Decaying turbulence and magnetic fields in galaxy clusters
  We explore the decay of turbulence and magnetic fields generated by
fluctuation dynamo action in the context of galaxy clusters where such a
decaying phase can occur in the aftermath of a major merger event. Using
idealized numerical simulations that start from a kinetically dominated regime
we focus on the decay of the steady state rms velocity and the magnetic field
for a wide range of conditions that include varying the compressibility of the
flow, the forcing wave number, and the magnetic Prandtl number. Irrespective of
the compressibility of the flow, both the rms velocity and the rms magnetic
field decay as a power-law in time. In the subsonic case we find that the
exponent of the power-law is consistent with the $-3/5$ scaling reported in
previous studies. However, in the transonic regime both the rms velocity and
the magnetic field initially undergo rapid decay with an $\approx t^{-1.1}$
scaling with time. This is followed by a phase of slow decay where the decay of
the rms velocity exhibits an $\approx -3/5$ scaling in time, while the rms
magnetic field scales as $\approx -5/7$. Furthermore, analysis of the Faraday
rotation measure reveals that the Faraday RM decays also decays as a power law
in time $\approx t^{-5/7}$; steeper than the $\sim t^{-2/5}$ scaling obtained
in previous simulations of magnetic field decay in subsonic turbulence. Apart
from galaxy clusters, our work can have potential implications in the study of
magnetic fields in elliptical galaxies.
