Radiative Cooling Changes the Dynamics of Magnetically Arrested Disks

Abstract

We study magnetically arrested disks (MADs) around rotating black holes (BHs) under the influence of radiative cooling. We introduce a critical value of the mass accretion rate ${\dot{M}}_{{\rm{crit}}}$ for which the cooling by the synchrotron process efficiently radiates the thermal energy of the disk. We find ${\dot{M}}_{{\rm{crit}}}\approx 1{0}^{-5.5}{\dot{M}}_{{\rm{Edd}}}$ , where ${\dot{M}}_{{\rm{Edd}}}$ is the Eddington mass accretion rate. The normalization constant depends on the saturated magnetic flux and on the ratio of electron to proton temperatures, but not on the BH mass. We verify our analytical estimate using a suite of general relativistic magnetohydrodynamic simulations for a range of BH spin parameters a ∈ {−0.94, −0.5, 0, 0.5, 0.94} and mass accretion rates ranging from $1{0}^{-7}{\dot{M}}_{{\rm{Edd}}}$ to $1{0}^{-4}{\dot{M}}_{{\rm{Edd}}}$ . We numerically observe that the MAD parameter and the jet efficiency vary by a factor of ≈2 as the mass accretion rate increases above ${\dot{M}}_{{\rm{crit}}}$ , which confirms our analytical result. We further detail how the forces satisfying the quasi-equilibrium of the disk change, with the magnetic contribution increasing as the thermal contribution decreases.

Keywords

• Black hole physics
• Magnetohydrodynamical simulations
• Accretion