Improving estimates of the growth rate using galaxy-velocity correlations: a simulation study

We present an improved framework for estimating the growth rate of large-scale structure, using measurements of the galaxy-velocity cross-correlation in configuration space. We consider standard estimators of the velocity auto-correlation function, $\psi_1$ and $\psi_2$, the two-point galaxy correlation function, $\xi_{gg}$, and introduce a new estimator of the galaxy-velocity cross-correlation function, $\psi_3$. By including pair counts measured from random catalogues of velocities and positions sampled from distributions characteristic of the true data, we find that the variance in the galaxy-velocity cross-correlation function is significantly reduced. Applying a covariance analysis and $\chi^2$ minimisation procedure to these statistics, we determine estimates and errors for the normalised growth rate $f\sigma_8$ and the parameter $\beta = f/b$, where $b$ is the galaxy bias factor. We test this framework on mock hemisphere datasets for redshift $z < 0.1$ with realistic velocity noise constructed from the L-PICOLA simulation code, and find that we are able to recover the fiducial value of $f\sigma_8$ from the joint combination of $\psi_1$ + $\psi_2$ + $\psi_3$ + $\xi_{gg}$, with 15\% accuracy from individual mocks. We also recover the fiducial $f\sigma_8$ to within 1$\sigma$ regardless of the combination of correlation statistics used. When we consider all four statistics together we find that the statistical uncertainty in our measurement of the growth rate is reduced by $59\%$ compared to the same analysis only considering $\psi_2$, by $53\%$ compared to the same analysis only considering $\psi_1$, and by $52\%$ compared to the same analysis jointly considering $\psi_1$ and $\psi_2$.