2MTF  VI. Measuring the velocity power spectrum
Abstract
We present measurements of the velocity power spectrum and constraints on the growth rate of structure fσ_{8}, at redshift zero, using the peculiar motions of 2062 galaxies in the completed 2MASS TullyFisher survey (2MTF). To accomplish this we introduce a model for fitting the velocity power spectrum including the effects of nonlinear 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 suboptimal 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 scaledependent constraints on the growth rate of structure in two bins, finding fσ _{8} = [0.55^{+0.16}_{0.13},0.40^{+0.16}_{0.17}] in the ranges k = [0.0070.055, 0.550.150] h Mpc^{1}. We also find consistent results using four bins. Assuming scaleindependence we find a value fσ _{8} = 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 (scaleindependent fσ_{8} and γ ≈ 0.55).
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 November 2017
 DOI:
 10.1093/mnras/stx1521
 arXiv:
 arXiv:1706.05130
 Bibcode:
 2017MNRAS.471.3135H
 Keywords:

 cosmological parameters;
 largescale structure of Universe;
 cosmology: observations;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 18 pages, 14 figures, 3 tables. Accepted for publication in MNRAS