Magnetic Flux Transport in Advection Dominated Accretion Flow Towards the Formation of Magnetically Arrested Disk

The magnetically arrested disks (MADs) have attracted much attention in recent years. The formation of MADs are 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 and the formation of a 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 disk is eventually formed at a region about several ten Schwarzschild radius outside the horizon. Due to the presence of strong large-scale magnetic field, the radial velocity of the accretion flow is significantly decreased. The angular velocity of the MAD region is highly subkeplerian with $Ω\sim (0.4-0.5)Ω_{\rm K}$ and the corresponding ratio of gas to magnetic pressure is about $β\lesssim 1$. Also, we find that MAD is unlikely to be formed through the inward flux advection process when the external magnetic field strength weak enough with $β_{\rm out}\gtrsim 100$ around $R_{\rm out}\sim 1000R_{\rm s}$. Based on the rough estimate, we find that the jet power of a black hole, with mass $M_{\rm BH}$ and spin $a_*$, surrounded by an ADAF with inner MAD region is about two order 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.