinfinite plasma in which the density varies exponentially. The dispersion relation has been solved numerically and it is found that the influence of the effects of both FLR and viscosity is stabilizing. The Coriolis forces are found to have a dual role, stabilizing for small wave numbers and destabilizing for large wave numbers. The range of the small wave numbers, over which the Coriolis forces have a stabilizing influence, is found to increase with Coriolis forces.     

The rayleigh-taylor instability of a stratified rotating fluid through a porous medium in a two-dimensional magnetic field

The effect of finite conductivity on the Rayleigh-Taylor instability of an incompressible, viscous rotating fluid through a porous medium has been studied in the presence of a two-dimensional horizontal magnetic field. It has been shown that the solution is characterized by a variational principle. By making use of the existence of the variational principle, proper solutions have been obtained for a semi-infinite fluid in which density has a one-dimensional (exponential) vertical stratification. The dispersion relation has been derived and solved numerically. It is found that finite resistivity and porosity have a destabilizing effect on the Rayleigh-Taylor instability while rotation has a stabilizing effect.     

Finite Larmor radius effects on the stability of a stratified plasma

The hydromagnetic stability of a cosmical plasma interacting with neutral gas has been studied to include the effects of ion viscosity and the finiteness of the ion Larmor radius. It is first shown that the system is characterized by a variational principle. The explicit solution has then been obtained, by making use of the existence of the variational principle, for a semi-infinite plasma in which the density is stratified, exponentially, along the vertical. It is found that FLR, ion viscosity as well as neutral gas friction have all a stabilizing influence.     

Role of nonthermal electrons in the heating of solar atmosphere during flares

Evolution of electron energy distributions have been studied by combining small-angle scattering with analytical treatment of large-angle collision using the Monte-Carlo technique. By use of these, the distributions and energy loss have been calculated as functions of column density, the heating functions have been calculated at different depths of the solar atmosphere. From the heating functions, an increase in temperature produced by the electrons at different column densities has been computed. It is found that rise in temperature increases with an increase in incident electron energy.     

On the behaviour of the hydrogen Lyman series in flares

The Lyman spectrum of hydrogen has been computed for a number of flare models, characterized by the column density of hydrogen atoms in the ground state (N ₁), the electron density (n _e) and the electron temperature (T _e). Broadening by the thermal Doppler effect and by Stark effect has been accounted for. The source functions for the individual lines of the series have been derived from non-LTE calculations of the excitation in hydrogen flares. The aim of the investigation is to evaluate the use of the intensities in between two successive Lyman lines for a determination of the value for N ₁, which is a physical parameter of the flare for which only indirect determinations are available. Whilst in principle this method could give reliable results, its practical application meets with difficulties which hardly can be overcome. Therefore, one probably has to base the N ₁ determination on the highest line resolvable in the spectrum.     

On the role of reverse current on the hard X-ray production in solar flares and time-lags between high- and low-energy photons

The evolution of energy and angular distributions of electrons has been studied accounting for the reverse current effect by combining analytically treated small angle multiple scatterings with large angle Monte-Carlo calculations. Reverse current and potential variations as function of column density have been computed. It is found that the reverse current decreases steeply with increase in electron energy. However, it becomes significant for low-energy electrons. By use of these distributions and bremsstrahlung crosssection, the X-ray energy spectrum has been calculated. The nature of the resulting X-ray spectrum integrated over all column depths is similar to the one without reverse current. The time-lag between high-and low-energy photon production has been calculated. It is found that there is a small difference between time-lags as function of observation angles. This fact can be used to test the validity of the beamed thick target model.     

Propagation of magnetogasdynamic spherical shock waves in an exponential decreasing medium

By use of the approximate method of Whitham (1958) the effect of magnetic field is investigated on a point explosion in a medium exihibiting exponential decrease of density and temperature. It has been found that the shock velocity and shock Mach number first decrease, but after a certain distance they start increasing.     

