The caustic ring singularity

Details The caustic ring singularity The caustic ring singularity

1999-02-15

arxiv.org/abs/astro-ph/9902210v3

Phys.Rev. D60 (1999) 063501

Astronomy and Astrophysics

Astrophysics

34 pages, 10 figures, a minor comment has been added

Scientific paper

10.1103/PhysRevD.60.063501

I investigate the caustics produced by the fall of collisionless dark matter in and out of a galaxy in the limit of negligible velocity dispersion. The outer caustics are spherical shells enveloping the galaxy. The inner caustics are rings. These are located near where the particles with the most angular momentum are at their distance of closest approach to the galactic center. The surface of a caustic ring is a closed tube whose cross-section is a $D_{-4}$ catastrophe. It has three cusps amongst which exists a discrete $Z_3$ symmetry. A detailed analysis is given in the limit where the flow of particles is axially and reflection symmetric and where the transverse dimensions of the ring are small compared to the ring radius. Five parameters describe the caustic in that limit. The relations between these parameters and the initial velocity distribution of the particles are derived. The structure of the caustic ring is used to predict the shape of the bump produced in a galactic rotation curve by a caustic ring lying in the galactic plane.

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