The Cosmic Mach Number: Comparison from Observations, Numerical Simulations and Nonlinear Predictions

We calculate the cosmic Mach number M – the ratio of the bulk flow of the velocity field on scale R to the velocity dispersion within regions of scale R. M is effectively a measure of the ratio of large-scale to small-scale power and can be a useful tool to constrain the cosmological parameter space. Using a compilation of existing peculiar velocity surveys, we calculate M and compare it to that estimated from mock catalogues extracted from the LasDamas (a ΛCDM cosmology) numerical simulations. We find agreement with expectations for the LasDamas cosmology at ∼ 1.5σ CL. We also show that our Mach estimates for the mocks are not biased by selection function effects. To achieve this, we extract dense and nearly-isotropic distributions using Gaussian selection functions with the same width as the characteristic depth of the real surveys, and show that the Mach numbers estimated from the mocks are very similar to the values based on Gaussian profiles of the corresponding widths. We discuss the importance of the survey window functions in estimating their effective depths. We investigate the nonlinear matter power spectrum interpolator PkANN as an alternative to numerical simulations, in the study of Mach number. Key words: galaxies: kinematics and dynamics – galaxies: statistics – cosmology: observations – cosmology: theory – large scale structure of Universe – methods: N-body simula-tions