Jointly setting upper limits on multiple components of an anisotropic
  stochastic gravitational-wave background
  With the increasing sensitivities of the gravitational wave (GW) detectors
and more detectors joining the international network, the chances of detection
of a stochastic GW background (SGWB) are progressively increasing. Different
astrophysical and cosmological processes are likely to give rise to backgrounds
with distinct spectral signatures and distributions on the sky. The observed
SGWB will therefore be a superposition of these components. Hence, one of the
first questions that will come up after the first detection of a SGWB will
likely be about identifying the dominant components and their distributions on
the sky. Both these questions were addressed separately in the literature,
namely, how to separate components of isotropic backgrounds and how to probe
the anisotropy of a single component. Here, we address the question of how to
separate distinct anisotropic backgrounds with (sufficiently) different
spectral shapes. We first obtain the combined Fisher information matrix from
folded data using an efficient analysis pipeline PyStoch, which incorporates
covariances between pixels and spectral indices. This is necessary for
estimating the detection statistic and setting upper limits. However, based on
a recent study, we ignore the pixel-to-pixel noise covariance that does not
have a significant effect on the results at the present sensitivity levels of
the detectors. We show that the joint analysis accurately separates and
estimates backgrounds with different spectral shapes and different sky
distributions with no major bias. This does come at the cost of increased
variance. Thus making the joint upper limits safer, though less strict than the
individual analysis. We finally set joint upper limits on the multicomponent
anisotropic background using Advanced LIGO data taken up to the first half of
the third observing run.