Statistical model of meteor streams. IV. A study of radio streams from the synoptic year

With the use of the most powerful stream-search technique in existence, we have detected 275 streams in the synoptic-year (December 2, 1968–December 14, 1969) sample of 19 698 radio meteors, most of which were not reported before. About 16% of all meteors in the sample belong to these streams. We have confirmed the existence of two-thirds of the 83 streams detected by us previously in the 1961–65 sample of radio meteors. Some of the new streams have most uncommon orbits. A new, rich stream with a revolution period of about 30yr has been discovered. Streams of low inclination are often detected at both nodes. A computer technique, developed for determining the two parameters of the D-distribution of meteor orbits in a stream, has been applied to the 275 streams. A number of known comet-meteor associations have been confirmed, and a few new possible associations established. The previously detected orbital similarity between the minor planet Adonis and a few radio streams (including a major, broad stream) has been reinforced, but we have so far failed to prove the evolutionary relationship more quantitatively. Several possible associations with other Earth-crossing asteroids, with the meteorite P?íbram, and with a few fireballs are suggested. The mean space density in streams is shown to be much below the sporadic density, but the central density may significantly exceed the sporadic density. The derived absolute stream-density values are in an order-of-magnitude agreement with space densities estimated from the cometary production rates of solid material of a comparable particle size. Plots on a height-velocity diagram of both the individual radio meteors and the radio streams fail to exhibit the discrete-level structure known to exist for photographic meteors.     

On the stability of a class of radiating viscous self-gravitating stars with axial symmetry

This study investigates the stability of a class of radiating viscous self-gravitating stars with axial symmetry having anisotropic pressure. We use perturbation technique to establish the perturbed form of the Einstein field equations and dynamical equations. The instability range in the Newtonian and post-Newtonian eras has been analyzed by constructing the collapse equation. It is found that the adiabatic index has a key role in the discussion of instability ranges which depends upon the physical parameters, i.e., energy density, anisotropic pressure and shear viscosity of the fluid and heat flux. We conclude that the shear viscosity decreases the instability range and makes the system more stable.     

Ion bombardment of interplanetary dust

The recent discovery of ion tracks in interplanetary dust and the increasing evidence for carbon and carburized materials in these objects are strongly suggestive that chemical processing by energetic charged-particle bombardment has occured during the dust lifetimes. The track density gives a measure of the total ion fluence experienced by the grains. We use this information and laboratory data on the modification of icy surfaces by incident ions and electrons to discuss the likelihood that chondritic interplanetary dust particles could have been proceed, by plasma bombardment, from aggregates of particles which had volatile and/or ogranic mantles. Such a processing would leave carbon and carburized deposits and can affect estimates of the temperature of formation of these dust grains.     

Effects of Hall currents and Coriolis forces on the instability of a self-gravitating plasma of variable density

The hydromagnetic instability of a self-gravitating, incompressible rotating plasma of variable density has been examined in the presence of Hall currents. The system is assumed to be permeated by a variable horizontal magnetic field. The solution of the relevant linearized perturbation equations has been obtained by the normal mode technique through a variational principle which is shown to characterize the problem. Proper solutions have been obtained for a semi-infinite plasma having exponential density stratification along the vertical. The dispersion relation has been derived and solved numerically for different values of the physical parameters involved. It is found that Hall currents and Coriolis forces have both destabilizing influence as the growth rate of the unstable modes is found to increase with the increase of both Hall currents and Coriolis forces.     

Hard X-rays from solar flares — time characteristics in correlation with energy and angular distributions of electrons

Fine time variation of hard X-rays has been explained in terms of a spread in the angle of incidence of the source electrons in non-thermal thick-target model for bremsstrahlung generation. The electron energy and angular distributions have been calculated by combining small angle scatterings using analytical treatment with a large angle collision using Monte Carlo calculations as a function of column density. The incidence angles of electrons are taken as 0, 30, and 60°. Using the Bethe-Heitler cross section and the above calculated electron distributions, the bremsstrahlung flux for different photon energies as a function of column density has been studied. The computed X-ray pulse as a function of column density has been converted into time profile. It corresponds well with the observed fine time structure. The calculated spectra of X-rays at the peak and valley are also consistent with the observations. The variation of photon flux with time has also been computed for photon energies 20, 50, and 100 keV for 90 and 180° observation angles together with the changes in spectral shapes of photon energy spectrum at different times for 90 and 180° observation angles.     

