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.     

A spectroscopic study of the microorganism model of interstellar grains

The microorganism model of interstellar grains is investigated by spectroscopy from the infrared (IR), visible to the ultraviolet (UV) wave regions.E. coli, yeast and spores ofBacillus subtilis exhibit absorption bands at =3.1 and 9.7 m; they also exhibit several absorptions at 68 m which are in agreement with the observed IS extinction curves.To obtain the extinction curves in the visible and UV regions, dry films of microorganism are prepared on a MgF₂ plate or synthesized quartz plate and their spectra measured. In the wavelength region 190400 nm, conventional spectrophotometers are adopted for the measurement. The extinction curve of the film ofE. coli is similar to the observed IS curve.For the wave-range 100<<400 nm, a vacuum UV spectrometer is adopted to avoid absorptions due to O₂ in the atmosphere. The extinction spectra by this method are in agreement with the result obtained by the conventional method where comparison is possible. The extinction curves ofE. coli and yeast are such that they incrase towards the short wavelength and exhibit a peak at -190 nm, which is different from the well-known IS peak at =220 nm. It remains to be seen whether interstellar low temperatures (1040 K) can shift the peak position in the extinction curve of biochemical materials.     

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.     

Isovortical orbits in uniformly rotating coordinates

For the conservative, two degree-of-freedom system with autonomous potential functionV(x,y) in rotating coordinates; $$\dot u - 2n\upsilon = V_x , \dot \upsilon + 2nu = V_y $$ , vorticity (v _x -u _y ) is constant along the orbit when the relative velocity field is divergence-free such that: $$u(x,y,t) = \psi _y , \upsilon (x,y,t) = - \psi _x $$ . Unlike isoenergetic reduction using the Jacobi, integral and eliminating the time,non-singular reduction from fourth to second-order occurs when (u,v) are determined explicitly as functions of their arguments by solving for ψ (x, y, t). The orbit function ψ satisfies a second-order, non-linear partial differential equation of the Monge Ampere type: $$2(\psi _{xx} \psi _{yy} - \psi _{xy}^2 ) - 2(\psi _{xx} + \psi _{yy} ) + V_{xx} + V_{yy} = 0$$ . Isovortical orbits in the rotating frame arenot level curves of ψ because it contains time explicitly due to coriolis effects. Rather, (x, y) coordinates along the orbit are obtained, from (u, v) either by numerical integration of the kinematic equations, or by partial differentiation of the Legendre transform ? of ψ. In the latter case, ? is shown to satisfy a non-linear, second-order partial differential equation in three independent variables, derived from the Monge-Ampere Equation. Complete reduction to quadrature is possible when space-time symmetries exist, as in the case of central force motion.     

Culgoora radio and skylab euv observations of emerging magnetic flux in the lower corona

Detailed comparisons of Culgoora 160 MHz radioheliograms of solar noise storms and Skylab EUV spectroheliograms of coronal loop structures are presented. It is concluded that: (1) there is a close association between changes in large-scale magnetic fields in the corona and the onset or cessation of noise storms; (2) these coronal changes result from the emergence of new magnetic flux at the photospheric level; (3) although new magnetic flux at the photospheric level is often accompanied by an increase in flare activity the latter is not directly responsible for noise storm activity; rather the new magnetic flux diffuses slowly outwards through the corona at rates 1–2 km s^–1 and produces noise storms at 160 MHz 1–2 days later; (4) the coronal density above or in large-scale EUV loop systems is sufficiently dense to account for noise storm emission at the fundamental plasma frequency; (5) the scatter in noise storm positions can be accounted for by the appearance and disappearance of individual loops in a system.     

Sunspot nests

For the period August 1959–December 1964 the Greenwich Photoheliographic Results were searched for sunspot nests. Such a nest is a sequence of sunspot groups that appear within a small area on the solar surface and that last for several months. The search procedure is described and data for 41 probable sunspot nests are given. At least three quarters of these nests appear to be real, and not chance clusters.The nests are the same type of activity sequences as the Fleckenherde discovered by Becker (1955) and the complexes of activity pointed out by Gaizauskas et al. (1983). The complexes of activity as defined by Bumba and Howard (1965) are different patterns, however; the relation between complexes and the nests is shown.Some properties of the nests are: (i) many nests appear as double structures; (ii) single nests and components of double nests are quite compact: the effective areas are comparable to those of medium-large sunspot groups; (iii) each nest rotates at its own steady rate about the Sun; (iv) the intrinsic scatter in the rotation rates is much larger than the trend in the differential rotation; (v) displacements in latitude are less than a few meters per second; (vi) many nests live for 6 to 15 Carrington rotation periods, the minimum lifetime is not yet determined; (vii) the fraction of the sunspot groups that are members of nests is large (at least 30%).     

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.     

The magnetic and thermodynamical structure of a coronal hole

A nonpolytropic model of a polar coronal hole at 2 R R 5 R is constructed. Our main assumptions are: (1) the magnetic structure of the Sun can be described by a combination of dipole-like and radial fields; (2) in the magnetically dominated region [(v ²/2) < (B ²/8)] the influence of the outflow on the magnetic structure is negligible. The magnetic and thermodynamic structures are obtained by solving the force balance equation for plasma with the observationally derived electron density. Profiles of velocities in the acceleration regime are presented and the influence of the outflow on the thermodynamic structure of the solar corona above the polar region is discussed.This paper is the first part of a joint project of the Space Environment Laboratory, the Joint Institute for Laboratory Astrophysics, and the High Altitude Observatory, NCAR. The second paper by Munro and Tzur is in preparation.Work done while at the Space Environment Laboratory, NOAA, ERL, Boulder, CO 80303, U.S.A.1982–83 Visiting Fellow at the Joint Institute for Laboratory Astrophysics, National Bureau of Standards and University of Colorado.The National Center for Atmospheric Research is sponsored by the National Science Foundation.Visitor at NCAR.