CMB Anisotropy Due to Tangled magnetic fields in re-ionized models

Primordial tangled cosmological Magnetic Fields source rotational velocity perturbations of the baryon fluid, even in the post-recombination universe. These vortical modes inturn leave a characteristic imprint on the temperature anisotropy of the Cosmic Microwave Background (CMB), if the CMB photons can be re-scatterred after recombination. Observations from WMAP indicate that the Universe underwent a relatively early re-ionization ($z_{ri} \sim 15$), which does indeed lead to a significant optical depth for re-scattering of CMB photons after the re-ionization epoch. We compute the resulting additional temperature anisotropies, induced by primordial magnetic fields in the post-recombination universe. We show that in models with early re-ionization, a nearly scale-invariant spectrum of tangled magnetic fields which redshift to a present value of $B_0 \sim 3 \times 10^{-9}$ Gauss, produce vector mode perturbations which in turn induce additional temperature anisotropy of about 0.3 to 0.4 $ \mu$K over very small angular scales, with $ l$ upto $\sim 10000 $ or so