An analytical framework to describe the orientation of dark matter halos
  and galaxies within the large-scale structure
  We provide a set of general tools for studying the alignments of dark matter
halos and galaxies with respect to the large scale structure. The statistics of
the positioning of these objects is represented by a Probability Distribution
Function (PDF) of their Euler angles. The PDF corresponding to halos located in
the shells of the cosmic voids is inferred from previous results. This PDF is
used to show how to recover the outcomes found for the alignments of the axes
of these halos in simulations. We also explore the orientation of the angular
momentum of the halos, both with respect to the halo axes and with respect to
the large scale structure. We present an expression which describes well
numerical results for the alignment of the angular momentum of the halo with
respect to the halo axes for randomly chosen halos. We also propose a model
that relates the orientation of the angular momentum with the halos axes
accounting for the orientation of the halo axes with the large scale structure.
This model is shown to recover accurately the observed PDF of the halo angular
momentum with respect to the void radial direction. In addition, we give an
expression for determining the degradation of the angular momentum intrinsic
alignment when observational errors are accounted. This expression is also used
to determine the departure of the observed value of the alignment from the
initial expectation (as provided by the tidal torque theory) due to the
rotation of the angular momentum of the halo with respect to the initial
torque. For voids, we find that the strength of the alignment is reduced to
half the original value. We discuss how to adapt the void results to other
cosmic large scale structures (i.e. filaments, walls, etc).
