Reconstructing cosmological initial conditions from galaxy peculiar
  velocities. II. The effect of observational errors
  The Reverse Zeldovich Approximation (RZA) is a reconstruction method which
allows to estimate the cosmic displacement field from galaxy peculiar velocity
data and to constrain initial conditions for cosmological simulations of the
Local Universe. In this paper, we investigate the effect of different
observational errors on the reconstruction quality of this method. For this, we
build a set of mock catalogues from a cosmological simulation, varying
different error sources like the galaxy distance measurement error (0 - 20%),
the sparseness of the data points, and the maximum catalogue radius (3000 -
6000 km/s). We perform the RZA reconstruction of the initial conditions on
these mock catalogues and compare with the actual initial conditions of the
simulation. We also investigate the impact of the fact that only the radial
part of the peculiar velocity is observationally accessible. We find that the
sparseness of a dataset has the highest detrimental effect on RZA
reconstruction quality. Observational distance errors also have a significant
influence, but it is possible to compensate this relatively well with Wiener
Filter reconstruction. We also investigate the effect of different object
selection criteria and find that distance catalogues distributed randomly and
homogeneously across the sky (such as spiral galaxies selected for the
Tully-Fisher method) allow for a higher reconstruction quality than if when
data is preferentially drawn from massive objects or dense environments (such
as elliptical galaxies). We find that the error of estimating the initial
conditions with RZA is always dominated by the inherent non-linearity of data
observed at z=0 rather than by the combined effect of the observational errors.
Even an extremely sparse dataset with high observational errors still leads to
a good reconstruction of the initial conditions on a scale of about 5 Mpc/h.
