  The origin of magnetic fields in clusters of galaxies is still an unsolved
problem, which is largely due to our poor understanding of initial seed
magnetic fields. If the seed magnetic fields have primordial origins, it is
likely that large-scale pervasive magnetic fields were present before the
formation of the large-scale structure. On the other hand, if they were ejected
from astrophysical bodies, they were highly localized in space at the time of
injection. In this paper, using turbulence dynamo models for high magnetic
Prandtl number fluids, we find constraints on the seed magnetic fields. The
hydrodynamic Reynolds number based on the Spitzer viscosity in the intracluster
medium (ICM) is believed to be less than $O(10^2)$, while the magnetic Reynolds
number can be much larger than that. In this case, if the seed magnetic fields
have primordial origins, they should be stronger than $O(10^{-11})$G, which is
very close to the upper limit of $O(10^{-9})$G set by the cosmic microwave
background (CMB) observations. On the other hand, if the seed magnetic fields
were ejected from astrophysical bodies, any seed magnetic fields stronger than
$O(10^{-9})$G can safely magnetize the intracluster medium. Therefore, it is
less likely that primordial magnetic fields are the direct origin of
present-day magnetic fields in the ICM.

Cosmology and Nongalactic Astrophysics;High Energy Astrophysical Phenomena