Spinning black holes magnetically connected to a Keplerian disk -- Magnetosphere, reconnection sheet, particle acceleration and coronal heating

International audienceContext: Accreting black holes (BHs) may be surrounded by a highly magnetized plasma threaded by a poloidal magnetic field. Non-thermal flares and high energy components could originate from a hot, collisionless and nearly force-free corona. The jets we often observe from these systems are believed to be rotation-powered and magnetically-driven. Aims: We study axisymmetric BH magnetospheres where some magnetic field lines anchored in a surrounding disk can connect to the event horizon of a rotating BH. We identify the sites of magnetic reconnection within 30 gravitational radii depending on the BH spin. Methods: With the fully general relativistic particle-in-cell code GRZeltron, we solve the time-dependent dynamics of the electron-positron pair plasma and of the electromagnetic fields around the BH. The disk is represented by a steady plasma in Keplerian rotation, threaded by a frozen dipolar field. Results: For prograde disks, twisted open magnetic field lines crossing the horizon power a Blandford-Znajek jet while beyond a critical distance, open field lines on the disk are open. In the innermost regions, coupling field lines ensure the transfer of significant amounts of angular momentum and energy between the BH and the disk. From the Y-point at the intersection, a current sheet forms where particle acceleration via magnetic reconnection takes place. We compute the synchrotron images of the current sheet emission. Conclusions: Our estimates for jet power and BH-disk exchanges match those derived from purely force-free models. Dissipation at the Y-point heats the corona and provides a physically motivated source of hard X-rays above the disk for reflection models. Episodic plasmoid ejection might explain millisecond flares observed in Cyg X-1. Particles flowing from the Y-point down to the disk could produce a hot spot at the footpoint of the outermost closed field line