While it is revealed that the cosmic microwave background (CMB) is linearly polarized at 10% level, it is predicted that there exists no significant intrinsic source for circular polarization ($CP$) in the standard cosmology. However, during the propagation through a magnetized plasma, the $CP$ of the CMB could be produced via the Faraday conversion (FC). The FC converts a preexisting linear polarization into $CP$ in the presence of a magnetic field with relativistic electrons. In this paper, we focus on the FC due to supernova remnants of the first stars, also called pop III stars. We derive an analytic form for the angular power spectrum of the $CP$ of the CMB generated by the general FC. We apply this result to the case of the FC triggered by explosions of the first stars and evaluate the angular power spectrum, $C_l^{VV}$. We show that the amplitude of $l(l+1)C_l^{VV}/(2\pi )$ $>10^{-2}\mu {\mathrm{K}}^2$ for $l>100$, with only one pop III star per halo, the age of pop III SN remnants as ${10}^4\text{years}$ and frequency of CMB observation as 1 GHz. We expect the $CP$ of the CMB to be a very promising probe of the yet unobserved first stars, primarily due to the expected high signal along with a unique frequency dependence.

• Received 19 March 2014

DOI:https://doi.org/10.1103/PhysRevD.92.123506