Probing anisotropies of gravitational-wave backgrounds with a space-based interferometer. III. Reconstruction of a high-frequency sky map

Abstract

We develop a numerical scheme to make a high-frequency skymap of gravitational-wave backgrounds (GWBs) observed via a space-based interferometer. Based on the cross correlation technique, the intensity distribution of anisotropic GWB can be directly reconstructed from the time-ordered data of cross correlation signals, with full knowledge of the detector's antenna pattern functions. We demonstrate how the planned space interferometer, LISA, can make a skymap of GWB for a specific example of anisotropic signals. At the frequency higher than the characteristic frequency ${f}_{*}=1/(2\ensuremath{\pi}L)$, where $L$ is the arm-length of the detector, the reconstructed skymap free from the instrumental noise potentially reaches the angular resolution up to the multipoles $\ensuremath{\ell}\ensuremath{\sim}10$. The presence of instrumental noises degrades the angular resolution. The resultant skymap has angular resolution with multipoles $\ensuremath{\ell}\ensuremath{\le}6\ensuremath{\sim}7$ for the anisotropic signals with signal-to-noise ratio $\mathrm{S}/\mathrm{N}>5$.