A note on the post-explosion gas depletion in the central region of normal spiral galaxies

The problem of post-explosive gas depletion in the central region of normal spiral galaxies like our own has been investigated. It has been calculated that with a plausible density law and with some restriction on gas temperature, a sufficient quantity of gas will be depleted from the central region over a time-scale ranging from a few times 10⁷ to a few times 10⁸ years, the exact time depending on the particular density law. Such a time-scale has been suggested by many authors as the period for one phase of activity in the nuclei of these galaxies. A similar time-scale has also been proposed by several authors as that for the formation and destruction of the spiral patterns of these galaxies.     

An ionosphere-plasmasphere global electron density model

Global Positioning System (GPS) satellites now provide a major source of data used in the study of the ionized regions that surround the Earth. With the greater use of GPS satellites in this role, understanding the effect the plasmasphere has on GPS radio signals has become increasingly important. The plasmasphere, with similar properties to the underlying ionosphere, can potentially contribute a significant fraction of the overall ionospheric error in radio signals transmitted from a GPS satellite to ground or space based receivers. A global plasmasphere-ionosphere electron density model has been developed to investigate this contribution. A variety of output examples that the model can produce are shown.     

Rayleigh-Taylor instability of a viscous compressible plasma of variable density

A study has been made of the problem of the Rayleigh-Taylor instability of a hydromagnetic plasma of varying density to investigate the influence of the simultaneous presence of the effects of compressibility and viscosity. The solution is shown to be characterized by a variational principle. Based on the variational principle proper solutions have been obtained for a semi-infinite plasma, in which the density has a one-dimensional gradient along the direction of a uniform vertical magnetic field, confined between two planes. Both the viscosity and magnetic field are found to have a stabilizing influence. The effect of compressibility is found to be destabilizing.     

Fluctuations of density and waves in nonlinear nuclear reactions in stellar cores

The space correlation of fluctuation of density in the nuclear reaction system inside the stars is investigated by using the theory of a generating function. Referring to the dynamical rate equation, we have introduced the gravitational force and temperature gradient terms into master equation of the probability distribution function of density, and a generalized master equation has been obtained. We take P-PI reactions of hydrogen-burning in the solar core as an example to solve this master equation for infinite medium. A series of waves have been obtained. The first branch is the average density wave which has already been obtained from the dynamical rate equation. Other branches describe the propagation of the fluctuation moments of the local density. They represent the propagation processes of the local distortion of the probability distribution function. Stability of the system may be related to an increase and decay of the waves. We have analysed the phase velocity of these waves.     

Roles of statistical mechanics in determining the density profile of mild relaxation

The r ^?4 law of cold collapse has been explained in other work. Here we try to explain the density profile of mild relaxation by statistical mechanics. In this paper we first generate many kinds of initial conditions with the same mass and energy to see whether there are other initial factors that can change the density profile of an isolated equilibrium self-gravitating system; then for a more general initial condition we discuss the role of mass and energy in determining the final density profile. Next we use our previous results obtained from statistical mechanics to fit these simulations, and find that when the masses of the particles in clumps are less than 5 % of the total mass, or the initial density is shallower than r ^?2, the whole virialized density profile (VDF) can be fitted well by our equation of state with three parameters, and some other cases can be explained by the theory with the r ^?4 law. We conclude that statistical physics may play an important role in determining the shape of VDF in the mild relaxation, mass and energy can control the values of the central density and the system’s radius, but there are still other initial configurations that can affect the VDF.     

Hydromagnetic stability of a compressible plasma with hall-currents

The hydromagnetic stability of an electrically conducting compressible plasma having variable density in the vertical direction has been investigated taking into account the effects of Hallcurrents. The solution is shown to be characterized by a variational principle. Based on the existence of variational principle, the dispersion relation has been obtained for the case of a plasma having exponentially varying density with special reference to stellar atmosphere. It is found that both compressibility of the medium and Hall-currents destabilize the configuration for the disturbances, for which it was stable otherwise. The Hall-currents even suppress the mode of maximum instability for large magnitudes.