Properties of a spherical galaxy with exponential energy distribution

Some analytical relations for the phase space functions of a self-consistent spherical stellar system are derived. The integral constraints on the distribution function by imposing a given (r) density distribution andN(E) fractional energy distribution are determined. For the case of radially-anisotropic velocity distribution in theE0 limit the constraint by an exponentialN(E) implies thatf(E, J ²) tends to zero in the order (–E)^3/2. This lends analytical support to the use of the Stiavelli and Bertin (1985) distribution function for modeling elliptical galaxies. Maximum phase space density constraint confirms the necessity of high collapse factors to produce such a distribution function. Limits on the steepness of an exponentialN(E) for the case when (r) resembles the emissivity law of ellipticals are also derived.     

Compressibility effects on hydromagnetic surface waves

The dispersion equation for hydromagnetic surface waves along a plasma-plasma interface has been solved as a function of the compressibility factor c ₁/v _A1, where c ₁ and v _A1 are the acoustic and Alfvén wave speed in one of the medium, for general wave propagation direction. Both slow and fast magnetosonic surface waves can exist. The nature and existence of these waves depends on the values of c ₁/v _A1 and , the angle of wave propagation. For low- plasmas only fast mode exists. The slow mode does not propagate below a critical value of c ₁. When c ₁ the phase velocity of the slow wave tend to the Alfvén surface wave velocity in the incompressible media and for large the phase velocity of the fast wave approaches this value. The phase velocity of the slow wave increases whereas for the fast wave it decreases with increase in the angle .     

Polarization of intrinsic radiation of tidally distorted stars with electron-scattering atmospheres

Linear polarization of radiation emitted by tidally distorted stars as a function of the binary system phase is computed, taking into account true absorption and the scattering of light on free and bound electrons within hot stellar atmospheres. Computations are made both for the linear distribution of true sources across the atmospheres and for radiative-stable model atmospheres presented by Kurcuzet al. (1974) and Kurucz (1979). Polarization variability was investigated as a function of wavelength . In a number of cases, polarization variability was found to be at an observable level. The most marked variability was expected in the ultraviolet range adjacent to the boundaries of the spectral series for H and He. Near the Lyman limit of approximately =912 Å for stars with an effective temperatureT _eff35 000 K and near the ionization boundary for HeII 226 Å for stars withT _eff>35 000 K, the amplitude of polarization variability is greater than in the case of pure electron atmospheres, sometimes reaching the level of 0.5–1%. For fairly long waves where the limb-darkening coefficient falls below a certain critical valueu _cr0.5, the plane of polarization is found to be turned by 90° as compared to the case of a pure electron atmosphere. For limb-darkening coefficients far from the value ofu _cr; the form of the polarization phase curves, as well as dependence on the parameters of a binary system, remain approximately the same as those in the case of pure electron scattering.     

Excitation of high-frequency Alfvén waves by plasma outflows from coronal reconnection events

We study a kinetic excitation mechanism for high-frequency dispersive Alfvén waves in the solar corona by magnetic reconnection events. The ion-cyclotron and Cerenkov kinetic effects are important for these waves which we call the ion-cyclotron kinetic Alfvén waves (IC KAWs). The plasma outflowing from the reconnection site sets up a neutralized proton beam in the surrounding plasma, providing free energy for the excitation of waves. The dependence of the phase velocity of the IC KAW on the parallel wavenumber is different from that on the perpendicular wavenumber. The phase velocity is an increasing function of the perpendicular wavenumber and overtakes the Alfvén velocity for sufficiently large values of k . However, the phase velocity is a decreasing function of k , and sufficiently large values of k result in a phase velocity below the Alfvén velocity. As a result, the IC KAWs can undergo the Cerenkov resonance with both super- and sub-Alfvénic particles, and for the waves to be excited the outflow velocity does not need to be super-Alfvénic, as for KAWs, but the beam/Alfvén velocity ratio can span a wide range of values. High growth rates of the order of 10⁴ s^–1 are found for the values of the plasma parameters typical for the low solar corona. The waves excited by (sub-)Alfvénic beams are damped mainly due to kinetic wave-particle interactions with ions at the cyclotron resonance (ion-cyclotron damping), and with ions and electrons at the Cerenkov resonance (Landau damping). Therefore, IC KAWs can heat the plasma species of the corona in both the parallel and perpendicular direction, giving rise to an anisotropic heating of the ions. The observational consequences of the processes under study are discussed.     

