The large scale velocity field from the Cosmicflows-4 data

The reconstruction of the large scale velocity field from the grouped Cosmicflows-4 (CF4) database is presented. The lognormal bias of the inferred distances and velocities data is corrected by the Bias Gaussianization correction (BGc) scheme, and the linear density and velocity fields are reconstructed by means of the Wiener filter (WF) and constrained realizations (CRs) algorithm. These tools are tested against a suite of random and constrained Cosmicflows-3-like mock data. The CF4 data consists of 3 main subsamples - the 6dFGS and the SDSS data - and the `others'. The individual contributions of the subsamples have been studied. The quantitative analysis of the velocity field is done mostly by the mean overdensity ($\Delta_L(R)$) and the bulk velocity ($V_{\mathrm{bulk}}(R)$) profiles of the velocity field out to $300\, h^{-1}{\rm Mpc}$. The $V_{\mathrm{bulk}}(R)$ and $\Delta_{\mathrm L}(R)$ profiles of the CF4 data without its 6dFGS component are consistent with the cosmic variance to within $1\sigma$. The 6dFGS sample dominates the $V_{\mathrm{bulk}}$ ($\Delta_{\mathrm L}$) profile beyond $\sim120\, h^{-1}{\rm Mpc}$, and drives it to roughly a $3.4\sigma$ ($-1.9\sigma$) excess (deficiency) relative to the cosmic variance at $R\sim250\ (190)\ \, h^{-1}{\rm Mpc}$. The excess in the amplitude of $V_{\mathrm{bulk}}$ is dominated by its Supergalactic X component, roughly in the direction of the Shapley Concentration. The amplitude and alignment of the inferred velocity field from the CF4 data is at $\sim(2\,-\,3)\,\sigma$ discrepancy with respect to the $\Lambda$CDM model. Namely, it is somewhat atypical but yet there is no compelling tension with the model.