Resistively controlled primordial magnetic turbulence decay

Abstract

Magnetic fields generated in the early Universe undergo turbulent decay during the radiation-dominated era. The decay is governed by a decay exponent and a decay time. It has been argued that the latter is prolonged by magnetic reconnection, which depends on the microphysical resistivity and viscosity. Turbulence, on the other hand, is not usually expected to be sensitive to microphysical dissipation, which affects only very small scales. We want to test and quantify the reconnection hypothesis in decaying hydromagnetic turbulence. We performed high-resolution numerical simulations with zero net magnetic helicity using the Pencil Code with up to $2048^3$ mesh points and relate the decay time to the Alfv\'en time for different resistivities and viscosities. The decay time is found to be longer than the Alfv\'en time by a factor that increases with increasing Lundquist number to the 1/4 power. The decay exponent is as expected from the conservation of the Hosking integral, but a timescale dependence on resistivity is unusual for developed turbulence and not found for hydrodynamic turbulence. In two dimensions, the Lundquist number dependence is shown to be leveling off above values of $\approx25,000$, independently of the value of the viscosity. Our numerical results suggest that resistivity effects have been overestimated in earlier work. Instead of reconnection, it may be the magnetic helicity density in smaller patches that is responsible for the resistively slow decay. The leveling off at large Lundquist number cannot currently be confirmed in three dimensions.