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An improved model for the nonlinear velocity power spectrum

The velocity divergence power spectrum is a key ingredient in modelling redshift space distortion effects on quasi-linear and nonlinear scales. We present an improved model for the z=0 velocity divergence auto and cross power spectrum which was originally suggested by Jennings et al. 2011. Using numerical simulations we measure the velocity fields using a Delaunay tesselation and obtain an accurate prediction of the velocity divergence power spectrum on scales k < 1 hMpc^{-1}. We use this to update the model which is now accurate to 2% for both P_{θθ} and P_{θδ} at z=0 on scales k <0.7 hMpc^{-1} and k <0.5 hMpc^{-1} respectively. We find that the formula for the redshift dependence of the velocity divergence power spectra proposed by Jennings et al. 2011 recovers the measured z>0 P(k) to markedly greater accuracy with the new model. The nonlinear P_{θθ} and P_{θδ} at z =1 are recovered accurately to better than 2% on scales k<0.2 hMpc^{-1}. Recently it was shown that the velocity field shows larger differences between modified gravity cosmologies and ΛCDM compared to the matter field. An accurate model for the velocity divergence power spectrum, such as the one presented here, is a valuable tool for analysing redshift space distortion effects in future galaxy surveys and for constraining deviations from general relativity.