The propagation of solar cosmic-ray bursts

A model is presented in which we show analytically the three phases of anisotropy which occur during solar cosmic-ray events observed in the 7.5 MeV to 21 MeV kinetic-energy interval and reported by McCracken et al. (1971): (i) a highly anisotropic, near field-aligned, initial phase, (ii) a convective phase, and (iii) a late-time phase in which the anisotropy is approximately perpendicular to the mean interplanetary magnetic field. The model is based on the cosmic-ray particles being convectively transported out from the Sun, undergoing anisotropic diffusion along the interplanetary magnetic-field lines, and losing energy by adiabatic deceleration or by collision processes. The event is seen simply as a pulse moving outward from the Sun after a cosmic-ray burst with a negative density-gradient in front of it and a positive gradient behind. The convective phase (ii) occurs as the spatial peak moves past the observer and has a propagation speed V _d associated with it; the anisotropy vector late in the decay phase (iii) is the result of a residual balance between the radial outward convection and the inward radial component of the anisotropic diffusion. The mathematical solutions are based upon a diffusion coefficient proportional to heliocentric radius and independent of energy and are thus rather special. However they yield formulae for the propagation speed of the convective phase and the direction in space of the long-time anisotropy which are useful as a guide to the dependence of these quantities on the solar wind speed V, the diffusion coefficient and the spectral index . In this model V _d increases with V, , and ; and , the angle between the anisotropy vector at infinite time and the outward radial direction increases with /V and decreases as is increased. These predictions of the dependence of and V _d upon V, , and are open to observational verification.     

Exact solution of the equation of transfer with planetary phase function

We have considered the transport equation for radiative transfer to a problem in semi-infinite atmosphere with no incident radiation and scattering according to planetary phase function w(1 + xcos ). Using Laplace transform and the Wiener-Hopf technique, we have determined the emergent intensity and the intensity at any optical depth. The emergent intensity is in agreement with that of Chandrasekhar (1960).     

Ubvri photometry of some lunar topographies

Examples of pure lunar mountains, dark and light maria, and cratered terrae have been observed with the UBVRI stellar photometry system. Johnson's (1965) absolute calibration was used to compute brightnesses. These brightnesses were reduced using Hapke's photometric model to a standard geometry (angle of incidence 60°, emergence 40°, phase 90°), and relative albedos were then computed.The mountains, as distinct from the other regions, appear to require a wavelength dependent phase function. The albedos for the four topographic types are approximately linear functions of wavelength. The terrae are redder than the maria. Very low contrast between the topographies is predicted for full-moon at wavelengths shorter than 0.30. On the basis of laboratory studies, the lunar particles are comparable to basalt grains having sizes less than 50m. Larger particle sizes are associated with the dark maria and smaller ones with the cratered highlands.     

Transformation from proper time on Earth to coordinate time in solar system barycentric space-time frame of reference

In order to obtain accurate computed values of Earth-based range and Doppler observables of a beep space probe, an expression is required for the time differencet–, wheret is coordinate time in the solar system barycentric space-time frame of reference and is proper time recorded on a fixed atomic clock on earth. This paper is part 1 of a two-part article which obtains an expression fort– which is suitable for use in obtaining computed values of observations of a spacecraft or celestial body located anywhere in the solar system. The expression can also be used in the computation of Very Long Baseline Interferometry data types. Part 1 obtains an expression fort– which is a function of position and velocity vectors of the major celestial bodies of the solar system and the atomic clock on Earth which reads . In Part 2, this expression will be transformed to a function of time and the Earth-fixed coordinates of the atomic clock.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under NASA Contract No. NAS 7-100.     

