Caustics in growing Cold Dark Matter Haloes

TL;DR

This study simulates dark matter halo growth, revealing that caustics contribute minimally to annihilation signals, especially in inner regions, due to complex orbital structures and rapid stream density drops.

Contribution

It introduces a novel simulation method tracking streams and caustics via geodesic deviation, providing detailed insights into halo structure and caustic effects.

Findings

Number of streams at 1% of turnaround radius is about 10^6.

Caustic contribution to annihilation radiation is significantly reduced in inner halo regions.

Outer caustics might be detectable, but inner caustics are unobservable.

Abstract

We simulate the growth of isolated dark matter haloes from self-similar and spherically symmetric initial conditions. Our N-body code integrates the geodesic deviation equation in order to track the streams and caustics associated with individual simulation particles. The radial orbit instability causes our haloes to develop major-to-minor axis ratios approaching 10 to 1 in their inner regions. They grow similarly in time and have similar density profiles to the spherical similarity solution, but their detailed structure is very different. The higher dimensionality of the orbits causes their stream and caustic densities to drop much more rapidly than in the similarity solution. This results in a corresponding increase in the number of streams at each point. At 1% of the turnaround radius (corresponding roughly to the Sun's position in the Milky Way) we find of order 10^6 streams in our simulations, as compared to 10^2 in the similarity solution. The number of caustics in the inner halo increases by a factor of several, because a typical orbit has six turning points rather than one, but caustic densities drop by a much larger factor. This reduces the caustic contribution to the annihilation radiation. For the region between 1% and 50% of the turnaround radius, this is 4% of the total in our simulated haloes, as compared to 6.5% in the similarity solution. Caustics contribute much less at smaller radii. These numbers assume a 100 GeV c^-2 neutralino with present-day velocity dispersion 0.03 cm s^-1, but reducing the dispersion by ten orders of magnitude only doubles the caustic luminosity. We conclude that caustics will be unobservable in the inner parts of haloes. Only the outermost caustic might potentially be detectable.