Studying the anisotropy of the gravitational wave stochastic background with LISA

A plethora of gravitational wave stochastic backgrounds populate the sensitivity window of the Laser Interferometer Space Antenna (LISA). We show that LISA can detect the anisotropy of the background corresponding to the multipole moments of order $l=2\mathrm{}$ and $4.$ The signal-to-noise ratio generated by galactic white dwarf binary systems could be as high as $\approx 60$ for 3 yr of integration, and LISA could provide valuable information on the spatial distribution of a variety of galactic sources. We also show that the cross correlation of the data sets from two interferometers could marginally lead to meaningful upper limits on the degree of isotropy of the primordial gravitational wave background.