Analytical Study on the Sunyaev-Zeldovich Effect for Clusters of Galaxies. II. comparison of covariant formalisms

We study a covariant formalism for the Sunyaev-Zeldovich effects developed in the previous papers by the present authors, and derive analytic expressions for the redistribution functions in the Thomson approximation. We also explore another covariant formalism recently developed by Poutanen and Vurm. We show that the two formalisms are mathematically equivalent in the Thomson approximation which is fully valid for the cosmic microwave background photon energies. The present finding will establish a theoretical foundation for the analysis of the Sunyaev-Zeldovich effects for the clusters of galaxies.Comment: Accepted version, 7 pages, 1 figure, accepted by Physical Review D for publicatio

On the Origin of Polarization near the Lyman Edge in Quasars

Optical/UV radiation from accretion disks in quasars is likely to be partly scattered by a hot plasma enveloping the disk. We investigate whether the scattering may produce the steep rises in polarization observed blueward of the Lyman limit in some quasars. We suggest and assess two models. In the first model, primary disk radiation with a Lyman edge in absorption passes through a static ionized "skin" covering the disk, which has a temperature about 3 keV and a Thomson optical depth about unity. Electron scattering in the skin smears out the edge and produces a steep rise in polarization at lambda < 912 A. In the second model, the scattering occurs in a hot coronal plasma outflowing from the disk with a mildly relativistic velocity. We find that the second model better explains the data. The ability of the models to fit the observed rises in polarization is illustrated with the quasar PG 1630+377.Comment: submitted to ApJ Letter

Sources of Radiation in the Early Universe: The Equation of Radiative Transfer and Optical Distances

We have derived the radiative-transfer equation for a point source with a specified intensity and spectrum, originating in the early Universe between the epochs of annihilation and recombination, at redshifts z_\s =10^8\div 10^4. The direct radiation of the source is separated from the diffuse radiation it produces. Optical distances from the source for Thomson scattering and bremsstrahlung absorption at the maximum of the thermal background radiation are calculated as a function of the redshift z.The distances grow sharply with decreasing z, approaching asymptotic values, the absorption distance increasing more slowly and reaching their limiting values at lower z. For the adopted z values, the optical parameters of the Universe can be described in a flat model with dusty material and radiation, and radiative transfer can be treated in a grey approximation.Comment: 14 pages, 2 figure

Zeldovich flow on cosmic vacuum background: new exact nonlinear analytical solution

A new exact nonlinear Newtonian solution for a plane matter flow superimposed on the isotropic Hubble expansion is reported. The dynamical effect of cosmic vacuum is taken into account. The solution describes the evolution of nonlinear perturbations via gravitational instability of matter and the termination of the perturbation growth by anti-gravity of vacuum at the epoch of transition from matter domination to vacuum domination. On this basis, an `approximate' 3D solution is suggested as an analog of the Zeldovich ansatz.Comment: 9 pages, 1 figure

The converging inflow spectrum is an intrinsic signature for a black hole: Monte-Carlo simulations of Comptonization on free-falling electrons

An accreting black hole is, by definition, characterized by the drain. Namely, the matter falls into a black hole much the same way as water disappears down a drain - matter goes in and nothing comes out. As this can only happen in a black hole, it provides an unique way to see it. The accretion proceeds almost in free fall close to the black hole horizon. In this paper we calculate (by using Monte -Carlo simulations) the specific features of X-ray spectra formed as a result of upscattering of the soft (disk) photons in the converging inflow (CI) within about 3 Schwarzschild radii of the black hole. The full relativistic treatment has been implemented to reproduce these spectra. We show that spectra in the soft state of black hole systems can be described as the sum of a thermal (disk) component and the convolution of some fraction of this component with the CI upscattering spread function. The latter boosted photon component is seen as an extended power-law at energies much higher than the characteristic soft photons energy. We demonstrate the stability of the power spectral index (alpha= 1.8) over a wide range of the plasma temperature 0-10 keV and mass accretion rates (higher than 2 in Eddington units). We also demonstrate that the sharp high energy cutoff occurs at energies of 200-400 keV which are related to the average rest energy of electrons impinging upon the horizon. The spectrum is practically identical to the standard thermal Comptonization spectrum when the CI plasma temperature is getting of order of 50 keV (hard state of BHS). Also, the change of spectral shapes from the soft to the hard X-ray state is clearly to be related with the temperature of the bulk flow. These Monte-Carlo simulated CI spectra are then a inevitable stamp of the BHS.Comment: 30 pages TeX format, 6 PS figures, accepted for ApJ Main Journa

Relativistic Kinetic Equation for Induced Compton Scattering of Polarized Radiation

