Dense Dark Matter Hairs Spreading Out from Earth, Jupiter and Other Compact Bodies

It is shown that compact bodies project out strands of concentrated dark matter filaments henceforth simply 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 $\Lambda$CDM. Using both an analytical model of planetary density and numerical simulations utilizing the Fast Accurate Integrand Renormalization (FAIR) algorithm (a fast geodesics calculator described below) 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 $10^7$ for Earth and $10^8$ 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 $10^6$~km from the planetary center with a density enhancement of around $10^9$ while for a gas giant like Jupiter, the root is located at around $10^{5}$~km with a enhancement of around $10^{11}$. Beyond the root, the hair density precisely reflects the density layers of the body providing a direct probe of planetary interiors.