Inverse Compton scattering in mildly relativistic plasma

We investigated the effect of inverse Compton scattering in mildly relativistic static and moving plasmas with low optical depth using Monte Carlo simulations, and calculated the Sunyaev-Zel'dovich effect in the cosmic background radiation. Our semi-analytic method is based on a separation of photon diffusion in frequency and real space. We use Monte Carlo simulation to derive the intensity and frequency of the scattered photons for a monochromatic incoming radiation. The outgoing spectrum is determined by integrating over the spectrum of the incoming radiation using the intensity to determine the correct weight. This method makes it possible to study the emerging radiation as a function of frequency and direction. As a first application we have studied the effects of finite optical depth and gas infall on the Sunyaev-Zel'dovich effect (not possible with the extended Kompaneets equation) and discuss the parameter range in which the Boltzmann equation and its expansions can be used. For high temperature clusters ($k_B T_e \gtrsim 15$ keV) relativistic corrections based on a fifth order expansion of the extended Kompaneets equation seriously underestimate the Sunyaev-Zel'dovich effect at high frequencies. The contribution from plasma infall is less important for reasonable velocities. We give a convenient analytical expression for the dependence of the cross-over frequency on temperature, optical depth, and gas infall speed. Optical depth effects are often more important than relativistic corrections, and should be taken into account for high-precision work, but are smaller than the typical kinematic effect from cluster radial velocities.Comment: LateX, 30 pages and 11 figures. Accepted for publication in the Astrophysical Journa

Scattering in the inner accretion disk and the waveforms and polarization of millisecond flux oscillations in LMXBs

The scattering by the inner accretion disk of X-ray radiation generated near the surface of a spinning neutron star in a low-mass X-ray binary (LMXB) has observable effects on the waveforms of millisecond X-ray flux oscillations produced e.g. during type-I bursts or in the millisecond pulsar SAX J1808.4--3658. We study these effects in the framework of a simplified model in which there is a single emitting spot on the stellar surface, which is visible both directly and in X-rays scattered from the disk. The main signature of scattering from a thin disk is that the pulse of scattered flux leads (if the star rotates in the same sense as the disk) or lags (in the contrary case) the primary pulse of direct emission by a quarter of a spin cycle. This is caused by Doppler boosting of radiation in the sub-relativistic Keplerian flow. The disk-scattered flux is revealed better in energy-resolved waveforms and the phase dependence of the polarized flux component. The phenomenon discussed permits direct testing of the presence of standard thin disks near the neutron stars in LMXBs and should be observable with future X-ray timing experiments having a few times better sensitivity than RXTE and also with sensitive X-ray polarimeters

Constraining the past X-ray luminosity of AGN in clusters of galaxies: the role of resonant scattering

Only a small fraction of galactic nuclei in the nearby universe are luminous, while most of them are currently dim. We investigate the feasibility of constraining the X-ray luminosity in the recent past (up to ~10^6 years ago) of the nucleus of a cluster dominant galaxy by measuring the contribution of scattered nuclear radiation to the surface brightness of the intracluster gas dominated by thermal emission. We show that resonance X-ray lines present advantage over the continuum near the lines, because the relative contribution of scattered radiation is typically larger in the line case by a significant factor of the order of 3-10. As an example, we estimate the level of constraints that could be derived from future fine spectroscopic observations on the past X-ray luminosity of the nearby M87 and Cyg A active galaxies. For comparison we show that already available XMM-Newton and Chandra data on the continuum emission from the X-ray haloes around these galaxies enable obtaining an order of magnitude weaker upper limits on their past luminosity. A similar method can be applied to distant powerful quasars (at redshifts z>1) if they have cluster-like gaseous coronae, as suggested by Rosat and Chandra observations of active galaxies at z> kT/(1+z) (where T is the gas temperature) should be dominated by redshifted scattered radiation from the quasar. Therefore, measurements with the next generation of X-ray telescopes could give information on the lifetime of quasars and parameters of the hot gas around them

