Tracing the cosmic velocity field at z ~ 0.1 from galaxy luminosities in
  the SDSS DR7
  Spatial modulations in the distribution of observed luminosities (computed
using redshifts) of ~ 5 $\times$ 10$^5$ galaxies from the SDSS Data Release 7,
probe the cosmic peculiar velocity field out to z ~ 0.1. Allowing for
luminosity evolution, the r-band luminosity function, determined via a
spline-based estimator, is well represented by a Schechter form with
M$^{\star}$(z) - 5log$_{10}$h = -20.52 - 1.6(z - 0.1) $\pm$ 0.05 and
$\alpha^{\star}$ = -1.1 $\pm$ 0.03. Bulk flows and higher velocity moments in
two redshift bins, 0.02 < z < 0.07 and 0.07 < z < 0.22, agree with the
predictions of the $\Lambda$CDM model, as obtained from mock galaxy catalogs
designed to match the observations. Assuming a $\Lambda$CDM model, we estimate
$\sigma_{8}$ $\approx$ 1.1 $\pm$ 0.4 for the amplitude of the linear matter
power spectrum, where the low accuracy is due to the limited number of
galaxies. While the low-z bin is robust against coherent photometric
uncertainties, the bias of results from the second bin is consistent with the ~
1% magnitude tilt reported by the SDSS collaboration. The systematics are
expected to have a significantly lower impact in future datasets with larger
sky coverage and better photometric calibration.
