X-ray-binary spectra in the lamp post model

Context. The high-energy radiation from black-hole binaries may be due to the reprocessing of a lamp located on the black hole rotation axis and emitting X-rays. The observed spectrum is made of three major components: the direct spectrum traveling from the lamp directly to the observer; the thermal bump at the equilibrium temperature of the accretion disk heated by the lamp; and the reflected spectrum essentially made of the Compton hump and the iron-line complex. Aims. We aim to accurately compute the complete reprocessed spectrum (thermal bump + reflected) of black-hole binaries over the entire X-ray band. We also determine the strength of the direct component. Our choice of parameters is adapted to a source showing an important thermal component. We are particularly interested in investigating the possibility to use the iron-line complex as a probe to constrain the black hole spin. Methods. We computed in full general relativity the illumination of a thin accretion disk by a fixed X-ray lamp along the rotation axis. We used the ATM21 radiative transfer code to compute the local, energy-dependent spectrum emitted along the disk as a function of radius, emission angle and black hole spin. We then ray traced this local spectrum to determine the final reprocessed spectrum as received by a distant observer. We consider two extreme values of the black hole spin (a = 0 and a = 0 : 98) and discuss the dependence of the local and ray-traced spectra on the emission angle and black hole spin. Results. We show the importance of the angle dependence of the total disk specific intensity spectrum emitted by the illuminated atmosphere when the thermal disk emission is fully taken into account. The disk flux, together with the X-ray flux from the lamp, determines the temperature and ionization structure of the atmosphere. High black hole spin implies high temperature in the inner disk regions, therefore, the emitted thermal disk spectrum fully covers the iron-line complex. As a result, instead of fluorescent iron emission line, we locally observe absorption lines produced in the hot disk atmosphere. Absorption lines are narrow and disappear after ray tracing the local spectrum. Conclusions. Our results mainly highlight the importance of considering the angle dependence of the local spectrum when computing reprocessed spectra, as was already found in a recent study. The main new result of our work is to show the importance of computing the thermal bump of the spectrum, as this feature can change considerably the observed iron-line complex. Thus, in particular for fitting black hole spins, the full spectrum, rather than only the reflected part, should be computed self-consistently.