The relativistic kinetic equations describing time evolution and space dependence of the density matrices of polarized photons and electrons interacting via Compton scattering are deduced from the quantum Liouville equation. The induced scattering and exclusion principle are taken into account. The Bogoliubov method is used in the frame of quantum electrodynamics. The equation for polarized radiation scattered by unpolarized electrons is considered as a particular case and is reformulated in terms of the Stokes parameters. The expressions for the scattering amplitudes and cross-sections are derived simultaneously.Comment: 19 pages; Astronomy & Astrophysics, in pres

Compton Scattering by Static and Moving Media I. The Transfer Equation and Its Moments

Compton scattering of photons by nonrelativistic particles is thought to play an important role in forming the radiation spectrum of many astrophysical systems. Here we derive the time-dependent photon kinetic equation that describes spontaneous and induced Compton scattering as well as absorption and emission by static and moving media, the corresponding radiative transfer equation, and their zeroth and first moments, in both the system frame and in the frame comoving with the medium. We show that it is necessary to use the correct relativistic differential scattering cross section in order to obtain a photon kinetic equation that is correct to first order in epsilon/m_e, T_e/m_e, and V, where epsilon is the photon energy, T_e and m_e are the electron temperature and rest mass, and V is the electron bulk velocity in units of the speed of light. We also demonstrate that the terms in the radiative transfer equation that are second-order in V usually should be retained, because if the radiation energy density is sufficiently large compared to the radiation flux, the effects of bulk Comptonization described by the terms that are second-order in V are at least as important as the effects described by the terms that are first-order in V, even when V is small. Our equations are valid for systems of arbitrary optical depth and can therefore be used in both the free-streaming and the diffusion regimes. We demonstrate that Comptonization by the electron bulk motion occurs whether or not the radiation field is isotropic or the bulk flow converges and that it is more important than thermal Comptonization if V^2 > 3 T_e/m_e.Comment: 31 pages, accepted for publication in The Astrophysical Journa

Vertical Structure of the Outer Accretion Disk in Persistent Low-Mass X-Ray Binaries

We have investigated the influence of X-ray irradiation on the vertical structure of the outer accretion disk in low-mass X-ray binaries by performing a self-consistent calculation of the vertical structure and X-ray radiation transfer in the disk. Penetrating deep into the disk, the field of scattered X-ray photons with energy $E\gtrsim10$\,keV exerts a significant influence on the vertical structure of the accretion disk at a distance $R\gtrsim10^{10}$\,cm from the neutron star. At a distance $R\sim10^{11}$\,cm, where the total surface density in the disk reaches $\Sigma_0\sim20$\,g\,cm$^{-2}$, X-ray heating affects all layers of an optically thick disk. The X-ray heating effect is enhanced significantly in the presence of an extended atmospheric layer with a temperature $T_{atm}\sim(2\div3)\times10^6$\,K above the accretion disk. We have derived simple analytic formulas for the disk heating by scattered X-ray photons using an approximate solution of the transfer equation by the Sobolev method. This approximation has a $\gtrsim10$\,% accuracy in the range of X-ray photon energies $E<20$\,keV.Comment: 19 pages, 8 figures, published in Astronomy Letter

Non-LTE Models and Theoretical Spectra of Accretion Disks in Active Galactic Nuclei. IV. Effects of Compton Scattering and Metal Opacities

We extend our models of the vertical structure and emergent radiation field of accretion disks around supermassive black holes described in previous papers of this series. Our models now include both a self-consistent treatment of Compton scattering and the effects of continuum opacities of the most important metal species (C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe, Ni). With these new effects incorporated, we compute the predicted spectrum from black holes accreting at nearly the Eddington luminosity (L/L_Edd = 0.3) and central masses of 10^6, 10^7, and 10^8 M_sun. We also consider two values of the Shakura-Sunyaev alpha parameter, 0.1 and 0.01. Although it has little effect when M > 10^8 M_sun, Comptonization grows in importance as the central mass decreases and the central temperature rises. It generally produces an increase in temperature with height in the uppermost layers of hot atmospheres. Compared to models with coherent electron scattering, Comptonized models have enhanced EUV/soft X-ray emission, but they also have a more sharply declining spectrum at very high frequencies. Comptonization also smears the hydrogen and the He II Lyman edges. The effects of metals on the overall spectral energy distribution are smaller than the effects of Comptonization for these parameters. Compared to pure hydrogen-helium models, models with metal continuum opacities have reduced flux in the high frequency tail, except at the highest frequencies, where the flux is very low. Metal photoionization edges are not present in the overall disk-integrated model spectra. In addition to our new grid of models, we also present a simple analytic prescription for the vertical temperature structure of the disk in the presence of Comptonization, and show under what conditions a hot outer layer (a corona) is formed.Comment: 22 pages, Latex. 19 figures. Uses corrected version of emulateapj.sty and apjfonts.sty (included). Accepted for publication in Ap