The Sunyaev-Zeldovich Effect and Its Cosmological Significance

Comptonization of the cosmic microwave background (CMB) radiation by hot gas in clusters of galaxies - the Sunyaev-Zeldovich (S-Z) effect - is of great astrophysical and cosmological significance. In recent years observations of the effect have improved tremendously; high signal-to-noise images of the effect (at low microwave frequencies) can now be obtained by ground-based interferometric arrays. In the near future, high frequency measurements of the effect will be made with bolomateric arrays during long duration balloon flights. Towards the end of the decade the PLANCK satellite will extensive S-Z surveys over a wide frequency range. Along with the improved observational capabilities, the theoretical description of the effect and its more precise use as a probe have been considerably advanced. I review the current status of theoretical and observational work on the effect, and the main results from its use as a cosmological probe.Comment: Invited review; in proceedings of the Erice NATO/ASI `Astrophysical Sources of High Energy Particles and Radiation'; 11 pages, 3 figure

About the measurements of the hard X-ray background

We analyze uncertainties in the cosmic X-ray background measurements performed by the INTEGRAL observatory. We find that the most important effect limiting the accuracy of the measurements is related to the intrinsic background variation in detectors. Taking into account all of the uncertainties arising during the measurements we conclude that the X-ray background intensity obtained in the INTEGRAL observations is compatible with the historic X-ray background observations performed by the HEAO-1 satellite.Comment: 20 pages, 4 figures, accepted for publication in Astrophysics and Space Scienc

Sunyaev-Zel'dovich Effect by Multiple Sctattering : Numerical Solution of the Transfer Equations

The radiative transfer equations for multiple inverse Compton scattering of the Cosmic Microwave Background Radiation (CMBR) by the hot intra-cluster electrons are solved numerically. The spherical isothermal and inhomogeneous $\beta$ model has been considered for the electron distribution. The anisotropy of the CMBR caused by scattering, known as thermal Sunyaev-Zel'dovich effect, along the radial axis of the medium is compared with the analytical solution of Kompaneets equation. The X-ray data of several clusters of galaxies at low redshifts provide an estimation of the central electron density $n_0$ to be of the order $10^{-3}$. It is found that for this value of $n_0$ the effect of multiple scattering is negligible. The numerically calculated anisotropy along the radial axis matches well with the analytical solution that describes single scattering. The result incorporating multiple scattering is fitted with the recent observation of Sunyaev-Zel'dovich effect in the cluster Abell 2163. It is shown that if $n_0$ is greater by an order of magnitude, which could be possible for cluster of galaxies at comparatively higher redshift, multiple scattering would play a significant role at the Wien region of the anisotropy spectrum. A fitting formula for the correction to the Sunyaev-Zel'dovich effect due to multiple scattering is provided.Comment: 9 pages, Latex, ws-ijmpa style (cls file included), 3 postscript figures, Accepted for publication by International Journal of Modern Physics

The profile of a narrow line after single scattering by Maxwellian electrons: relativistic corrections to the kernel of the integral kinetic equation

