Linear Polarization of the 21 cm Line from the Epoch of Reionization
  The 21 cm linear polarization due to Thomson scattering off free electrons
can probe the distribution of neutral hydrogen in the intergalactic medium
during the epoch of reionization, complementary to the 21 cm temperature
fluctuations. Previous study (Babich & Loeb 2005) estimated the strength of
polarization with a toy model and claimed that it can be detected with 1-month
observation of the Square Kilometre Array (SKA). Here we revisit this
investigation with account of nonlinear terms due to inhomogeneous
reionization, using seminumerical reionization simulations to provide the
realistic estimation of the 21 cm TE and EE angular power spectra ($C^{\rm
TE}_\ell$ and $C^{\rm EE}_\ell$). We find that (1) both power spectra are
enhanced on sub-bubble scales but suppressed on super-bubble scales, compared
with previous results; (2) $C^{\rm TE}_\ell$ displays a zero-crossing at
$\ell<100$, and its angular scale is sensitive to the scale-dependence of H I
bias on large scales; (3) the ratios of the power spectrum to its maximum value
during reionization at a given $\ell$, i.e. $C^{\rm TE}_\ell / C^{\rm
TE}_{\ell,{\rm max}} $ and $C^{\rm EE}_{\ell}/C^{\rm EE}_{\ell,{\rm max}}$,
show robust correlations with the global ionized fraction. However, measurement
of this signal will be very challenging not only because the overall strength
is weaker than the sensitivity of SKA, but also because of the polarized
foregrounds from diffuse synchrotron emission, and Faraday rotation which
modifies the observed polarization. Nevertheless, the 21 cm linear polarization
signal may still likely be detectable through other approaches, e.g. its
cross-correlation with other probes.
