Gravitational influences on magnetic field structure in accretion disks

Abstract

Black holes and compact objects are often surrounded by structures known as accretion disks which consist of ionized plasma. Due to the immense forces present in the disk, interesting and complex magnetic field structures can be set up within the disk. The influence of gravity on these structures is explored via a higher-order expansion of the gravitational potential. We consider several cases: the case when the Lorentz force is negligible and the case when the Lorentz force becomes significant in the dynamics of the disk. When the Lorentz force is negligible, we find using the Ferraro Co-rotation Theorem that the strength of the magnetic field increases near the event horizon. As the strength of the Lorentz force increases and it is included in our analysis, we discover that it leads to a periodic "crystal" structure of concentric rings of current. This structure is significantly affected by gravitational forces: we find a solution to the equations of motion that shows a composite structure within the disk. We discuss the general relativistic effects near the event horizon using the Pseudo- Newtonian potential in this limit. In addition, we consider an alternate derivation of the equation of motion describing the behavior of the magnetic field and discuss its consequences.