Spectral energy distribution and long-term variations in gamma cassiopeiae

Newly measured continuum energy distribution data of a typical Be star, Cas, is presented in the visible region (3200–8000 Å). The behaviour of the continuum over the broader wavelength range covering the ultraviolet, visible, and infrared regions is summarized. It is found that Cas exhibits large variations in the continuum which are connected with variations in the strength of ultraviolet and infrared excess emissions.From the analysis of the existing data in the visible region it transpires that this star possesses interesting long-term changes of different parameters like colour temperature (T _c ), visual magnitude (m _v ), total strength of Balmer emission lines (E _H ), ratio of violet to red emission component (V/R), and equivalent width of Balmer lines (W _H ). The most interesting aspect is the fact that all these parameters are related with one another during the so-called Great Outburst (GO) period which occurred during 1932–1942. The parametersT _c ,m _v , andE _H are also found to be connected to each other throughout their long-term variations.The present investigation shows that Cas has exhibited three phases—Be, Be shell, and normal B — in the past. Since 1866, the first Be phase, lasting about 60 to 70 years, was followed by spectacular variations of about 10 years duration (1932–1942). During this spectacular episode ending with a quasi-normal B phase, two strong shell phases followed by very intense emission phases were observed. Since then, a new, slowly irregularly increasing Be phase which is still persisting has been observed. So far this last Be phase has not shown any outstanding variable characteristics.The present behaviour of the long-term variation ofm _v shows that since 1985 Cas has again entered a new phase of activity. We hope that this star will again pass through some new outstanding variability phase during the coming decade.     

Solution of a transfer equation by a Modified Spherical Harmonic Method in a thin anisotropically scattering atmosphere

Wan, Wilson and Sen (1986) have examined the scope of Modified Spherical Harmonic Method in a plane medium scattering anisotropically. They have used the phase functionp(µ, µ) = 1 +aµµ. In this paper, the Transfer Equation has been solved by the Modified Spherical Harmonic Method using the phase functionp(µ, µ) = 1 + ₁ P ₁(µ)P ₁(µ) + ₂)P ₂(µ)P ₂(µ) and a few sets of numerical solution have been predicted for three different cases.     

Penumbral filaments: A dissipation form of the magnetic field

In this paper we suggest that penumbral filaments are a phenomenon of magnetohydrodynamic instability, developed in a stable and uniform magnetic field of sunspots during a dissipation process. We have solved local magnetohydrodynamic disturbance equations and have obtained the necessary condition for filament instability mode, that the ratio of filament length to width must be larger than the ratio of Alfvén speed to sound speed. We have also obtained correlations between two fluctuations from their phase difference. Although there are two correlations between the fluctuation of temperature (or filament intensity) and (1) the fluctuation of magnetic field, and (2) the fluctuation of the flow during the phases of developing and dissipating of the filament, we cannot distinguish whether the correlation is associated with the light filament or dark filament and we cannot decide whether the phase difference is 0° or 180° from tg() = 0. However, we can make a judgment: if the correlation is associated with a light filament during its development phase, it will be associated with a dark filament during its dissipation phase, andvice versa. In addition, there are no correlations between the fluctuations mentioned above for a stable filament, because the phase difference of the filament is changing with time.The phase differences of filaments are related to the existence of a gravitational field.     

Simultaneous hard X-ray and optical observations of Sco X-1 and a model of semi-opaque X-ray sources

Simultaneous observations of hard X-ray and optical emission from Sco X-1 were carried out at Hyderabad, India, on April 16 and 19, 1972. During the first and the second observations Sco X-1 was on the average in a bright phase ofB=12.5 mag. and a slightly darker phase ofB=12.7 mag. respectively. During the first observation the X-ray intensity in the energy range 20–40 keV measured with balloon borne scintillation counters showed an enhancement of a factor of about two in coincidence with an optical flare ofB0.2 mag., whereas the apparent temperature derived from the X-ray spectrum observed in the energy range 20–35 keV showed no appreciable change. Both the X-ray intensity and the apparent temperature observed on April 19 are considerably lower than those observed on April 16. Taking into account the effect of radiative transfer in a hot plasma, the electron density and the optical depth for electron scattering of the plasma cloud are derived asn _e 3×10¹⁶ cm^–3 and _es 10 for the quiescent bright phase. The flare is explained by an increase of the plasma mass by about 30% and an increase of _es by _es 1 without appreciable change of the plasma temperature. The results on April 19 is interpreted as indicating that the quiescent dark phase may be characterized by a decrease of the plasma mass, its contraction and lower temperature.     

