Compton Scattering in Static and Moving Media. II. System-Frame Solutions for Spherically Symmetric Flows

I study the formation of Comptonization spectra in spherically symmetric, fast moving media in a flat spacetime. I analyze the mathematical character of the moments of the transfer equation in the system-frame and describe a numerical method that provides fast solutions of the time-independent radiative transfer problem that are accurate in both the diffusion and free-streaming regimes. I show that even if the flows are mildly relativistic (V~0.1, where V is the electron bulk velocity in units of the speed of light), terms that are second-order in V alter the emerging spectrum both quantitatively and qualitatively. In particular, terms that are second-order in V produce power-law spectral tails, which are the dominant feature at high energies, and therefore cannot be neglected. I further show that photons from a static source are upscattered by the bulk motion of the medium even if the velocity field does not converge. Finally, I discuss these results in the context of radial accretion onto and outflows from compact objects.Comment: 28 pages, 9 figures; minor changes, to appear in the Astrophysical Journa

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

A high-frequency study of the Sunyaev-Zel'dovich effect morphology in galaxy clusters

High-frequency, high-resolution imaging of the Sunyaev-Zel'dovich (SZ) effect is an important technique to study the complex structures of the atmospheres of merging galaxy clusters. Such observations are sensitive to the details of the electron spectrum. We show that the morphology of the SZ intensity maps in simulated galaxy clusters observed at 345 GHz, 600 GHz, and 857 GHz are significantly different because of SZ relativistic corrections. These differences can be revealed by high-resolution imaging instruments. We calculate relativistically corrected SZ intensity maps of a simulated, massive, merging galaxy cluster and of the massive, merging clusters 1E0657-558 (the Bullet Cluster) and Abell 2219. The morphologies of the SZ intensity maps are remarkably different between 345 GHz and 857 GHz for each merging cluster. We show that high-resolution imaging observations of the SZ intensity maps at these frequencies, obtainable with the LABOCA and HERSCHEL-SPIRE instruments, allow to fully exploit the astrophysical relevance of the predicted SZ morphological effect.Comment: 9 pages, 14 figures, accepted for publication in MNRA

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

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

Diffusion compton dans un gaz d'électrons Maxwelliens

We develop the relativistic Boltzmann equation for photon transport with non coherent scattering in the form of a Fokker-Planck equation usable for thermal photons. We give an expression of the corresponding equation in the spherical harmonies approximation. Finally, we establish formulae for energy exchange between radiation and matter.On développe l'équation de Boltzmann relativiste applicable au transfert des photons avec diffusion non cohérente sous forme d'une équation de Fokker-Planck utilisable pour les photons thermiques. On donne l'expression des équations de transfert correspondant à l'approximation des harmoniques sphériques. Enfin, on établit diverses formules applicables à l'échange d'énergie matière-rayonnement