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

¹ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
² School of Physics and Astronomy, University of Southampton, Highfield, Southampton, SO17 1BJ, UK
³ JILA, University of Colorado and National Institute of Standards and Technology, 440 UCB, Boulder, CO, 80309-0440, USA
⁴ Department of Astrophysial and Planetary Sciences, University of Colorado, 391 UCB, Boulder, CO, 80309-0391, USA
⁵ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 OHA, UK
⁶ Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, PL-00-716 Warszawa, Poland

^⋆ Corresponding author; nicolas.scepi@gmail.com

Received: 18 July 2024
Accepted: 11 October 2024

Abstract

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 ≳0.3L_Edd, transitioning to a soft spectral state that survives with decreasing luminosities down to ∼10⁻²L_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.