Probing anisotropies of gravitational-wave backgrounds with a space-based interferometer. II. Perturbative reconstruction of a low-frequency skymap

We present a perturbative reconstruction method to make a skymap of gravitational-wave backgrounds (GWBs) observed via space-based interferometer. In the presence of anisotropies in GWBs, the cross-correlated signals of observed GWBs are inherently time dependent due to the nonstationarity of the gravitational-wave detector. Since the cross-correlated signal is obtained through an all-sky integral of primary signals convolving with the antenna pattern function of gravitational-wave detectors, the nonstationarity of cross-correlated signals, together with full knowledge of antenna pattern functions, can be used to reconstruct an intensity map of the GWBs. Here, we give two simple methods to reconstruct a skymap of GWBs based on the perturbative expansion in low-frequency regime. The first one is based on harmonic-Fourier representation of data streams and the second is based on ``direct'' time-series data. The latter method enables us to create a skymap in a direct manner. The reconstruction technique is demonstrated for the case of the Galactic gravitational-wave background observed via planned space interferometer, LISA. Although the angular resolution of low-frequency skymap is rather restricted, the methodology presented here would be helpful in discriminating the GWBs of galactic origins by those of the extragalactic and/or cosmological origins.