Asymptotic solutions of the viscous solar wind equations

There is one and only one solution of the viscous solar wind equations which is asymptotically represented for large distances from the sun by a formal solution of Y. C. Whang, C. K. Liu, and C. C. Chang as a power series in the inverse one third power of the distance.     

Non-thermal shielding effects on the Compton scattering power in astrophysical plasmas

The non-thermal shielding effects on the inverse Compton scattering are investigated in astrophysical non-thermal Lorentzian plasmas. The inverse Compton power is obtained by the modified Compton scattering cross section in Lorentzian plasmas with the blackbody photon distribution. The total Compton power is also obtained by the Lorentzan distribution of plasmas. It is found that the influence of non-thermal character of the plasma suppresses the inverse Compton power in astrophysical Lorentzian plasmas. It is also found that the non-thermal effect on the inverse Compton power decreases with an increase of the temperature. In addition, the non-thermal effect on the total Compton power with Lorentzan plasmas increases in low-temperature photons and, however, decreases in intermediate-temperature photons with increasing Debye length. The variation of the total Compton power is also discussed.     

The power of blazar jets

We estimate the power of relativistic, extragalactic jets by modelling the spectral energy distribution of a large number of blazars. We adopt a simple one-zone, homogeneous, leptonic synchrotron and inverse Compton model, taking into account seed photons originating both locally in the jet and externally. The blazars under study have an often dominant high-energy component which, if interpreted as due to inverse Compton radiation, limits the value of the magnetic field within the emission region. As a consequence, the corresponding Poynting flux cannot be energetically dominant. Also the bulk kinetic power in relativistic leptons is often smaller than the dissipated luminosity. This suggests that the typical jet should comprise an energetically dominant proton component. If there is one proton per relativistic electrons, jets radiate around 2–10 per cent of their power in high-power blazars and 3–30 per cent in less powerful BL Lacs.     

Inverse Compton scattering – revisited

The inverse Compton scattering of high energy electrons by photons is discussed and a simple derivation of the total power radiated is presented. The derivation is completely classical and exhibits clearly why similar formulas are applicable in the case of inverse compton scattering and synchroton radiation.     

BeppoSAX observations of 1-Jy BL Lacertae objects – I

We present new BeppoSAX observations of seven BL Lacertae objects selected from the 1-Jy sample plus one additional source. The collected data cover the energy range     (observer's frame), reaching ∼50 keV for one source (BL Lac). All sources characterized by a peak in their multifrequency spectra at infrared/optical energies (i.e., of the low-energy peaked BL Lac type, LBL) display a relatively flat     X-ray spectrum, which we interpret as inverse Compton emission. Four objects (two-thirds of the LBLs) show some evidence for a low-energy steepening, which is probably due to the synchrotron tail merging into the inverse Compton component around ∼     . If this were generally the case with LBLs, it would explain why the     ROSAT spectra of our sources are systematically steeper than the BeppoSAX ones     . The broad-band spectral energy distributions fully confirm this picture, and a synchrotron inverse Compton model allows us to derive the physical parameters (intrinsic power, magnetic field, etc.) of our sources. Combining our results with those obtained by BeppoSAX on BL Lacs covering a wide range of synchrotron peak frequency, ν _peak, we confirm and clarify the dependence of the X-ray spectral index on ν _peak originally found in ROSAT data.     

Relativistic large-scale jets and minimum power requirements

The recent discovery, by the Chandra satellite, that jets of blazars are strong X-ray emitters at large scales     , lends support to the hypothesis that emitting plasma is still moving at highly relativistic speeds on these scales. In this case in fact the emission via inverse Compton scattering off cosmic background photons is enhanced and the resulting predicted X-ray spectrum accounts well for the otherwise puzzling observations. Here we point out another reason to favour relativistic large-scale jets, based on a minimum power argument: by estimating the Poynting flux and bulk kinetic powers corresponding to, at least, the relativistic particles and magnetic field responsible for the emission, one can derive the value of the bulk Lorentz factor for which the total power is minimized. It is found that both the inner and extended parts of the jet of PKS     satisfy such a condition.     

