On the spectrum of relativistic electrons accelerated in cosmic-ray sources

The data on the spectrum of the cosmic-ray electron component near the earth, on the radio-spectra of radio-galaxies, quasars and the Crab Nebula, as well as the data pertaining to the X-ray spectrum of the cosmic background, all agree that the sources of cosmic-ray electrons (such as supernovae and galactic nuclei) inject particles characterized by a power spectrumN(E)=KE ^–0, with 01.5–2.5. A mechanism is known in which the source emits a proton-nuclear component of cosmic rays with a spectrumN _n (E)=K _n E ^– _n, _n = + 2, =w cr/(w–w cr), wherew cr is the cosmic-ray energy density in the source, andw=w cr+w n+w _turb, the total energy density. We obtain =2.5 in agreement with observations on the natural assumption that =0.5. Within the framework of the same model with some additional assumptions, the electrons in the source, as well as those ejected by the source, are shown to have a power-spectrum characterized with _{0 n} = + 2. Thus the model discussed gives an adequate spectrum for both the proton-nuclear and the electron components of cosmic rays.     

Symmetric periodic orbits in Størmer's problem

The hypothesis on the -ray burst generation in the process of the collapse of surpermassive bodies in the nuclei of active galaxies is considered. It is shown that -ray burst properties observed may be interpreted within the frames of the given model. A statistical test for choosing a hypotheses on -ray burst nature is discussed.     

Percolation theory and the geometry of photospheric magnetic flux concentrations

The magnetic field in solar active regions forms a highly structured pattern without an apparent length scale. We study this pattern in detail for a plage and its surroundings observed with the Swedish Solar Observatory on La Palma. The magnetogram has a resolution of about 1/3, after image optimisation. We analysed the geometric properties of isolated patches of magnetic flux. Patches with a linear size up to 3 appear to be statistically self-similar, with a fractal dimension ofD _f = 1.54 ± 0.05 for the relation between area and linear size. This value agrees very well with the dimensionD _f = 1.56 which is found in percolation theory for clusters of tracers placed randomly on a lattice with a tracer density below a critical threshold. The distribution of observed cluster areas also agrees with that of clusters on such a random lattice. The correspondence between properties of observations and of clusters on randomly filled lattices suggests that- well after emergence - the magnetic flux on the Sun is randomly distributed at least up to sizes of about 3 and possibly larger.     

The projection of fractal objects

Motivated by several recent studies on the geometry of molecular cloud structures, we perform two experiments that consider the projection of fractal images onto a two-dimensional screen. Evidence is presented to support the proposition that the dimensionD _P of the contours surrounding the projected images are given byD _s–1, whereD _s>2 is the fractal dimension of the object itself. A brief survey of the geometry of astrophysical cloud structures is also presented.     

Stochastic gravitational fluctuations of stellar or galactic systems with a fractal distribution of field sources

The stochastic gravitational fluctuations for a fractal mass distribution are analyzed by means of a functional integral approach. A general method is developed for evaluating the stochastic properties of vectorial additive random fields generated by a variable number of point sources obeying inhomogeneous Poisson statistics. A closed expression for the generating functional of the field is given in terms of the generating functional of the sources. The moments of the resulting vectorial field are finite if the correlation functions of the sources have short tails. In this case all cumulants of the field can be computed exactly: they are averages of the central moments of sources computed in terms of the probability density of the position of a source. The method is applied for analyzing the stochastic gravitational fluctuations generated by a fractal distribution of field sources (stars or galaxies). For a Newtonian force law the correlation functions of the sources are slowly decaying, the cumulants of the stochastic gravitational field are infinite and the probability density of the field intensityF is given by a Lévy fractal stable law with a scaling exponentH depending on the fractal dimensiond _f of the distribution of stars or galaxies:H =d _f /2.     

Analysis of the hyades giant stars ε and γ Tau

Two hyades giant stars, and Tau, have been studied from an analysis of strong line profiles. We get for Tau,T _e =4750K and logg=2.7, and for Tau,T _e =4700K and logg=2.8. Hydrogen-to-metal ratio for the two stars is nearly the same as that of solar value.     

