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.