Open AccessSelf‐similar spherical collapse with non‐radial motions
Author(s) -
Nusser Adi
Publication year - 2001
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2001.04527.x
Subject(s) - physics , angular momentum , radius , perturbation (astronomy) , radial velocity , orbit (dynamics) , circular orbit , classical mechanics , astrophysics , stars , quantum mechanics , computer security , computer science , engineering , aerospace engineering
We derive the asymptotic mass profile near the collapse centre of an initial spherical density perturbation, δ∝M −ε , of collisionless particles with non‐radial motions. We show that angular momenta introduced at the initial time do not affect the mass profile. Alternatively, we consider a scheme in which a particle moves on a radial orbit until it reaches its turnaround radius, r ∗. At turnaround the particle acquires an angular momentum L=ℒ√GM * r * per unit mass, where M ∗ is the mass interior to r ∗. In this scheme, the mass profile is M∝r 3/(1+3ε) for all ε>0 , in the region r/r t ≪ℒ , where r t is the current turnaround radius. If ℒ≪1 then the profile in the region ℒ≪r/r t ≪1 is M∝r for ε<2/3 , and remains M∝r 3/(1+3ε) for ε≥2/3 . The derivation relies on a general property of non‐radial orbits which is that the ratio of the pericentre to apocentre is constant in a force field k(t)r n with k ( t ) varying adiabatically.