The Cosmic microwave background (CMB) is linearly polarized. It is predicted that there is no significant intrinsic circular polarization (CP) in the standard cosmology. In this paper, we study the circular polarization of the CMB due to the Faraday conversion (FC), in particular FC due to the supernova remnants of the First stars, also called the Pop III stars. The mechanism of Faraday conversion channels a pre-existing linear polarization into circular polarization, in presence of magnetic field and scattering of photons with relativistic electrons. We derive an analytic form for the angular power spectrum of the CP of the CMB generated by the FC. We apply this result to the particular case of the FC triggered by explosions of the first stars and estimate the angular power spectrum, Clvv . We show that the amplitude of l(l + 1)Clvv /(2pi) > 0.001 in the units of micro kelvin squared for l > 100, with the age of the Pop III SN remnant to be 10,000 years and frequency of CMB observation as 30 GHz. We expect CP of the CMB to be a very promising probe of the yet unobserved first stars, primarily due to the expected high signal with no appreciable foreground, along with an unique frequency dependence.
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