Gaussianity of cosmic velocity fields and linearity of the velocity--gravity relation

Abstract

We present a numerical study of the relation between the cosmic peculiar velocity field and the gravitational acceleration field. We show that on mildly non‐linear scales (4–10 h−1 Mpc Gaussian smoothing), the distribution of the Cartesian coordinates of each of these fields is well approximated by a Gaussian. In particular, their kurtoses and negentropies are small compared to those of the velocity divergence and density fields. We find that at these scales the relation between the velocity and gravity field follows linear theory to good accuracy. Specifically, the systematic errors in velocity–velocity comparisons due to assuming the linear model do not exceed 6 per cent in β. To correct for them, we test various non‐linear estimators of velocity from density. We show that a slight modification of the α‐formula proposed by Kudlicki et al. yields an estimator which is essentially unbiased and has a small variance.

Likelihood analysis of the Local Group acceleration revisited

“…It is commonly approximated by a multivariate Gaussian (Strauss et al 1992, hereafter S92; Schmoldt et al 1999, hereafter S99). This approximation has support from numerical simulations (Kofman et al 1994; Cieciela̧g et al 2003), where the measured non‐Gaussianity of g and v is small. This is rather natural to expect since, for example, gravity is an integral of density over effectively a large volume, so the central limit theorem can at least partly be applicable (but see Catelan & Moscardini 1994).…”

Cosmic velocity-gravity relation in redshift space

“…In this section we perform controlled numerical experiments to test the velocity–gravity relation, both in real and redshift space, on the dark matter distribution. These analyses extend the work of Cieciela̧g et al (2003) who performed similar work but only in real space and on simulations using a pure hydrodynamic code approximating the dynamics of dark matter, namely the Cosmological Pressureless Parabolic Advection code of Kudlicki, Plewa & Różyczka (1996, see also Kudlicki et al 2000).…”

“…Furthermore, since the low‐ v regime converges to linear theory, all the curves corresponding to superpose in that regime, creating a ‘caustic’ of best likelihood nearby the maximum of the joint PDF, explaining the very good agreement with linear expectation in that region. As a result, we now understand, thanks to the spherical top‐hat model, both the ‘propeller’ shape of the bivariate PDF, as well as the remarkable agreement with linear theory prediction nearby its maximum, even in the highly non‐linear regime (see also Cieciela̧g et al 2003). The arguments developed here are oversimplified, but capture the main features of the dynamics of the large‐scale structures prior to shell crossing in real space.…”

“…The conditional variance is then equal to (1 − r 2 ) σ 2 g (see e.g. appendix B of Cieciela̧g et al 2003). Thus, for Gaussian velocity and gravity fields in redshift space we have where r is the cross‐correlation coefficient defined in .…”

Precision cosmology with voids: definition, methods, dynamics

“…These two quantities are highly linear. It has been directly shown for velocity fields by Ciecielg et al (2003) and indirectly shown by Mohayaee et al (2006) and Lavaux et al (2008a) for the displacement field. This linearity helps us at constructing an analytical statistical model of the voids.…”