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

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/(2πL), 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 ℓ∼10. The presence of instrumental noises degrades the angular resolution. The resultant skymap has angular resolution with multipoles ℓ≤6∼7 for the anisotropic signals with signal-to-noise ratio S/N>5.