The frequency distribution of photons in frequency that results from single Compton scattering of monochromatic radiation on thermal electrons is derived in the mildly relativistic limit. Algebraic expressions are given for (1) the photon redistribution function, K(nu,Omega -> nu',Omega'), and (2) the spectrum produced in the case of isotropic incident radiation, P(nu -> nu'). The former is a good approximation for electron temperatures kT_e < 25 keV and photon energies hnu < 50 keV, and the latter is applicable when hnu(hnu/m_ec^2) < kT_e < 25 keV, hnu < 50 keV. Both formulae can be used for describing the profiles of X-ray and low-frequency lines upon scattering in hot, optically thin plasmas, such as present in clusters of galaxies, in the coronae of accretion disks in X-ray binaries and AGNs, during supernova explosions, etc. Both formulae can also be employed as the kernels of the corresponding integral kinetic equations (direction-dependent and isotropic) in the general problem of Comptonization on thermal electrons. The K(nu,Omega -> nu',Omega') kernel, in particular, is applicable to the problem of induced Compton interaction of anisotropic low-frequency radiation of high brightness temperature with free electrons in the vicinity of powerful radiosources and masers. Fokker-Planck-type expansion (up to fourth order) of the integral kinetic equation with the P(nu -> nu') kernel derived here leads to a generalization of the Kompaneets equation. We further present (1) a simpler kernel that is necessary and sufficient to derive the Kompaneets equation and (2) an expression for the angular function for Compton scattering in a hot plasma, which includes temperature and photon energy corrections to the Rayleigh angular function.Comment: 29 pages, 17 figures, accepted for publication in ApJ, uses emulateapj.sty, corrects misprints in previous astro-ph versio

Phase diagram of Eu magnetic ordering in Sn-flux-grown Eu(Fe1−x_{1-x}Cox_{x})2_{2}As2_{2} single crystals

The magnetic ground state of the Eu$^{2+}$ moments in a series of Eu(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ single crystals grown from the Sn flux has been investigated in detail by neutron diffraction measurements. Combined with the results from the macroscopic properties (resistivity, magnetic susceptibility and specific heat) measurements, a phase diagram describing how the Eu magnetic order evolves with Co doping in Eu(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ is established. The ground-state magnetic structure of the Eu$^{2+}$ spins is found to develop from the A-type antiferromagnetic (AFM) order in the parent compound, via the A-type canted AFM structure with some net ferromagnetic (FM) moment component along the crystallographic $\mathit{c}$ direction at intermediate Co doping levels, finally to the pure FM order at relatively high Co doping levels. The ordering temperature of Eu declines linearly at first, reaches the minimum value of 16.5(2) K around $\mathit{x}$ = 0.100(4), and then reverses upwards with further Co doping. The doping-induced modification of the indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the Eu$^{2+}$ moments, which is mediated by the conduction $\mathit{d}$ electrons on the (Fe,Co)As layers, as well as the change of the strength of the direct interaction between the Eu$^{2+}$ and Fe$^{2+}$ moments, might be responsible for the change of the magnetic ground state and the ordering temperature of the Eu sublattice. In addition, for Eu(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ single crystals with 0.10 $\leqslant$ $\mathit{x}$ $\leqslant$ 0.18, strong ferromagnetism from the Eu sublattice is well developed in the superconducting state, where a spontaneous vortex state is expected to account for the compromise between the two competing phenomena.Comment: 10 pages, 9 figure

Backward asymmetry of the Compton scattering by an isotropic distribution of relativistic electrons: astrophysical implications

The angular distribution of low-frequency radiation after single scattering by an isotropic distribution of relativistic electrons considerably differs from the Rayleigh angular function. In particular, the scattering by an ensemble of ultra-relativistic electrons obeys the law p=1-cos(alpha), where alpha is the scattering angle; hence photons are preferentially scattered backwards. We discuss some consequences of this fact for astrophysical problems. We show that a hot electron-scattering atmosphere is more reflective than a cold one: the fraction of incident photons which become reflected having suffered a single scattering event can be larger by up to 50 per cent in the former case. This should affect the photon exchange between cold accretion disks and hot coronae or ADAF flows in the vicinity of relativistic compact objects; as well as the rate of cooling (through multiple inverse-Compton scattering of seed photons supplied from outside) of optically thick clouds of relativistic electrons in compact radiosources. The forward-backward scattering asymmetry also causes spatial diffusion of photons to proceed slower in hot plasma than in cold one, which is important for the shapes of Comptonization spectra and the time delays between soft and hard radiations coming from variable X-ray sources.Comment: 20 pages, 3 figures, to appear in Astronomy Letters, added reference