Maximum likelihood map-making with the Laser Interferometer Space
  Antenna
  Given the recent advances in gravitational-wave detection technologies, the
detection and characterisation of gravitational-wave backgrounds (GWBs) with
the Laser Interferometer Space Antenna (LISA) is a real possibility. To assess
the abilities of the LISA satellite network to reconstruct anisotropies of
different angular scales and in different directions on the sky, we develop a
map-maker based on an optimal quadratic estimator. The resulting maps are
maximum likelihood representations of the GWB intensity on the sky integrated
over a broad range of frequencies. We test the algorithm by reconstructing
known input maps with different input distributions and over different
frequency ranges. We find that, in an optimal scenario of well understood noise
and high frequency, high SNR signals, the maximum scales LISA may probe are
$\ell_{\rm max} \lesssim 15$. The map-maker also allows to test the directional
dependence of LISA noise, providing insight on the directional sky sensitivity
we may expect.
