Dynamical effects of dark matter in systems of galaxies

SeveralN-body experiments were performed in order to simulate the dynamical behaviour of systems of galaxies gravitationally dominated by a massive dark background.We discuss mass estimates from the dynamics of the luminous component (M _VT) under the influence of such a background, assuming a constant dark/luminous mass ratio (M _D/M _L) and plausible physical conditions. We extend in this way previous studies (Smith, 1980, 1984) about the dependence ofM _VT on the relative distributions of dark and luminous matter (Limber, 1959). We found that the observed ratio of the virial theorem mass to luminosity (M _VT/L) in systems of galaxies of different sizes could be the result of different stages of their post-virialisation evolution as was previously suggested by White and Rees (1978) and Barnes (1983). This evolution is mainly the result of the dynamical friction that dark matter exerts on the luminous component. Thus our results give support to the idea that compact groups of galaxies are dynamically more evolved than large clusters, which is expected from the hierarchical clustering picture for the formation of such structures.     

Evolution of galaxies: One-zone model with a birth-rate stellar function depending on gas density and temperature

In this paper closed one-zone models with a birth-rate stellar function depending on gas density and temperature are built up, in order to make a zeroth order approximation of thermo-chemical evolution of galaxies. To get a more realistic picture, the models are allowed first to expand with the universe and then to contract according to three successive time-scales, in order to simulate violent relaxation, rapid contraction, and slow contraction processes.Star formation occurs according to a birth-rate (m, t) _g ⁿ T ^r m ^p ( _g , gas density;T, gas temperature; andm, star mass), which reproduces the usual Schmidt-type law in the limitr0. Further we suppose that synthesized metals and helium are instantaneously mixed when returned to gas component at star death, and that relative metal abundances are time-independent: ( any element heavier than He, ). An energy fraction of each typical supernova event is assumed to heat interstellar medium, which is also though always to maintain a steady state.Under these hypotheses it becomes possible to use the interstellar cooling function of Dalgarno and McCray (1972), which is related to a special cosmic abundance of elements, to express analytically an interstellar cooling function related to any abundance. At this stage, numerical computations are performed up to about 12 Gy and the results analyzed in order to reproduce some morphological features observed in the galaxy, namely: (i) the extreme scarcity of stars with nearly zero metal content; (ii) the metal content and mass fraction of halo stars; (iii) the metal content and mass fraction of disk stars; and (iv) the ratio of the present-day birth-rate to the past birth-rate averaged over the age of the disk. It is found that a whole class of theoretical models exist, with slope of the mass spectrum between –2.5 and –2.6, which range from a Schmidt's law limitn=1.3 andr=0 to the opposite limitn=0 andr=–1.2, and are able to fit more or less at the same extent the observations mentioned above. On the analysis of further computations, it is also shown that an universal birth-rate stellar function is in contradiction with neither a dynamical hystory starting from the initial expansion of proto-galaxies, nor a morphological sequence where the amount of angular momentum is the only free parameter for any given mass, at least for what concerns spiral types. Finally, possible refinements for future work are briefly outlined.     

Discrete Alfvén waves in planar flux tubes

Properties of discrete Alfvén wave modes are derived, at frequencies up to the ion-cyclotron frequency, for current-carrying plasma slabs with non-uniform densities. It is shown that the essential features of the dispersion relations can be derived by examining the dominant terms in the potential function, when the wave equation is cast in the Schrödinger equation form. Analytical predictions for a class of mass and current density profiles are compared with numerically calculated dispersion relations and wavefields for particular profiles.     

An estimate of the contribution of high nergy cosmic-ray protons to the absorbed dose inventory of a cometary nucleus

We discuss the contribution of cosmic-ray protons at all energies above 1 MeV to the absorbed doses of the surface layers of a comet. Since there exists no calculation which takes into account proton energy losses by means of losses to electrons and nuclear collisions (in a cascade process), and losses due to the low energy end-products of the cascade, we have made a rough estimate of all of these contributions. An analytical formula is proposed that allows a rapid estimate of ranges and the dose absorbed at any depth. We give dose-depth curves for two extreme values of the energy at which nuclear collisions begin to dominate the slowing-down process, and for an intermediate value we display the dose-depth curve down to 20 m from the surface. The relevance of these findings to dosimetry in comets and some alterations of cometary material are considered. The need for improving the analytical expression proposed is stressed.     

