Algorithm of the MONTE CARLO Simulation

Our Monte Carlo code is based on the standard algorithm given in Pozdnyakov, Sobol' & Sunyaev (1983). It simulates inverse Compton scattering of photons off relativistic Maxwellian electrons in a plasma of arbitrary electron temperature and optical depth. The scattering probability and the mean-free-path of the photons is determined according to the prescription in Pozdnyakov, Sobol' and Sunyaev (1983) for relativistic Maxwellian electrons. We consider a spherically symmetric case, with the source of photons at the centre of a plasma cloud. The plasma cloud is divided into a shell and a spherical core, each with different temperatures and optical depths (fig. 1). The cloud is illuminated by a central source of blackbody photons with injection taken to be a delta function in time. In the simulations we fix the outermost radius of the cloud to be 1.0 light second across.

When a photon crosses the boundary from the inner to the outer-corona it is brought back to the boundary, and (without changing its propagation direction) a new mean free path is calculated based on the temperature and optical depth of the outer-corona. After the photon has entered the outer cloud and scattered, a routine will determine if the photon is heading back towards the inner cloud. Photons that subsequently re-enter the inner-corona are again placed on the boundary, and the optical depth and temperature are reset to their values in the inner cloud. Photons that escape from the plasma cloud are binned in energy to produce the observed spectrum.

The pathlength traveled by each photon is tracked and summed to give the total distance traveled (in units normalized to the outer cloud radius). This is converted into an escape time from the cloud which is binned to give the light curves, that is, the intensity in various bands as a function of time. These light curves are therefore Green's functions in the sense that they represent the response of the system to a delta-function source term.

The Fourier time-lags were then produced from the light curves using the FFT routines in IDL. Results were checked with those obtained numerically by Kazanas, Hua & Titarchuk (1997).

б© Copyright Astronomical Society of Australia 1997