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We investigate the sensitivity of the Laser Interferometer Space Antenna(LISA) to the anisotropies of the Stochastic Gravitational Wave Background(SGWB). We first discuss the main astrophysical and cosmological sources ofSGWB which are characterized by anisotropies in the GW energy density, and webuild a Signal-to-Noise estimator to quantify the sensitivity of LISA todifferent multipoles. We then perform a Fisher matrix analysis of the prospectsof detectability of anisotropic features with LISA for individual multipoles,focusing on a SGWB with a power-law frequency profile. We compute the noiseangular spectrum taking into account the specific scan strategy of the LISAdetector. We analyze the case of the kinematic dipole and quadrupole generatedby Doppler boosting an isotropic SGWB. We find that $\beta\, \Omega_{\rmGW}\sim 2\times 10^{-11}$ is required to observe a dipolar signal with LISA.The detector response to the quadrupole has a factor $\sim 10^3 \,\beta$relative to that of the dipole. The characterization of the anisotropies, bothfrom a theoretical perspective and from a map-making point of view, allows usto extract information that can be used to understand the origin of the SGWB,and to discriminate among distinct superimposed SGWB sources.

Probing Anisotropies of the Stochastic Gravitational Wave Background with LISA