Probing anisotropies of gravitational-wave backgrounds with a space-based interferometer: Geometric properties of antenna patterns and their angular power

We discuss the sensitivity to anisotropies of stochastic gravitational-wave backgrounds (GWBs) observed via space-based interferometer. In addition to the unresolved galactic binaries as the most promising GWB source of the planned Laser Interferometer Space Antenna (LISA), the extragalactic sources for GWBs might be detected in the future space missions. The anisotropies of the GWBs thus play a crucial role to discriminate various components of the GWBs. We study general features of antenna pattern sensitivity to the anisotropies of GWBs beyond the low-frequency approximation. We show that the sensitivity of space-based interferometer to GWBs is severely restricted by the data combinations and the symmetries of the detector configuration. The spherical harmonic analysis of the antenna pattern functions reveals that the angular power of the detector response increases with frequency and the detectable multipole moments with effective sensitivity h_eff∼10^-20 Hz^-1/2 may reach ℓ∼8 10 at f∼f_*=10 mHz in the case of the single LISA detector. However, the cross correlation of optimal interferometric variables is blind to the monopole (ℓ=0) intensity anisotropy, and also to the dipole (ℓ=1) in some case, irrespective of the frequency band. Besides, all the self-correlated signals are shown to be blind to the odd multipole moments (ℓ=odd), independently of the frequency band.