  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.