A comment on some oscillatory models of adiabatic stars

Three different oscillatory models of adiabatic stars are reinvestigated. These are the homogenous model, the inverse square model and the Roche model. The ratio between the amplitude of the oscillations and the distance from the center is developed in a power series. For physical conclusions to be drawn, it turns out to be crucial if the power series is divergent or convergent. Mathematical arguments are given which show that the power series are really divergent for all three models.     

Hyper-elliptic orbits

A survey of classes of elliptical orbits outside the usual ones due to the attractive direct power and inverse square force laws reveals some extremely interesting orbits with surprising dynamical characteristics. Particular elliptical orbits of interest in celestial mechanics are discussed.     

A classical derivation of inverse Compton radiation

A classical method is used to derive formulas describing inverse Compton radiation in vacuo. It is shown that several expressions, including the power radiated and the rate at which photons are scattered, can be calculated exactly for the case of isotropically distributed unpolarized waves scattered by particles with any energy.     

Propagation of blast waves in Roche model

A non-similarity solution for propagation of magnetogasdynamic blast waves in Roche model is obtained. The density outside the central core varies according to some inverse power of distance from the centre of explosion. The strength of the shock surface heading the disturbance as well as the total energy of the wave vary with time.     

Symbolic analytical developments of the zero pressure cosmological model of the universe

In the present paper, literal analytical solutions in power series forms are developed for the radius of curvature and the expansion velocity of the zero pressure cosmological models of the universe at any time t. Also, we develop literal analytical solutions in power series forms for the inverse problem of the zero pressure cosmological model, that is to find the time $t=\tilde{t}$ (say) at which the radius of curvature of the model $R=\tilde{R}$ (say) is known. The importance of these analytical power series representations is that, they are invariant under many operations because, addition, multiplication, exponent ion, integration, different ion, etc of a power series is also a power series. A fact which provides excellent flexibility in dealing with analytical as well as computational developments of the problems related to zero pressure cosmological models.For computational developments of these solutions, an efficient method using continued fraction theory is provided. By means of the present methods we able to analyze some known zero-pressure cosmological models, of these are Einstein and De Sitter models. In addition we also analyzed some other models by which one can know if the universe keep expanding forever, or will it reach a maximal size and then turn into contraction stage.     

Theory of relativistic hydrodynamic fluctuations before H-recombination

Using a previously developed relativistic extension of the Landau-Lifshitz theory of hydrodynamic fluctuations, the spectrum of energy density fluctuations before hydrogen recombination is calculated both for the radiation-dominated and the matter-dominated cases. The spectrum consists of a high frequency adiabatic and a low frequency isobar part. The isobar part is proportional to the inverse proton number density multiplied by the squared ratio of the rest energy density and the radiation energy density in the radiation dominated era. In the matter dominated era it is proportional to the inverse proton number density.The adiabatic part is proportional to the inverse photon number density in both cases. In the spectrum of temperature fluctuations the adiabatic part is the dominating one.The general part of the analysis is performed within a gauge invariant formalism.     

Performance characteristics of TreePM codes

We present a detailed analysis of the error budget for the TreePM method for doing cosmological N-body simulations. It is shown that the choice of filter for splitting the inverse square force into short and long range components suggested in Bagla [Bagla, J.S., 2002a. JApA 23, 185; Bagla, J.S., 2002b. Preprint. To appear in Proceedings of the Numerical Simulations in Astrophysics, Tokyo, July 2002] is close to optimum. We show that the error in the long range component of the force contributes very little to the total error in force. Errors introduced by the tree approximation for the short range force are different from those for the inverse square force, and these errors dominate the total error in force. We calculate the distribution function for error in force for clustered and unclustered particle distributions. This gives an idea of the error in realistic situations for different choices of parameters of the TreePM algorithm. We test the code by simulating a few power law models and checking for scale invariance.     

Nonlinear methods of statistic simulation of virtual parameter values for investigating uncertainties in orbits determined from observations

Determination of orbital parameters from observations is formally a nonlinear inverse problem for solving which evidently nonlinear methods are required. Meanwhile, an accompanying stage in solving the inverse problem is the evaluation of parametric accuracy to which, however, linear methods are conventionally applied. This is quite justified if parametric errors caused by observation errors are rather small, otherwise this is not at all since the nonlinearity of the inverse problem can be considerable to influence on the evaluations of parametric accuracy especially when the observations are very few. With the advent of quick-operating and multiprocessor computers, recently one tends to employ statistic simulation of virtual parameter values for investigating uncertainties in orbits determined from observations. In the paper are just discussed the methods designed specially for nonlinear statistic simulation of virtual parameter values. Their efficiency is investigated in application to estimating uncertainties in the orbit of Jovian satellite S/2003 J04 whose orbital parameters are ill-determined owing to scanty available observations. Indices of nonlinearity are introduced for making decision in the choice between linear and nonlinear methods.     

