The Sloan Digital Sky Survey Peculiar Velocity Catalogue
  We present a new catalogue of distances and peculiar velocities (PVs) of
$34,059$ early-type galaxies derived from Fundamental Plane (FP) measurements
using data from the Sloan Digital Sky Survey (SDSS). This
$7016\,\mathrm{deg}^{2}$ sample comprises the largest set of peculiar
velocities produced to date and extends the reach of PV surveys up to a
redshift limit of $z=0.1$. Alongside the data, we produce an ensemble of
$2,048$ mock galaxy catalogues that reproduce the data selection function, and
are used to validate our fitting pipelines and check for systematics. We
uncover a significant trend between group richness and mean surface brightness
within the sample, which hints at an environmental dependence within the FP and
can result in biased peculiar velocities. This is removed using multiple FP
fits as function of group richness, a procedure made tractable through a new
analytic derivation for the integral of a 3D Gaussian over non-trivial limits.
Our catalogue is calibrated to the zero-point of the CosmicFlows-III sample
with an uncertainty of $0.004$ dex, which is cross-validated using the
independent, predicted zero-point from the 2M++ reconstruction of our local
velocity field. We achieve a mean uncertainty on the PVs of $\sim23\%$ compared
to the CMB-frame redshift. Finally, as an example of what is possible with our
new catalogue, we obtain preliminary bulk flow measurements up to a depth of
$135\,h^{-1}\mathrm{Mpc}$. We find a slightly larger-than-expected bulk flow,
although this could be caused by the presence of the Shapley supercluster lying
just beyond the bounds of our data.
