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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

I present an analytic model for the early post-collapse evolution of aspherical density peak on the coherence scale of the initial fluctuations in auniverse filled with collisionless and pressure-free "dust". On a time-scalewhich is short compared to the peak's collapse time $t_0$, its inner regionssettle into an equilibrium cusp with a power-law density profile, $\rho\proptor^{-12/7}$. Within this cusp, the circular orbit period $P$ at each radius isrelated to the enclosed mass $M$ by $P = t_0 (M/M_c)^{2/3}$ where $M_c$ is asuitably defined characteristic mass for the initial peak. The relaxationmechanism which produces this cusp gives insight into those which are active inhigh-resolution simulations of first halo formation in Cold or Warm Dark Matteruniverses, and, indeed, a simple argument suggests that the same power-lawindex $\gamma=-12/7$ should describe the prompt cusps formed during thecollapse of generic peaks, independent of any symmetry assumption. Further workis needed to investigate whether additional factors are required to explain theslightly flatter exponent, $\gamma\approx -1.5$, found in high-resolutionnumerical simulations of peak collapse.

Prompt cusp formation from the gravitational collapse of peaks in the initial cosmological density field