2MTF VI. Measuring the velocity power spectrum

Abstract

We present measurements of the velocity power spectrum and constraints on the growth rate of structure $f\ddot{I}{ƒ}_8$, at redshift zero, using the peculiar motions of 2,062 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 $k=0.2h{\mathrm{Mpc}}^{-1}$ 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 \cite{Watkins2015} is suitable for measuring the velocity power spectrum, but sub-optimal for the 2MTF data compared to using magnitude fluctuations $\hat{I}´m$, and that, whilst our fits are robust to a change in fiducial cosmology, future peculiar velocity surveys with more constraining power may have to marginalise over this. We obtain \textit{scale-dependent} constraints on the growth rate of structure in two bins, finding $f\ddot{I}{ƒ}_8=[0.55_{-0.13}^{+0.16},0.40_{-0.17}^{+0.16}]$ in the ranges $k=[0.007-0.055,0.55-0.150]h{\mathrm{Mpc}}^{-1}$. We also find consistent results using four bins. Assuming scale-\textit{independence} we find a value $f\ddot{I}{ƒ}_8=0.51_{-0.08}^{+0.09}$, a $\sim 16\%$ measurement of the growth rate. Performing a consistency check of General Relativity (GR) and combining our results with CMB data only we find ${\hat{I}}^3=0.45_{-0.11}^{+0.10}$, 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 $f\ddot{I}{ƒ}_8$ and ${\hat{I}}^3\approx 0.55$).

18 pages, 14 figures, 3 tables. Accepted for publication in MNRAS