Canonical transformations depending on a small parameter

The concept of a Lie series is enlarged to encompass the cases where the generating function itself depends explicity on the small parameter. Lie transforms define naturally a class of canonical mappings in the form of power series in the small parameter. The formalism generates nonconservative as well as conservative transformations. Perturbation theories based on it offer three substantial advantages: they yield the transformation of state variables in an explicit form; in a function of the original variables, substitution of the new variables consists simply of an iterative procedure involving only explicit chains of Poisson brackets; the inverse transformation can be built the same way.     

Multichannel Three-Dimensional SOLA Inversion for Local Helioseismology

Inversions for local helioseismology are an important and necessary step for obtaining three-dimensional maps of various physical quantities in the solar interior. Frequently, the full inverse problems that one would like to solve prove intractable because of computational constraints. Due to the enormous seismic data sets that already exist and those forthcoming, this is a problem that needs to be addressed. To this end, we present a very efficient linear inversion algorithm for local helioseismology. It is based on a subtractive optimally localized averaging (SOLA) scheme in the Fourier domain, utilizing the horizontal-translation invariance of the sensitivity kernels. In Fourier space the problem decouples into many small problems, one for each horizontal wave vector. This multichannel SOLA method is demonstrated for an example problem in time–distance helioseismology that is small enough to be solved both in real and Fourier space. We find that both approaches are successful in solving the inverse problem. However, the multichannel SOLA algorithm is much faster and can easily be parallelized.     

Modelling of self-similar cylindrical shock wave in radiating magnetogasdynamics,I

Self-similar flows of a perfect gas behind a cylindrical blast wave with radiation heat flux in the presence of an azimuthal magnetic field have been investigated. The effects of radiation flux and magnetic field together on the other flow variables have been studied in the region of interest. The magnetic field and density distribution vary as an inverse power of radial distance from the axis of symmetry. The electrical conductivity of the gas is taken to be infinite. The total energy of the flow between the inner expanding surface and the shock is assumed to be constant. We also have supposed the gas to be grey and opaque and the shock to be transparent and isothermal.     

High-redshift Faranoff–Riley type II radio galaxies: X-ray properties of the cores

We present an extensive X-ray spectral analysis of the cores of 19 Faranoff–Riley type II sources in the redshift range 0.5 < z < 1.0 which were selected to be matched in isotropic radio power. The sample consists of 10 radio galaxies (RGs) and nine quasars. We compare our results with the expectations from a unification model that ascribes the difference between these two types of sources to the viewing angle to the line of sight, beaming and the presence of a dust and gas torus. We find that the spectrum of all the quasars can be fitted with a single power law, and that the spectral index flattens with decreasing angle to the line of sight. We interpret this as the effect of increasingly dominant inverse Compton X-ray emission, beamed such that the jet emission outshines other core components. For up to 70 per cent of the RGs we detect intrinsic absorption; their core spectra are best fitted with an unabsorbed steep power law of average spectral index Γ= 2.1 and an absorbed power law of spectral index Γ= 1.6, which is flatter than that observed for radio-quiet quasars (RQQs). We further conclude that the presence of a jet affects the spectral properties of absorbed nuclear emission in active galactic nuclei. In RGs, any steep-spectrum component of nuclear X-ray emission, similar to that seen in RQQs, must be masked by a jet or by jet-related emission.     

Time-dependent models for a decade of SN 1993J

A classical and a relativistic law of motion for a supernova remnant (SNR) are deduced assuming an inverse power law behavior for the density of the interstellar medium and applying the thin layer approximation. A third equation of motion is found in the framework of relativistic hydrodynamics with pressure, applying momentum conservation. These new formulas are calibrated against a decade of observations of SN 1993J. The existing knowledge of the diffusive processes of ultrarelativistic electrons is reviewed in order to explain the behavior of the ‘U’ shaped profile of intensity versus distance from the center of SN 1993J.