Wave optics effects from gravitational wave propagation through dark matter halos

Gravitational wave (GW) propagation is usually studied under the geometric optics approximation. However, when GWs propagate through structures of sizes similar to their wavelength, this approximation breaks down. To study this situation, we present a scheme for numerically evolving linearised plane GWs through stationary, spherical astrophysical structures in both weak and strong gravity regimes. Our simulations evolve the full Einstein equations (with all 10 components) for Gaussian, NFW and Burkert potentials. Our simulations show that the scattering of the GWs depends not only on the mass of the lens but also strongly on the gravitational potential distribution of the lens. Among our most important results, we find that the GWs do not propagate along null geodesics when propagating through the Gaussian density, neither in the strong nor weak gravity setting. Another significant finding is that in the strong gravity case of the Burkert potential, the convexity of the wave is flipped when leaving the structure. We compare our results with the linearized scalar wave predictions and find that the difference between these and the exact GW modes are of order one when the wave is inside the central potential. However, the difference reduces to only a few percent when the wave has passed through the structure. Although these effects are small, future GW detectors and Pulsar Timing Arrays (PTAs) could be sensitive to these signals which could thus potentially help in constraining the structure of dark matter spikes or halos.