Does magnetic field promote or suppress fragmentation in AGN disks? Results from local shearing box simulations with simple cooling

Accretion disks in Active Galactic Nuclei (AGN) are predicted to become gravitationally unstable substantially interior to the black hole's sphere of influence, at radii where the disk is simultaneously unstable to the magnetorotational instability (MRI). Using local shearing box simulations with net vertical flux and a simple cooling prescription, we investigate the effect of magnetic fields on fragmentation in the limit of ideal magnetohydrodyamics. Different levels of in-disk magnetic field from the magnetorotational instability are generated by varying the initial vertical-field plasma beta $\beta_0$. We find that the disk becomes magnetically dominated when $\beta_0 < 10^3$, and that this transition is accompanied by a drastic drop in fragmentation (as measured by the bound mass fraction) and gravitational stress. The destabilizing influence of radial magnetic fields, which are present locally and which may promote fragmentation via magnetic tension effects, is overwhelmed by magnetic elevation, which significantly reduces the mid-plane density. The magnetic suppression of fragmentation in magnetically elevated disks has implications for the radial extent of the accretion flow in AGN disks, and for the efficiency of in situ formation of disk-embedded stars that are progenitors for single and binary compact objects.