General-Relativistic Gauge-Invariant Magnetic Helicity Transport: Basic Formulation and Application to Neutron Star Mergers

Dynamo processes are ubiquitous in astrophysical systems. In relativistic astrophysical systems, such as accretion disks around black holes or neutron stars, they may critically affect the launching of winds and jets that can power electromagnetic emission. Dynamo processes are governed by several microscopic parameters, one of them being magnetic helicity. As a conserved quantity in nonresistive plasmas, magnetic helicity is transported across the system. One important implication of helicity conservation is, that in the absence of helicity fluxes some mean-field dynamos can be quenched, potentially affecting the large-scale evolution of the magnetic field. One of the major challenges in computing magnetic helicity is the need to fix a meaningful electromagnetic gauge. We here present a fully covariant formulation of magnetic helicity transport in general-relativistic plasmas based on the concept of relative helicity by Berger & Field and Finn & Antonsen. This formulation is separately invariant under gauge-transformation of the Maxwell and Einstein equations. As an application of this new formalism we present the first analysis of magnetic helicity transport in the merger of two neutron stars. We demonstrate the presence of global helicity fluxes into the outer layers of the stellar merger remnant, which may impact subsequent large-scale dynamo amplification in these regions.