Resistive ballooning modes in line-tied coronal fields

The resistive stability of coronal loops to perturbations with short wavelength across the magnetic field is analysed, taking full account of the line tying effect due to the presence of the photosphere. The results presented are similar to those previously obtained for arcades: configurations with a pressure profile decreasing with distance from the loop axis at some point are found to be always unstable, the growth rate increasing monotonically with the wavenumber (n) and scaling approximately as (n ² D _r)^1/3 in the limit of large n.     

Special Families of Orbits in the Direct Problem of Dynamics

The direct problem of dynamics in two dimensions is modeled by a nonlinear second-order partial differential equation, which is therefore difficult to be solved. The task may be made easier by adding some constraints on the unknown function = f _y /f _x , where f(x, y) = c is the monoparametric family of orbits traced in the xy Cartesian plane by a material point of unit mass, under the action of a given potential V(x, y). If the function is supposed to verify a linear first-order partial differential equation, for potentials V satisfying a differential condition, can be found as a common solution of certain polynomial equations.The various situations which can appear are discussed and are then illustrated by some examples, for which the energy on the members of the family, as well as the region where the motion takes place, are determined. One example is dedicated to a Hénon—Heiles type potential, while another one gives rise to families of isothermal curves (a special case of orthogonal families). The connection between the inverse/direct problem of dynamics and the possibility of detecting integrability of a given potential is briefly discussed.This revised version was published online in October 2005 with corrections to the Cover Date.     

Covariance function analysis and the clustering of galaxies

Data on a statistic derived from the angular covariance function show that (contrary to the claim of Peebles that galaxies are distributed continuously with no distinct scales), superclusters and the maximum size of clusters are probably defined at scales of 15 and 2.0h ^–1 Mpc. This suggests some stepped-density profile like the idealized models of de Vaucouleurs and Wertz: consideration is therefore given to a semi-continuous hierarchy in which there are galaxies outside clusters, clusters outside superclusters etc. Theories of the origin of clustering by gravitational clumping and the escape of galaxies from clusters suggests the hypothesis that the average mass (m _g) of galaxies outside clusters is smaller than that of those inside (=fractionf of the total), a hypothesis supported by results on the continuity of the angular and spatial covariance functions. In a semi-continuous hierarchy, the overall packing fractionf _e and the fraction (1-f) of galaxies outside clusters both appear to increase as the distancer from a local origin increases, because a line-of-sight to greater depths intersects systems of the hierarchy of continually greater size (R _i). If the hypothesis is valid thatm _g inside clusters is slightly larger thanm _g outside, the apparent effect is to makem _g systematically distance-dependent from a local origin with and ₁0.3. No direct data on galaxy masses exist to refute such a small trend, but since the absolute magnitudes of galaxies are known to be correlated (very weakly) with their masses, a semi-continuous hierarchy has a location-dependent luminosity function, (M). Within uncertainties as to the steepness of (M) at the bright end, the model is consistent with optical number counts to a limiting photographic magnitudem _pg (isotropic slope,q=0.6; semicontinuous modelq=0.64; observation,q=0.67±0.03, standard error.) this removes the discrepancy between the determinations by de Vaucouleurs and Sandageet al. of the thinning factor (1.7). Predictions of the semi-continuous model are made which are at present observationally feasible to carry out. In particular, it is predicted thatq(20<|M|<22)/q(14<|M|<19)2(±0.2).     

A spectrophotometric study of galaxies with UV excess

We present the results of a spectral study of 17 galaxies with UV excess from the lists of [1–3]. We determine the equivalent widths of lines, the relative intensities of emission lines for 3 galaxies, the electron densities of the gas components of 9 galaxies, and the gas masses of 2 galaxies. It is shown that the gas component of Galaxy No. 235 has extremely low excitability. In the spectrum of this galaxy the lines [Fell] 4951, 4947 are seen to be distinct, not merging with the line [OIII] 4959. The line H in the spectrum of Galaxy No. 128 has two emission peaks, which seem to have been formed by an absorption component midway between the lines. The line H in the spectrum of Galaxy No. 350 is detected both in emission and absorption, the absorption component lying in the longwave part of the line.Translated fromAstrofizika, Vol. 37, No. 3, 1994.     

