Magnetic fields in elliptical galaxies: Using the Laing-Garrington
  effect in radio galaxies and polarized emission from background radio sources
  Magnetic fields in elliptical galaxies are poorly constrained due to a lack
of significant synchrotron emission from them. This paper explores properties
of magnetic fields in ellipticals via two methods. First, we exploit the
Laing-Garrington effect (asymmetry in the observed polarization fraction
between radio galaxy jets) for 57 galaxies with redshifts up to $0.5$. We use
the differences in polarization fraction and rotation measure between the jet
and counterjet to estimate the small- and large-scale magnetic fields in and
around ellipticals (including their circumgalactic medium). We find that the
small-scale field (at scales smaller than the driving scale of turbulence,
approximately $300~{\rm pc}$) lies in the range $0.1~\text{--}~2.75~\mu{\rm
G}$. The large-scale field (at scales of $100~{\rm kpc}$) is an order of
magnitude smaller than the small-scale field. In the second method, we
cross-match the Faraday rotation measures (RM) of a few hundred (out of $3098$)
extragalactic radio sources with galaxy catalogs to explore the effect of the
number and morphology of intervening galaxies on the observed RM distribution.
We use both Gaussian and non-Gaussian functions to describe the RM distribution
and derive its statistical properties. Finally, using the difference in the
observed polarization fraction between the intervening spirals and ellipticals,
we estimate the small-scale magnetic fields at the center of ellipticals to be
$\sim6~\mu{\rm G}$. Both methods with different observations and analysis
techniques give magnetic field strengths consistent with previous studies
($\leq10\mu{\rm G}$), and the results can be used to constrain dynamo theories
and galaxy evolution simulations.
