38 research outputs found
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 \,keV exerts a significant influence on
the vertical structure of the accretion disk at a distance
\,cm from the neutron star. At a distance \,cm,
where the total surface density in the disk reaches
\,g\,cm, 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
\,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 \,% accuracy in the range of X-ray photon
energies \,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