Cosmic Flow Measurement and Mock Sampling Algorithm of Cosmicflows-4
  Tully-Fisher Catalogue
  Measurements of cosmic flows enable us to test whether cosmological models
can accurately describe the evolution of the density field in the nearby
Universe. In this paper, we measure the low-order kinematic moments of the
cosmic flow field, namely bulk flow and shear moments, using the Cosmicflows-4
Tully-Fisher catalogue (CF4TF). To make accurate cosmological inferences with
the CF4TF sample, it is important to make realistic mock catalogues. We present
the mock sampling algorithm of CF4TF. These mock can accurately realize the
survey geometry and luminosity selection function, enabling researchers to
explore how these systematics affect the measurements. These mocks can also be
further used to estimate the covariance matrix and errors of power spectrum and
two-point correlation function in future work. In this paper, we use the mocks
to test the cosmic flow estimator and find that the measurements are unbiased.
The measured bulk flow in the local Universe is 376 $\pm$ 23 (error) $\pm$ 183
(cosmic variance) km s$^{-1}$ at depth $d_{\text{MLE}}=35$ Mpc $h^{-1}$, to the
Galactic direction of $(l,b)=(298\pm 3^{\circ}, -6\pm 3^{\circ})$. Both the
measured bulk and shear moments are consistent with the concordance $\Lambda$
Cold Dark Matter cosmological model predictions.
