Effect of Magnetic Fields on the Dynamics and Gravitational Wave Emission of Papaloizou-Pringle Instability-Saturated Self-Gravitating Accretion Disks: Simulations in Full GR

We explore the effect magnetic fields have on self-gravitating accretion disks around spinning black holes via numerical evolutions in full dynamical magnetohydrodynamic spacetimes. The configurations we study are unstable to the Papaloizou-Pringle instability (PPI). PPI-saturated accretion tori have been shown to produce gravitational waves, detectable to cosmological distances by third-generation gravitational wave (GW) observatories. While the PPI operates strongly for purely hydrodynamic disks, the situation can be different for disks hosting initially small magnetic fields. Evolutions of disks without self-gravity in fixed black hole (BH) spacetimes have shown that small seed fields can initiate the rapid growth of the magneto-rotational instability (MRI), which then strongly suppresses the PPI. Since realistic astrophysical disks are expected to be magnetized, PPI-generated GW signals may be suppressed as well. However, it is unclear what happens when the disk self-gravity is restored. Here, we study the impact of magnetic fields on the PPI-saturated state of a self-gravitating accretion disk around a spinning BH ($\ensuremath{\chi}=0.7$) aligned with the disk angular momentum, as well as one around a nonspinning BH. We find the MRI is effective at reducing the amplitude of PPI modes and their associated GWs, but the systems still generate GWs. Estimating the detectability of these systems across a wide range of masses, we show that magnetic fields reduce the maximum detection distance by Cosmic Explorer from 300 Mpc (in the pure hydrodynamic case) to 45 Mpc for a $10{M}_{\ensuremath{\bigodot}}$ system, by LISA from 11500 to 2700 Mpc for a $2\ifmmode\times\else\texttimes\fi{}{10}^{5}{M}_{\ensuremath{\bigodot}}$ system, and by DECIGO from $z\ensuremath{\approx}5$ down to $z\ensuremath{\approx}2$ for a $1000{M}_{\ensuremath{\bigodot}}$ system.