Asymmetry of compton scattering by relativistic electrons with an isotropic velocity distribution: Astrophysical implications

The angular distribution of low-frequency radiation after a single scattering by relativistic electrons with an isotropic velocity distribution differs markedly from the Rayleigh angular function. In particular, the scattering by an ensemble of ultrarelativistic electrons is described by the law p=1?cosα, where α is the scattering angle. Thus, photons are mostly scattered backward. We discuss some consequences of this fact for astrophysical problems. We show that a hot atmosphere of scattering electrons is more reflective than a cold one: the fraction of incident photons reflected after a single scattering can be larger than that in the former case by up to 50%. This must affect the photon exchange between cold accretion disks and hot coronae (or advective flows) near relativistic compact objects, as well as the rate of cooling (through multiple inverse-Compton scattering of the photons supplied from outside) of optically thick clouds of relativistic electrons in compact radio sources. Scattering asymmetry also causes the spatial diffusion of photons to proceed more slowly in a hot plasma than in a cold one, which affects the shapes of Comptonization spectra and the time delay in the detection of soft and hard radiation from variable X-ray sources.     

Gas heating inside radio sources to mildly relativistic temperatures via induced compton scattering

The measured brightness temperatures of the low-frequency synchrotron radiation from intense extragalactic sources reach 10¹¹–10¹² K. If there is some amount of nonrelativistic ionized gas within such sources, it must be heated through induced Compton scattering of the radiation. If cooling via inverse Compton scattering of the same radio radiation counteracts this heating, then the plasma can be heated up to mildly relativistic temperatures kT～10–100 keV. In this case, the stationary electron velocity distribution can be either relativistic Maxwellian or quasi-Maxwellian (with the high-velocity tail suppressed), depending on the efficiency of Coulomb collisions and other relaxation processes. We derive several simple approximate expressions for the induced Compton heating rate of mildly relativistic electrons in an isotropic radiation field, as well as for the stationary electron distribution function and temperature. We give analytic expressions for the kernel of the integral kinetic equation (one as a function of the scattering angle, and the other for an isotropic radiation field), which describes the photon redistribution in frequency through induced Compton scattering in thermal plasma. These expressions can be used in the parameter range [in contrast to the formulas written out previously in Sazonov and Sunyaev (2000), which are less accurate].     

Multiple compton scattering of electrons in a photon field

Consideration is given to the motion of electrons in a photon field of the monoenergetic or power-law spectrum under the conditions when the main mechanism of energy loss is the inverse Compton scattering by field photons. This process changes the primary spectrum of electrons and converts low-energy field photons to high-energy gamma-quanta for which the electron confinement region is assumed to be optically thin. The electron and gamma-ray spectra have been obtained in a wide energy interval including the Klein-Nishina and Thomson regions. A simple qualitative dependence of the solutions found on the field parameters and the primary spectrum of electrons has been established.The electron and gamma-ray spectra have been obtained by numerically solving the kinetic equation dependent on two variables: the energy of electrons and their path (or the time of motion) in a photon field. The results dramatically differ from the solution of the steady-state kinetic equation which depends only on the electron energy and is frequently used in the given problem.     

On induced Compton scattering by relativistic particles

Induced Compton scattering by independent relativistic particles in a radiation field is considered from both quantum mechanical and classical viewpoints. Quantum mechanically, the particle recoil causes an imperfect cancellation of the induced scattering rates between pairs of photon states. This results in a net energy transfer from the radiation field to the particle. Classically, the electrodynamical effects are manifestations of non-linear coupling between different wave amplitudes in the equation of motion. The results from these two approaches are related and shown to be equivalent.     

Compton scattering of relativistic electrons in compact X-ray sources

The problem of single Compton scattering is considered and the resulting spectrum, angular distribution and polarization of scattered photons in a general case are obtained. The inverse Compton scattering (ICS) for arbitrary energies of electronsE and photons ₀ is investigated in detail. In the case of isotropically-distributed initial photons and relativistic electrons, a strong rise of the scattered spectrum near the upper edge takes place, starting from the values of the characteristic parameterb4E ₀10 (in units of mc²=1). The energy-loss rate of relativistic electrons due to ICS is calculated. It is shown that the relativistic electrons of the energiesE100 MeV, when scattering on the X-rays with ₀~10KeV, transmit the dominant part of their energy to the photons which fall after scattering into the energy range of the electrons (100 MeV).The radiation spectrum of ICS, as well as the energy-losses of relativistic electrons distributed by power-lawE ^–, are calculated. The radiation spectrum reveals the power-law behaviour with the different indices in two limits: the dependence ^–(1)/2 at ₀1 gradually changes to ^–(+1) ln (₀) law for ₀1.     

