Interaction between disk and extended corona in a general relativistic framework

Context. The energy equilibrium between the corona and the underlying disk in a two-phase accretion flow sets a lower limit on the achievable photon index. A slab coronal geometry may not adequately explain the hard state observations of X-ray binaries (XRBs). Aims. We incorporated energy feedback to the accretion disk resulting from illumination by an extended corona, and vice versa. The interaction between these two components makes it possible to find an energetically self-consistent equilibrium solution for a given disk–corona system. Methods. We upgraded the existing Monte Carlo radiative transfer code, MONK, to incorporate the interaction between the disk and the extended corona within the general relativistic framework. We introduced an albedo parameter to specify the fraction of the incident flux that is reflected by the disk, while the remainder is absorbed and added to the intrinsic dissipation. Reflection was modeled assuming a semi-infinite electron atmosphere. For a given disk–corona system, Comptonization by the corona and disk illumination are iteratively computed to reach equilibrium, under the constraint that the total observed luminosity equals the total available accretion power. Results. We find global equilibrium solutions not only for the hard state but also for intermediate states, with partial contributions from the disk and from the corona. A higher black hole spin, higher coronal temperature, and higher albedo all lead to harder spectra. For typical coronal temperatures and disk albedos, the lowest achievable photon index with a static slab corona fully covering the disk is approximately 1.7−1.8. Under the assumption of a spatially uniform, extended slab corona, energy must flow from the inner to the outer annuli if local equilibrium is imposed between the disk and the corona at each radial annulus, in addition to the global equilibrium condition. Conclusions. With the upgraded version of MONK, we are now able to achieve global energy equilibrium for a given disk–corona system. This approach holds significant potential for constraining the coronal geometry using not only the observed flux, but also polarization. A static slab does not appear to be a favorable coronal geometry for the hard state of X-ray binaries, even when global energy balance between the disk and corona is taken into account. In future work, we will explore truncated disk geometries and outflowing coronae as potential alternatives.