textit{BMAD}-Circumbinary Magnetically Arrested Disks around Stellar or Black Hole Binaries: Hot Accretion Flows, Disk Properties, and Angular Momentum Transfer

Binary systems surrounded by a circumbinary accretion flow can be subject to strong magnetic fields, potentially altering the character of the accretion flow itself, the evolution of the orbital dynamics, and outflow properties from the system. Here we focus on a regime where magnetic fields become so strong that the outer circumbinary flow becomes magnetically arrested, establishing a (circum)binary magnetically arrested disk ($\textit{BMAD}$) state. Such flows feature quasi-periodic magnetic flux eruptions, power jet-like magnetic tower outflows, and consequently alter the predominant contribution to angular momentum transfer inside the circumbinary disk. In this work, we provide a comprehensive analysis of the properties of these flows around equal-mass binary systems on circular orbits ultilizing massively parallel three-dimensional Newtonian magnetohydrodynamics simulations. We investigate the impact of the equation of state and of dynamical cooling, as well as that of the (large-scale) magnetic field topology. Our findings are as follows: (1) A magnetically arrested accretion flow through the cavity can generally be achieved, so long as the initial seed field is strong enough. (2) The cavity, and magnetic flux tube properties and their subsequent propagation are subject to the choice of equation of state/cooling physics. (3) We find tentative evidence that in some regimes the BMAD state, particularly during a flux eruption cycle, can aid shrinking of the binary's orbit. The regimes we explore have implications for multi-messenger transients to stars, supermassive and stellar black hole binaries and their orbital evolution in gaseous environments.