Magnetic fields in elliptical galaxies: an observational probe of the
  fluctuation dynamo action
  Fluctuation dynamos are thought to play an essential role in magnetized
galaxy evolution, saturating within $\sim0.01~$Gyr and thus potentially acting
as seeds for large-scale dynamos. However, unambiguous observational
confirmation of the fluctuation dynamo action in a galactic environment is
still missing. This is because, in spiral galaxies, it is difficult to
differentiate between small-scale magnetic fields generated by a fluctuation
dynamo and those due to the tangling of the large-scale field. We propose that
observations of magnetic fields in elliptical galaxies would directly probe the
fluctuation dynamo action. This is motivated by the fact that in ellipticals,
due to their lack of significant rotation, the conventional large-scale dynamo
is absent and the fluctuation dynamo is responsible for controlling the
magnetic field strength and structure. By considering turbulence injected by
Type Ia supernova explosions and possible magnetic field amplification by
cooling flows, we estimate expected magnetic field strengths of $0.2~-~1
\,\mu{\rm G}$ in quiescent elliptical galaxies. We use a semi-analytic model of
galaxy formation to estimate the distribution and redshift evolution of field
strengths, tentatively finding a decrease in magnetic field strength with
decreasing redshift. We analyse a sample of radio sources that exhibit the
Laing-Garrington (LG) effect (radio polarization asymmetry in jets) and infer
magnetic field strengths between $0.14~-~1.33 \,\mu{\rm G}$ for a uniform
thermal electron density and between $1.36~-~6.21\,\mu{\rm G}$ for the thermal
electron density following the King profile. We examine observational
techniques for measuring the magnetic field saturation state in elliptical
galaxies, focusing on Faraday RM grids, the LG effect, synchrotron emission,
and gravitational lensing, finding appealing prospects for future empirical
analysis.
