A fully covariant mean-field dynamo closure for numerical 3+1 resistive GRMHD

Abstract

The powerful high-energy phenomena typically encountered in astrophysics invariably involve physical engines, like neutron stars and black hole accretion disks, characterized by a combination of highly magnetized plasmas, strong gravitational fields, and relativistic motions. In recent years numerical schemes for General Relativistic MHD (GRMHD) have been developed to model the multidimensional dynamics of such systems, including the possibility of an evolving spacetime. Such schemes have been also extended beyond the ideal limit including the effects of resistivity, in an attempt to model dissipative physical processes acting on small scales (sub-grid effects) over the global dynamics. Along the same lines, magnetic fields could be amplified by the presence of turbulent dynamo processes, as often invoked to explain the high values of magnetization required in accretion disks and neutron stars. Here we present, for the first time, a further extension to include the possibility of a mean-field dynamo action within the framework of numerical 3+1 (resistive) GRMHD. A fully covariant dynamo closure is proposed, in analogy with the classical theory, assuming a simple alpha-effect in the comoving frame. Its implementation into a finite-difference scheme for GRMHD in dynamical spacetimes [the X-ECHO code: (Bucciantini and Del Zanna 2011)] is described, and a set of numerical test is presented and compared with analytical solutions wherever possible.