Hydrogen and Helium under high pressure: A case for a classical theory of dense matter

When subject to high pressure, H₂ and ³He are expected to undergo phase transitions, and to become metallic at a sufficiently high pressure. Using a semiclassical theory of dense matter proposed by Savi and Kaanin, calculations of phase transition and metallisation pressure have been performed for these two materials. In hydrogen, metallisation occurs at p _M= (3.0 ± 0.2) Mbar, while for helium the corresponding value is p _M= (106 ± 1) Mbar. A phase transition occurs in helium at p _tr= (10.0 ± 0.4) Mbar. These values are close to the results obtainable by more rigorous methods. Possibilities of experimental verification of the calculations are briefly discussed.     

The evolutionary history of PSR 0655+64 and PSR 1913+16

We intend to point out that existing evolutionary scenario for the genesis of the binary radio pulsars like PSR 0655+64 (P1 d) and 1913+16 (P8 hr) having short orbital periods and relatively massive companion (>0.5M _*) is inconsistent in that it does not allow for a prolonged phase of angular momentum transfer. We propose here a modified evolutionary scenario where there is such a prolonged phase of angular momentum transfer from a low mass helium star to the neutron star mediated by an accretion disk along the so-called caseB evolutionary track.     

RS CVn-type variables

Photometric observation of HR 1099 inV andB obtained on 18 nights between January and March 1977 is presented. The amplitude of the asymmetric light curve is found to be 0^m.10±0^m.004 both inV andB. On three occasions—namely, JD 2443164. 17, JD 2443176. 14 and JD 2443177.12—the star brightened by 0^m.05. Four H spectrograms at 42 Å mm^–1 dispersion were obtained during October–November 1978. The profile and equivalent width of H of 14 November, 1978 suggest a probable major outburst.Analysis of all available photometry shows that (1) the amplitude and shape of the light curve change in a few orbital periods, (2) the phase of the minimum light migrated towards decreasing orbital phase during the interval JD 2442720 to JD 2443000 and from JD 2443200, there is almost a linear increase of the phase of the minimum light and (3) the phase of the light minimum sometimes shows to and fro behaviour suggesting the migration of the wave is not taking place smoothly.     

An exact solution of the equation of transfer with three-term scattering indicatrix in an exponential atmosphere

The general equation for radiative transfer in the Milne-Eddington model is considered here. The scattering function is assumed to be quadratically anisotropic in the cosine of the scattering angle and Planck's intensity function is assumed for thermal emission. Here we have taken Planck's function as a nonlinear function of optical depth, viz.,B _v(T)=b _o+b ₁ e ^–. The exact solution for emergent intensity from the bounding face is obtained by the method of the Laplace transform in combination with the Wiener-Hopf technique.     

Asymmetric librations in exterior resonances

The purpose of this paper is to present a general analysis of the planar circular restricted problem of three bodies in the case of exterior mean-motion resonances. Particularly, our aim is to map the phase space of various commensurabilities and determine the singular solutions of the averaged system, comparing them to the well-known case of interior resonances.In some commensurabilities (e.g. 1/2, 1/3) we show the existence of asymmetric librations; that is, librations in which the stationary value of the critical angle =(p+q)₁–p–q is not equal to either zero or . The origin, stability and morphogenesis of these solutions are discussed and compared to symmetric librations. However, in some other resonances (e.g. 2/3, 3/4), these fixed points of the mean system seem to be absent. Librations in such cases are restricted to =0 mod(). Asymmetric singular solutions of the planar circular problem are unkown in the case of interior resonances and cannot be reproduced by the reduced Andoyer Hamiltonian known as the Second Fundamental Model for Resonance. However, we show that the extended version of this Hamiltonian function, in which harmonics up to order two are considered, can reproduce fairly well the principal topological characteristics of the phase space and thereby constitutes a simple and useful analytical approximation for these resonances.     

