Improving estimates of the growth rate using galaxy–velocity correlations: a simulation study. Issue 2 (25th January 2021) - Turner, Ryan J; Blake, Chris; Ruggeri, Rossana
ABSTRACT: 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 autocorrelation function, ψ1 and ψ2, the two-point galaxy correlation function, ξgg, and introduce a new estimator of the galaxy–velocity cross-correlation function, ψ3 . 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 χ 2 minimization procedure to these statistics, we determine estimates and errors for the normalized growth rate f σ8 and the parameter β = f / b, where b is the galaxy bias factor. We test this framework on mock hemisphere data sets 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 σ8 from the joint combination of ψ1 + ψ2 + ψ3 + ξgg, with 15 per cent accuracy from individual mocks. We also recover the fiducial f σ8 to within 1σ 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 per cent compared to the same analysis only considering ψ2, by 53 per cent compared to the same analysis only considering ψ1, and by 52 per cent compared to the same analysis jointly considering ψ1 and ψ2 .