http://arxiv.org/abs/1501.07075
In paper I of this series, we examined triaxial collapse in terms of the dynamics of eigenvalues of three important tensors: the Hessian of the gravitational potential, the tensor of velocity derivatives and the deformation tensor. The first paper focussed on the joint gravity-velocity dynamics and here we focus on the deformation tensor, which is directly related to the axes’ evolution. We examine the evolution of the minor to major and intermediate to major axes ratios ($s$ and $q$) and the triaxiality parameter $T$ as function of mass scale and redshift. We find that the ellipticity and prolateness increase with decreasing mass scale and decreasing redshift. These trends, while in agreement with previous analytic studies, contradict numerical simulations. Nevertheless, we find that a suitable transformation of $s$, motivated by the scaling used in recent analysis of the Millennium XXL simulations by Bonamigo {\it et al} (2014), has a universal log-normal distribution function that matches their numerical results. Similarly, the transformation ${\tilde q} = (q-s)/(1-s)$ also has a universal beta distribution that is valid over a decade in mass range and over a wide range of redshift scales, indicating that the variable ${\tilde q}$ can be thought of as an invariant of the phase space dynamics.
S. Nadkarni-Ghosh and A. Singhal
Thu, 29 Jan 15
33/49
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