English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We investigate the evolution of axis ratios of triaxial haloes using thephase space description of triaxial collapse. In this formulation, theevolution of the triaxial ellipsoid is described in terms of the dynamics ofeigenvalues of three important tensors: the Hessian of the gravitationalpotential, the tensor of velocity derivatives and the deformation tensor. Theeigenvalues of the deformation tensor are directly related to the parametersthat describe triaxiality, namely, the minor to major and intermediate to majoraxes ratios ($s$ and $q$) and the triaxiality parameter $T$. Using the phasespace equations, we evolve the eigenvalues and examine the evolution of the PDF(probability distribution function) of the axes ratios as a function of massscale and redshift for Gaussian initial conditions. We find that theellipticity and prolateness increase with decreasing mass scale and decreasingredshift. These trends agree with previous analytic studies but differ fromnumerical simulations. However, the PDF of the scaled parameter ${\tilde q} =(q-s)/(1-s)$ follows a universal distribution over two decades in mass rangeand redshifts which is in qualitative agreement with the universality forconditional PDF reported in simulations. We further show using the phase spacedynamics that, in fact, ${\tilde q}$ is a phase space invariant and isconserved individually for each halo. These results, demonstrate that the phasespace analysis is a useful tool that provides a different perspective on theevolution of perturbations and can be applied to more sophisticated models inthe future.

Evolution of axis ratios from phase space dynamics of triaxial collapse