Chaotic magnetic disconnections trigger flux eruptions in accretion flows channeled onto magnetically saturated Kerr black holes

Magnetized accretion flow onto a black hole (BH) may lead to accumulation of poloidal magnetic flux across its horizon, which for high BH spin can power far-reaching relativistic jets. The BH magnetic flux is subject to a saturation mechanism by means of magnetic flux eruptions involving relativistic magnetic reconnection. Such accretion flows have been described as magnetically arrested (MAD) or choked (MCAF). The main goal of this work is to describe the onset of relativistic reconnection and initial development of magnetic flux eruption in accretion flow onto magnetically saturated BH. We analyze the results of 3D ideal GRMHD numerical simulations in the Kerr metric, starting from weakly magnetized geometrically thick tori rotating either prograde or retrograde. We integrate large samples of magnetic field lines in order to probe magnetic connectivity with the BH horizon. The boundary between magnetically connected and disconnected domains coincides roughly with enthalpy equipartition. The geometrically constricted innermost part of the disconnected domain develops a rigid structure of magnetic field lines - rotating slowly and insensitive to the BH spin orientation. The typical shape of innermost disconnected lines is a double spiral converging to a sharp inner tip anchored at the single equatorial current layer. The footpoints of magnetic flux eruptions are found to zip around the BH along with other azimuthal patterns. Magnetic flux eruptions from magnetically saturated accreting BHs can be triggered by minor density gaps in the disconnected domain, resulting from chaotic disconnection of plasma-depleted magnetospheric lines. Accretion flow is effectively channeled along the disconnected lines towards the current layer, and further towards the BH by turbulent cross-field diffusion. Rotation of flux eruption footpoints may contribute to the variability of BH crescent images.