The effect of Silk damping on primordial magnetic fields

We study the effects of plasma viscosity on the dynamics of primordial magnetic fields by simulating magnetohydrodynamics in the early universe by appropriate non-linear cascade models. We find numerically that even in the presence of large kinetic viscosity, magnetic energy is transferred to large length scales. There are indications, however, that the inverse cascade stops at a given time which depends on the magnitude of viscosity. For realistic viscosities we do not find equipartition between magnetic and kinetic energies. [email protected]; [email protected]; [email protected] There are many ways that magnetic fields could have been generated at various stages in the early universe. In the theory of galactic magnetism such fields are often referred to as “cosmological” or “primordial”, because they are created well before galaxies are formed. These fields may play the role of an initial condition for the galactic dynamo, a mechanism that would amplify magnetic fields and convert kinetic energy into magnetic [1]. There are two major problems when invoking primordial magnetic fields as possible seed magnetic fields for the galactic dynamo. One problem is the very small length scale of such magnetic fields. The horizon scale at the time of the electroweak phase transition is just a few centimeters, corresponding to about 1 AU at the present time. This is nine orders of magnitude shorter than the radius of typical galaxies. However, this view is too simplistic, because nonlinear effects inherent in the magnetohydrodynamic (MHD) equations can lead to a redistribution of magnetic energy over different length scales. Unfortunately, MHD in 3+1 exceeds the possibilities of present day computers. Therefore one has to resort to models which simulate the MHD equations. In a previous paper [2], hereafter referred to as Paper 1, we developed a fully relativistic 3+1 d version of the so-called cascade model [3] appropriate for MHD and found that an inverse cascade is operative, whereby magnetic energy is continuously tranferred to larger length scales. The other problem is that around the time of recombination photon diffusion becomes very large and could smooth out all fluctuations [4]. This may then also destroy the magnetic field [5]. The purpose of this paper is to show that this too is too simplistic a viewpoint, and that nonlinear effects most likely prevent this from happening. The basic equations have been presented and discussed in Paper 1. We started out from the fully relativistic MHD equations in expanding (flat) space and showed that all the terms arising from the expansion can be removed by using rescaled quantities and conformal time, t = ∫