2MTF-VI. Measuring the velocity power spectrum

We present measurements of the velocity power spectrum and constraints on the growth rate of structure fσ₈, at redshift zero, using the peculiar motions of 2062 galaxies in the completed 2MASS Tully–Fisher survey (2MTF). To accomplish this we introduce a model for fitting the velocity power spectrum including the effects of non-linear redshift space distortions (RSD), allowing us to recover unbiased fits down to scales k = 0.2 h Mpc⁻¹ without the need to smooth or grid the data. Our fitting methods are validated using a set of simulated 2MTF surveys. Using these simulations we also identify that the Gaussian distributed estimator for peculiar velocities of Watkins & Feldman is suitable for measuring the velocity power spectrum, but sub-optimal for the 2MTF data compared to using magnitude fluctuations δm, and that, whilst our fits are robust to a change in fiducial cosmology, future peculiar velocity surveys with more constraining power may have to marginalize over this. We obtain scale-dependent constraints on the growth rate of structure in two bins, finding fσ₈ = [0.55^+0.16_−0.13,0.40^+0.16_−0.17] in the ranges k = [0.007–0.055, 0.55–0.150] h Mpc⁻¹. We also find consistent results using four bins. Assuming scale-independence we find a value fσ₈ = 0.51^+0.09_−0.08⁠, a ∼16 per cent measurement of the growth rate. Performing a consistency check of general relativity (GR) and combining our results with cosmic microwave background data only we find γ = 0.45^+0.10_−0.11⁠, a remarkable constraint considering the small number of galaxies. All of our results are completely independent of the effects of galaxy bias, and fully consistent with the predictions of GR (scale-independent fσ₈ and γ ≈ 0.55).