Inverse Compton reflection - Time-dependent theory

Abstract

We consider time-dependent behavior in inverse Compton reflection, in which an external flux of soft photons is incident upon a hot, thermal plasma of large scattering depth and small absorption depth. Fluctuations are assumed to arise from variability in the input of soft photons. Our treatment is largely analytic. We calculate in detail the spectral evolution during a fluctuation and show how such observables as the frequency-dependent rise time and the spectral hardness ratio may be used to derive the plasma parameters and soft photon frequency, or perhaps rule out an inverse Compton model altogether. Some of the results are qualitatively applicable to inverse Compton processes in general. Such considerations may be relevant to models for rapidly fluctuating X-ray sources. Subject headings: plasmas-radiative transfer-X-rays: sources I. INTRODUCTION A remarkable and distinguishing feature of quasars and active galactic nuclei is their rapid time variability at all emitted wavelengths. In the case of the compact radio emitters, where fluctuations occur on time scales as short as a month, theoretical calculations involving synchrotron emission from a relativistically evolving component have been reasonably successful in explaining the observed temporal and spectral evolution. A much larger fraction of these objects may be strong X-ray emitters (Weedman 1978; Gursky and Schwartz 1977), where fluctuations occur on time scales as short as a day (Mushotzky, Holt, and Serlemitsos 1978) or even an hour (Tananbaum et al. 1978). In contrast to the radio fluctuations mentioned above, these relatively shorter time scales suggest that the compact X-ray source may be a more direct probe of the ultimate power supply. With the increasing spectral and temporal resolution of X-ray satellites and the increasing theoretical delineation of the nature of extragalactic compact X-ray sources (see, e.g., review by Fabian and Rees 1978), it seems timely to consider the theory of time variability expected from the fundamental X-ray emission mechanisms. In principle, comparison of such time-dependent calculations to observations can help distinguish between possible emission mechanisms and provide information about the source parameters unobtainable from the steady emission. In this paper we consider time-dependent effects in the radiative process of inverse Compton reflection, in which an external flux of soft photons is incident upon a hot thermal plasma of large scattering depth and small absorption depth. The steady-state treatment of this radiative process (Lightman and Rybicki 1979a, b) yields a hard, universal number spectrum dNIdvjdt oc (In vlv 0)~ 3l2 v~ 1 over a large frequency range and suggests that the process may be important when the X-ray emitting plasma is bathed in a strong flux of soft photons from larger radii. Although the functional dependences are different, the reflection problem is closely related to the transmission problem, in which soft photons originate within the scattering medium (Katz 1976; Shapiro, Lightman, and Eardley 1976; Pozdnyakov, Sobol, and Sunyaev 1976). Previous treatments of time-dependent effects in inverse Compton processes have employed either direct numerical integration of the Kompaneets equation for homogeneous, infinite media (Illarionov and Syunyaev 1972; Katz 1976), or, for the more realistic case of finite media with an escape surface, Monte Carlo calculations (e.g., Cañizares 1976). In their study of Comptonization of X-rays by low-temperature electrons, Illarionov et al. (1979) find a steady solution to the Compton transmission problem by first obtaining a time-dependent solution and then integrating the latter over time. In this paper we obtain an analytic solution for the Green's function in the inverse Compton reflection problem. Our solution is valid for nonrelativistic electrons, kT < m e c 2 , and emergent photons in the energy range hv 0 « hv < kT, where hv Q is the energy of the input photons. We discuss some characteristic features of the time-dependent spectral evolution, give examples, and relate the fluctuation rise times and spectral hardness ratios to the frequency of input photons, to the density, temperature, and size of the X-ray emitting region, and to the time scale of the input of soft photons. Many of these features are qualitatively the same for the Compton transmission problem as well as the Compton reflection problem.