The contribution of normal galaxies to the low energy gamma-ray cosmic diffuse background

Theories to explain the origin of the cosmic diffuse -ray background generally fall into one of two broad categories: those which attribute the emission to particle interctions in intergalactic space and those which attribute it to the summation of numerous, unresolved discrete sources, including normal field galaxies, active galactic nuclei and clusters of galaxies. Strong support for the latter interpretation is given by recent measurements of -ray emission from external galaxies, mainly Seyfert galaxies. Their summed contribution has been evaluated elsewhere; here instead, we use recent observational data on the -ray emission from our own galaxy to estimate the contribution of normal galaxies to the cosmic diffuse -radiation. Our result indicates that this contribution is limited to less than 0.1% and can therefore be neglected.     

Inverse radiative transfer problem with delta-Eddington phase function in a nonsymmetric model

A radiative transfer problem with the delta-Eddington phase function for a nonsymmetric model in a finite slab is considered. By an inverse treatment the albedosw, f, andg of the said phase function have been determined.     

The bimetric theory of gravitation with a dynamic background metric

We study the bimetric theory of gravitation with background metric _ik. In contrast to the accepted point of view, in which _ik, is a metric given a priori, we assume that _ik is a dynamic variable determined from the condition that the total action of the gravitating system must be an extremum. As a result it turns out that (1) _ik can be described by the Einstein equation in space-time with the metric _ik and (2) the energy-momentum tensor of the graviational field _ik, is the source of _ik. In this sense _ik can be considered a secondary field in relation to g_ik. We determine the conditions for existence of integral covariant conservation laws. Two of the latter have no analogs in the theory with the background metric given a priori.Translated fromAstrofizika, Vol. 37, No. 3, 1994.The author is grateful to the participants in the seminar of the Department of Theoretical Physics at Erevan State University, and also to W. Bleier, K. A. Bronnikov, V. N. Mel'nikov, and G. Yu. Treder for discussions and valuable remarks. The investigations presented in this paper were partly financed by the International Scientific Fund, grant Ph1-262-0902.     

Damping constant and turbulence in the solar atmosphere

In the region of the formation of weak and medium-strong lines, the microturbulence increases with height (V _ver=0.7–0.9 km s^-1, V _hor= 1.1–1.5 km s^-1), the macroturbulence decreases (V _ver=1.6–1.4 km s^-1, V _hor= 2.4–1.5 km s^-1), and the total velocity field (vertical component) is depth-independent (1.7 km s^-1). The empirical damping constants for Fe, Ti, Cr, Ni lines are equal 1.3₆, 1.7₆, 1.6₆, 1.6₆, respectively. The correlation length (the Kubo-Anderson process has been used) in the solar photosphere is 520–550 km.     

A hypothesis to explain the virial discrepancy in clusters of galaxies

On the basis of numerical experiments onn-body binding energies we tentatively consider the following hypothesis: If the distance between two galaxies forming a binary system isa _g, and a cluster of galaxies that is substructured in a hierarchical fashion onall scales froma _g upwards has a total massM, then the total gravitational binding energy of the cluster is _TH = –GM ²/2a _g . As an explanation for missing masses up to order 100 we test this hypothesis in three different ways, finding remarkable agreement with observation, with no need for physical missing mass.     

The distribution law of stellarp-modes

We show that the overall densityg() of asymptotic acoustic frequencies of a star obeys a Weyl lawg() ^D–1, whereD is the dimensionality of the oscillating stellar configuration. For realistic stars with a finite non-zero surface sound speed,D is equal to the actual dimensionality of the star,D=3. For formal models with a vanishing sound velocity at the surface, heuristic arguments lead to a dimensionality parameterD=4.5. The empirical frequencies of Eddington's standard model are found to be consistent with the latter distribution, with reasonable agreement already occurring in the low-frequency range > _i 2× fundamental radial mode. We argue that real stars obey this 3.5-power law in some finite frequency interval _i << _f , _f being a very high frequency critically depending on the surface sound velocity, while the full asymptotic law, withD=3, holds for > _f .     

