Generalized Hellings-Downs function for an anisotropic electromagnetic wave background

Abstract

In pulsar timing, the Hellings-Downs function is the overlap reduction function characterizing a pulsar system's correlated response to an isotropic and unpolarized stochastic gravitational wave (GW) background. In this paper, we will construct a generalized Hellings-Downs function for electromagnetic waves. Here instead of using pulsars we use a dipole antenna as our receiving system. Moreover, we assume that the electromagnetic wave background is unpolarized and anisotropic. The anisotropy is modeled by writing the angular part of the polarization tensor in terms of the standard spherical harmonics Y_ℓ^m(θ,ϕ). We find that the dipole antennas are only sensitive to (ℓ = 0, m = 0), (ℓ = 2, m = 0) and (ℓ = 2, m = ±1) modes.