Thermal solutions of strongly magnetized disks and the hysteresis in X-ray binaries

Context. X-ray binaries (XRBs) exhibit a spectral hysteresis for luminosities in the range 10 −2 ≲ L / L Edd ≲ 0.3, with a hard X-ray spectral state that persists from quiescent luminosities up to ≳0.3 L Edd , transitioning to a soft spectral state that survives with decreasing luminosities down to ∼10 −2 L Edd . Aims. We present a possible approach to explain this behavior based on the thermal properties of a magnetically arrested disk simulation. Methods. By post-processing the simulation to include radiative effects, we solved for all the thermal equilibrium solutions as the accretion rate, Ṁ , varies during the XRB outburst. Results. For an assumed scaling of the disk scale height and accretion speed with temperature, we find that two solutions exist in the range of 10 −3 ≲ Ṁ / Ṁ Eddington ≲ 0.1 at r = 8 r g (4 × 10−2 ≲ Ṁ / Ṁ Eddington ≲ 0.5 at r = 3 r g ): a cold, optically thick solution, and a hot, optically thin one. This opens the possibility of a natural thermal hysteresis in the right range of luminosities for XRBs. We stress that our scenario for the hysteresis does not require us to invoke the strong advection-dominated accretion flow principle, nor does it require the magnetization of the disk to change during the XRB outburst. In fact, our scenario requires a highly magnetized disk in the cold soft state to reproduce the transition from soft to hard state at the right luminosities. Our scenario therefore predicts a jet, although possibly very weakly dissipative, in the soft state of XRBs. We also predict that if active galactic nuclei have similar hysteresis cycles and are strongly magnetized, they undergo a transition from soft to hard state at much lower L / L Edd than XRBs.