Signature of cosmic string wakes in the CMB polarization

Abstract

We calculate a signature of cosmic strings in the polarization of the cosmic microwave background. We find that ionization in the wakes behind moving strings gives rise to extra polarization in a set of rectangular patches in the sky whose length distribution is scale-invariant. The length of an individual patch is set by the comoving Hubble radius at the time the string is perturbing the cosmic microwave background. The polarization signal is largest for string wakes produced at the earliest post-recombination time, and for an alignment in which the photons cross the wake close to the time the wake is created. The maximal amplitude of the polarization relative to the temperature quadrupole is set by the overdensity of free electrons inside a wake which depends on the ionization fraction $f$ inside the wake. For a cosmic string wake coming from an idealized string segment, the signal can be as high as $0.06\text{ }\text{ }\ensuremath{\mu}\mathrm{K}$ in degree scale polarization for a string at high redshift (near recombination) and a string tension $\ensuremath{\mu}$ given by $G\ensuremath{\mu}={10}^{\ensuremath{-}7}$.