Estimates of proton energies in extragalactic radio sources

It is shown that inelastic proton collisions in extragalactic radio sources can account for their radio and -ray emissions. The proton Lorentz-factor _p responsible for -ray emission is estimated to lie between 1.4 and 86. But for the radio emission (with _e ~ 10³-10⁴) the estimated _p values lie between 7 to 300. The estimates of total particle and magnetic energy for a typical radio source is in agreement with equipartition theory.     

Simulation for electron acceleration by DC electric field in the presence of ion sound waves and associated hard X-ray emission

Time-dependent Fokker-Planck equation was numerically solved to demonstrate the dynamics of electrons in a uniform coronal loop with an applied axial DC electric field in the presence of ion-sound waves. This electric field is attributed to an anomalous resistivity due to the ion-sound turbulence caused by an initially given critical current density.The electron momentum distribution becomes a steady state in the whole turbulent region in a short time for which some electrons can be accelerated to the maximum electric potential K _c. The steady energy distribution of electrons flowing out the end of the turbulent region has a very hard power-law-like spectrum with an index of about 0.75. The associated hard X-rays from a thick target also show a hard spectrum with a photon spectral index of 1.3. In order for to be much greater as observed in impulsive X-ray bursts, it is required that the source is a sum of many elementary loops with a power-law-like distribution in K _c with an index = – + 2.5.     

Local Field of Galaxy Velocities

A sample of 145 galaxies having radial velocities relative to the centroid of the Local Group V _LG < 500 km/sec and estimated photometric distances D < 8 Mpc is considered. The field of peculiar velocities of these galaxies is estimated using the tensor of the local value of the Hubble constant H _ij , with principal values of 81:62:48 in km/sec·Mpc, which have a standard error of 4 km/sec·Mpc. The minor axis of the Hubble ellipsoid is oriented almost along the polar axis of the Local Supercluster, while the major axis forms an angle = (29 ± 5)° with the direction toward the center of the Virgo Cluster. Such a configuration of the peculiar-velocity field shows unsatisfactory agreement with the model of a spherically symmetric flow of galaxies toward the Virgo Cluster. Rotation of the Local Supercluster may be one reason for this difference. The peculiar velocities of galaxies within a volume with D < 8 Mpc are characterized by a dispersion _V = 74 km/sec, a considerable part of which is due to the virial motions of galaxies in groups and to distance errors. For field galaxies, located in a layer of 1 < D < 3 Mpc around the Local Group, the radial-velocity dispersion does not exceed 25 km/sec. The velocity—distance relation, constructed from the 20 closest galaxies around the Local Group with D < 3 Mpc and with errors (D) < 0.2 Mpc, exhibits the expected effect of gravitational deceleration. Using the estimate of R ₀ = (0.96 ± 0.05) Mpc for the observed radius of the zero-velocity sphere, we determined the total mass of the Local Group to be (1.2 ± 0.2)·10¹² M , which agrees well with the sum of the virial masses of the subgroups of galaxies around the Local Group and M31. The ratio of the Local Group's total mass (within R ₀) to its luminosity is M/L = (23 ± 4) M /L , which does not require the existence of supermassive dark halos around our Galaxy and M31.     

Ion acoustic instability in the presence of plasma turbulence in the solar wind

The adiabatic theory of interaction between high and low frequency waves has been studied for the case of electron plasma oscillations and ion acoustic waves and the results are applied to the solar wind. The modified dispersion relation for ion acoustic waves has been derived, taking a Gaussian distribution for plasmons. Two limiting cases of the spectrum are studied. For a broad spectrum, the plasma turbulence has a destabilising effect by introducing a growth rate denoted by turbulence, which is positive for k ₀ > (m _e/ m _i )^1/2 _De ^–1 , k ₀ being the central wave numger of the spectrum, _De the electron Debye length. Also, even for v _d(drift velocity between electrons and ions) < c _s, we arrive at unstable ion acoustic modes. For narrow spectrum, the plasma turbulence has a stabilising effect.