NASA has a need to determine the distribution of dark matter around planets like Earth. Doing so necessitates the ability to repeatedly solve the geodesic equation in simulations of weakly interacting particles streaming through bodies described by a Schwarzschild metric. Geodesolver numerically solves the geodesic equation orders of magnitudes faster than Runge-Kutta for arbitrary density profiles.

Using geodesolver, it was shown that compact bodies project out strands of concentrated dark matter (CDM) filaments called hairs. These hairs are a consequence of the fine-grained stream structure of dark matter halos, and as such constitute a new physical prediction of CDM. Using both an analytical model of planetary density and numerical simulations utilizing the Fast Accurate Integrand Renormalization (FAIR) algorithm with realistic planetary density inputs, dark matter streams moving through a compact body are shown to produce hugely magnified dark matter densities along the stream velocity axis going through the center of the body.

Typical hair density enhancements are 107 for Earth and 108 for Jupiter. The largest enhancements occur for particles streaming through the core of the body that mostly focus at a single point called the root of the hair. For the Earth, the root is located at about 106 km from the planetary center, with a density enhancement of around 109; for a gas giant like Jupiter, the root is located at around 105 km, with an enhancement of around 1011.

This work was done by Gary M. Prezeau of Caltech for NASA's Jet Propulsion Laboratory. This software is available for license through the Jet Propulsion Laboratory, and you may request a license here . NPO-50012.