Graviton-photon conversion in stochastic magnetic fields

We study graviton-photon conversion in the presence of stochastic magnetic fields. Assuming Gaussian magnetic fields that may possess nontrivial helicity, and unpolarized gravitational waves (GWs) as the initial state, we obtain expressions for the intensity and linear/circular polarizations of GWs after propagation over a finite distance. We calculate both the expectation values and variances of these observables, and find their nontrivial dependence on the typical correlation length of the magnetic field, the propagation distance, and the photon plasma mass. Our analysis reveals that an observationally favorable frequency range with narrower variance can emerge for the intensity, while a peak structure appears in the expectation value of the circular polarization when the magnetic field has nonzero helicity. We also identify a consistency relation between the GW intensity and circular polarization.