The spectra of radiation and relativistic electrons formed by Compton scattering at non-zero particle fluxes

The formation of steady-state spectra of radiation or particles by Compton scattering is discussed for the case when the flux from the source is present. Power-law distributions, or those characterized by a power-law asymptotic behaviour, can appear under these conditions.The power indices and normalizations have been found as well as the flux directions for the electron and photon distributions in two cases. The first case is that of differential energy transfer over the electron spectrum (interaction with soft radiation). For the case of integrated transfer, relations have been found between the indices.The possibility of a power-law electron spectrum (with an index =2) has been shown for scattering by equilibrium radiation (the black-body background included).     

Induced Compton scattering by relativistic particles

Equations describing the evolution of isotropic distributions of unpolarized electromagnetic waves and of scattering of any energy due to spontaneous and induced Compton scattering are derived in the semi-classical approximation for unshielded particles.It is shown that induced Compton scattering of high frequency waves by relativistic electrons in synchrotron sources is a negligible effect contrary to the conclusions of Oster (1968b) and of Kaplan and Tsytovich (1969).     

Inverse compton scattering in anisotropic synchrotron sources

Models of compact, high brightness temperature sources such as quasars and active galactic nuclei often predict substantial inverse-compton scattered flux to be produced at high frequencies. As these fluxes are not observed, it is necessary to assume that extreme relativistic and/or anisotropic effects dominate the source. The often used equations to include these effects however are derived with several simplifying assumptions, which may not always be consistent with the derived source parameters (for example, the assumption of no time dependence in a violently variable quasar may not be appropriate). We therefore present here an explicit derivation of the dependence of the rate of inverse compton scattering on anisotropies in the source, to emphasise the importance and number of assumptions required in the derivation.     

Inverse compton scattering in a strong magnetic field

In this paper, I discuss inverse Compton scattering in a strong magnetic field. Using the standard technique in quantum electrodynamics, the solution of Dirac's equation for an electron in a uniform magnetic field and the accurate propagator of electron in a magnetic field, I have calculated the scattering matrix elements in the coordinate representation, the transition probabilities, and found the general formulae for the energy distribution of the scattered photons, and the differential and total scattering cross-sections.     

Inference of relativistic electron spectra from measurements of inverse compton radiation

The inference of relativistic electron spectra from spectral measurement of inverse Compton radiation is discussed for the case where the background photon spectrum is a Planck function. The problem is formulated in terms of an integral transform that relates the measured spectrum to the unknown electron distribution. A general inversion formula is used to provide a quantitative assessment of the information content of the spectral data. It is shown that the observations must generally be augmented by additional information if anything other than a rudimentary two or three parameter model of the source function is to be derived. It is also pointed out that since a similar equation governs the continuum spectra emitted by a distribution of black-body radiators, the analysis is relevant to the problem of stellar population synthesis from galactic spectra.     

Generalized compton effect and resonance scattering in astrophysical spectra

The analysis of the Skylab measurements on the ultraviolet limb spectra confirm the presence of a generalized Compton effect in the solar spectrum which can be explained by Thomson scattering theory. The present measurements on the Orion spectrum and interstellar line towards -Arae give a large generalized Compton effect which could be explained by a resonance scattering theory. These numerical results cannot be due to random errors in the measurements, as follows from the statistical discussion. The need for further measurements is pointed out.     

Compton attenuation coefficient in scattering by maxwellian electrons

Equations for the coefficient of attenuation of radiation due to Compton scattering by a thermal electron gas with an arbitrary temperature are summarized. A new representation is also obtained for the integral through which the attenuation coefficient, averaged over a relativistic, Maxwellian energy distribution of electrons, is expressed. This representation enables one to efficiently calculate the coefficient for a hightemperature electron gas. The accuracy of an approximate expression for the attenuation coefficient, corresponding to the assumption that scattering is isotropic in the rest frame of an electron, is also estimated. Translated from Astrofizika, Vol. 43, No. 3, pp. 473-482, July–September, 2000.     

Interplanetary type III radiobursts and relativistic electrons

For the time periods 1979 April 22–May 17 and 1980 May 9–June 10, when the HELIOS spacecraft were located inside 0.5 AU, we compared the antenna temperature T _A of the 466 kHz type III bursts measured by the SBH instrument on ISEE 3 with the fluxes of 0.5 MeV electrons measured by HELIOS. For 51 flare-associated kilometric type III bursts (FAIII bursts) with log(T _A) > 10 we find: (1) 25 bursts (49%) are accompanied by a relativistic electron event in interplanetary space, (2) the probability for detection of an electron event decreases from more than 74% inside a cone of ± 20 ° to 56% inside a cone of ± 60° around the flare site, (3) there is only a small correlation between the brightness temperature of the radio burst and the size of the electron event, and (4) despite the broad scatter of these values there is a clear indication that for a given size of the relativistic electron event the intensity of the type III burst is about a factor of 5 higher if it is accompanied by a type II burst. These results give evidence (a) that at least part of the relativistic electrons frequently is accelerated together with non-relativistic electrons and (b) that the coronal shock associated with the metric type II burst has a weaker effect on relativistic than on non-relativistic electrons.Now at DFVLR, Oberpfaffenhofen, Germany.