http://arxiv.org/abs/1612.04275
We study the evolution of spherical symmetric overdense regions in tidal gravitational fields. The evolution of the overdensity is governed by the Raychaudhuri equation, sourced by self gravity and external fields, the latter are described by first order Lagrangian perturbation theory. The tidal tensor is decomposed into a symmetric and anti-symmetric part, using the commutator and the anti-commutator with the inertia tensor respectively which are then identified with shear and rotation.
The inertia tensor is obtained from the curvature of the density field, which is correlated with the values of the tidal tensor. By estimating by how much an ellipsoidal region of the same mass as the spherical region would spin up due to the misalignment of the eigenframes of the inertia and tidal tensor, i.e. tidal torquing, we are able to identify the invariants $\sigma^2$ and $\omega^2$ induced by the external gravitational tidal field.
Within this framework we find that $\omega^2 \le \sigma^2$ holds exactly and not only in a statistical sense if we restrict our considerations to maxima in the density field. This shows that the collapse will always proceed faster than in the case without tidal gravitational field. We also investigate their scaling with mass and the influence on $\delta_\mathrm{c}$ and find similar results as in Reischke et al. (2016a), namely roughly one percent deviations from the standard spherical collapse model. As a consequence, cluster counts could build up an additional $\sim 1\sigma$ in cosmological parameters.
R. Reischke, F. Pace, S. Meyer, et. al.
Wed, 14 Dec 16
24/67
Comments: 8 pages, 5 figures, submitted to MNRAS
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