A note on the total mass of comets in the solar system

The assumption that the very low albedo determined for Halley's comet is typical of all short period comets, taken together with the assumption that the average sizes of long and short period comets are approximately equal, leads to an increase in the total mass of comets in the solar system by almost two orders of magnitude. If gravitational ejection from the Uranus - Neptune zone during the later phases of planet formation is indeed responsible for the classical Oort cloud between 10⁴–10¹⁵ AU, then the mass of comets in this transplanetary region during cosmogonie times has to exceed the combined masses of Uranus and Neptune by over an order of magnitude. Furthermore, if the recent arguments for as many as 10¹⁴ comets in an inner Oort cloud between ~40– 10⁴AU are valid, then the total mass of comets in the solar system approaches 2% of a solar mass.     

Emission curve of growth for Feii in chromospheric limb spectra

The 270 chromospheric emission lines of Feii ranging between 2000 and 3200 Å observed by Skylab at a height of 4 (2900 km) above the limb of the quiet Sun are analyzed by the emission curve of growth method, using newly calculated gf-values. It is derived that the excitation temperature is 7.2 × 10³ K and that the turbulent velocity is consistent with the previous results that the microturbulent velocity is lower than 10 km s^–1 in the cool (<10⁴ K) region of the chromosphere.Contributions from the Kwasan and Hida Observatories, University of Kyoto, No. 270.     

Energy interconnection between the plasma cloud ejected from the active region and the shock wave

The relation between the ejected plasma cloud and the shock wave propagating ahead of it is examined for 27 pairs of such events. The flare sprays and the eruptive prominences observed in H line as well as the fast-moving sources of type-IV radio bursts have been considered as such ejected plasma clouds. Propagation of the shock wave in the solar corona has been examined from the observations of type-II radio bursts. Using the Parker model of the propagation of a shock wave, the shock wave velocity has been compared with the plasma cloud velocity. Energy interconnection between these two events has been studied. In the majority of the investigated cases there exists an energetic interconnection between the plasma cloud and the shock wave.     

The skin friction in the unsteady free-convection flow past an accelerated plate

In this paper the unsteady laminar free-convection flow of a viscous incompressible fluid, past an accelerated infinite vertical porous plate subjected to a constant suction (or injection) in considered. Numerical results for the skin-friction on the plate are obtained for the class of accelerated motions whose velocity is of the formU ₀ t ⁿ wheret is time,U ₀ a constant, andn is a positive integer. The skin friction tends to zero with increasingt when the Grashof number Gr=², the Prandtl number =1,n=0, and >0 which corresponds to suction.On leave of absence from the Department of Mathematics, University of Dhaka, Bangladesh.On leave from absence from the Department of Mathematics, University of Dar-es-Salaam, Tanzania.     

Properties of r-modes in the Sun

Global oscillations of the Sun (r-modes) with very long periods 1 month are reviewed and studied. Such modes would be trapped in an acoustic cavity formed either by most of the convective envelope or by most of the radiative interior. A turning point frequency giving cavity boundaries is defined and the run of eigenvalues for angular harmonics l 3 are plotted for a conventional solar convection zone. The r-modes show equipartition of oscillatory energy among shells which each contain one antinode in the radial dimension. Toroidal motion is dominant to at least the 14^th radial harmonic mode. Viscosity from convective turbulence is strong and would damp any mode in just a few solar rotations if it were the only significant nonadiabatic effect. Radial fine splitting which lifts the degeneracy in n is very small (20 nHz or less) for all n 14 trapped in the envelope. But, if splitting could be detected, we would have a valuable new constraint on solar convection theories.     

Use of the population potential model for predicting the growth of cities in a region (with reference to Moscow Oblast)

"A modification of the population potential model is used to analyze the structure of the potential of population for cities of the Moscow region, to develop a relationship between population potential and city size, and to use this procedure to forecast future population change in Moscow Oblast cities." Cities in the region with a population of 50,000 or more at the censuses of 1959, 1970, and 1979 are included.