Magnetic Flux Transport in Advection-dominated Accretion Flow toward the Formation of a Magnetically Arrested Disk

Abstract Magnetically arrested disks (MADs) have attracted much attention in recent years. The formation of MADs is usually attributed to the accumulation of a sufficient amount of dynamically significant poloidal magnetic flux. In this work, the magnetic flux transport within an advection-dominated accretion flow (ADAF) and the formation of an MAD are investigated. The structure and dynamics of an inner MAD connected with an outer ADAF are derived by solving a set of differential equations with suitable boundary conditions. We find that an inner MAD is eventually formed at a region about several 10 R S outside the horizon. Due to the presence of a strong large-scale magnetic field, the radial velocity of the accretion flow is significantly decreased. The angular velocity of the MAD region is highly sub-Keplerian with Ω ∼ (0.4–0.5)Ω K , and the corresponding ratio of gas to magnetic pressure is about β ≲ 1. Also, we find that an MAD is unlikely to be formed through the inward flux advection process when the external magnetic field strength is weak enough with β out ≳ 100 around R out ∼ 1000 R s . Based on a rough estimate, we find that the jet power of a black hole, with mass M BH and spin a * , surrounded by an ADAF with an inner MAD region is about 2 orders of magnitude larger than that of a black hole surrounded by a normal ADAF. This may account for the powerful jets observed in some Fanaroff–Riley type I galaxies with a very low Eddington ratio.