A direct hydrodynamical approach to the evolution of the density correlations in an expanding flat Friedmann Universe

A direct approach of the dynamical equation for the evolution of the two-point density correlation function is given in an expanding flat Friedmann Universe in the Newtonian approximation. If the third and higher moments are neglected, a wave-like equation of third-order for the two-point density correlation function is found. The exact solution of this equation shows, in the large time limit, the usual Jeans instability t ^4/3. It is suggested that the highern-point correlation function of the density grow liket ^2n/3 in the same approximation. This indicates that every truncation procedure of the hierarchy of the equations is inapplicable at least for large timest.     

Zeeman-doppler imaging: A new option for magnetic field study of Ap and solar-type stars

In the task of studying stellar magnetic fields, polarimetric methods have been intensively used in Ap stars. But the observational material classically used to reconstruct stellar magnetic structures (average longitudinal magnetic field as a function of rotational phase) is not rich enough in spatial information to derive geometries more complex than centered or decentered dipoles.In solar-type stars, all evidences of activity recently detected on their surfaces (starspots, flares, ...) indicate they are most likely magnetic stars. But polarimetric methods have always failed in these stars, probably due to the complex magnetic topologies encountered which even prevented until now a simple detection (Borra, Edwards, and Mayor, 1984). With the Zeeman broadening measurement technique proposed by Robinson (1980), no reliable results can be derived for rapid rotators, which are otherwise presumed to be the best candidates for magnetic detections. Once more, if temperature inhomogeneity charts are already available for solar-type stars (Vogt, 1987), spatial information on their magnetic distributions has conversely not yet been obtained.The new option, recently proposed by Semel (1989) and qualified by Donati, Semel, and Praderie (1989), is based on the rotational modulation study of a rapid rotator Stokes parameter V(), obtained with both high spectral resolution R, and high signal-to-noise ratio S/N. Since the magnetic information used refers to localized strips on the stellar disc (as a consequence of the star rotation), multipolar structures can thus be resolved.A new instrumentation and observing procedure have been defined for ZDI, in order to obtain very high S/N data. The method has been successfully tested on two bright magnetic Ap stars: a magnetic detection was obtained on UMa and a 15-point phase coverage of ² CVn is available for the reconstruction of complete 2D abundance and magnetic mappings of its photosphere.Concerning solar-type stars, a numerical simulation was carried out in order to determine the observational constraints required for the detection of typical magnetic field similar to those reported in slow rotators with the Robinson method (Saar, 1988). The specifications needed are S/N 400 per 40 mÅ pixel and R - 6 × 10⁴.     

Unsteady MHD flow past a porous plate with step function change in suction at slip flow regime

Unsteady two-dimensional hydromagnetic flow of an electrically conducting viscous incompressible fluid past a semi-infinite porous flat plate with step function change in suction velocity is studied allowing a first order velocity slip at the boundary condition. The solution of the problem is obtained in closed form and the results are discussed with the aid of graphs for various parameters entering in the problem.Notations B intensity of magnetic field - H magnetic field parameter,H=(M+1/4)^1/2–1/2 - h rarefaction parameter - L ₁ slip coefficient; ;I, mean free path of gas molecules;f, Maxwell's reflection coefficient - M magnetic field parameter - r suction parameter - t time - t dimensionless time - u velocity of the fluid - u dimensionless velocity of the fluid - U velocity of the fluid at infinity - v suction velocity - v ₁ suction velocity att<=0 - v ₂ suction velocity att>0 - x distance parallel to the plate - y distance normal to the plate - y nondimensional distance normal to the plate - v kinematic viscosity - electric conductivity of the fluid - density of the fluid - shear stress at the wall - nondimensional shear stress at the wall - erf error function - erfc complementary error function