Constrained realizations of 2MRS density and peculiar velocity fields: growth rate and local flow

We generate constrained realizations (CRs) of the density and peculiar velocity fields within $200 \; h^{-1} \, \mathrm{Mpc}$ from the final release of the Two-Micron All-Sky Redshift Survey (2MRS) $-$ the densest all-sky redshift survey to date. The CRs are generated by combining a Wiener filter estimator in spherical Fourier-Bessel space with random realizations of log-normally distributed density fields and Poisson-sampled galaxy positions. The algorithm is tested and calibrated on a set of semi-analytic mock catalogs mimicking the environment of the Local Group (LG), to rigorously account for the statistical and systematic errors of the reconstruction method. By comparing our peculiar velocity CRs with the observed velocities from the Cosmicflows-3 catalog, we constrain the normalized linear growth rate to $f \sigma_8^\mathrm{lin} = 0.367 \pm 0.060$, which is consistent at the $1.1 \sigma$ level with the latest Planck results as well as other direct probes. Simultaneously, we estimate a bulk flow contribution from sources beyond the 2MRS reconstruction volume of $B^\mathrm{ext} = 199 \pm 68 \; \mathrm{km} \, \mathrm{s}^{-1}$ towards $l = 299 \pm 18^\circ$, $b = 8 \pm 19^\circ$. The total reconstructed velocity field at the position of the LG, smoothed with a $1 \; h^{-1} \, \mathrm{Mpc}$ Gaussian, is $685 \pm 75 \; \mathrm{km} \, \mathrm{s}^{-1}$ towards $l = 270.6 \pm 6.6^\circ$, $b = 35.5 \pm 7.2^\circ$, in good agreement with the observed CMB dipole. The total reconstructed bulk flow within different radii is compatible with other measurements. Within a $50 \; h^{-1} \, \mathrm{Mpc}$ Gaussian window we find a bulk flow of $274 \pm 50 \; \mathrm{km} \, \mathrm{s}^{-1}$ towards $l = 287 \pm 9^\circ$, $b = 11 \pm 10^\circ$. The code used to generate the CRs and obtain these results, dubbed CORAS, is made publicly available.