Viscosity and Turbulence Dynamo in the Intracluster Medium

The origin of magnetic fields in the intracluster medium (ICM) is uncertain: it can be either primordial or astrophysical. Turbulence plays important roles in the origin of magnetic fields in the ICM. This is because turbulence can amplify a weak seed magnetic field very efficiently. The efficiency of the turbulence dynamo critically depends on the magnitude of viscosity: the smaller the viscosity is, the more efficient the turbulence dynamo is. In this talk, I'll discuss turbulence dynamo in both very small viscosity limit and very large viscosity limit. I'll show that when the viscosity in the ICM is comparable to the Spitzer viscosity, the origin of magnetic field in the ICM is likely to be astrophysical. On the other hans, when the viscosity is much smaller than the Spitzer value, the origin of magnetic field can be either astrophysical or primordial.