A halo of trapped interstellar matter surrounding the solar system

This paper shows that gravitating bodies travelling through the Galaxy can trap lighter interstellar particles that pass nearby with small relative velocities onto temporarily-bound orbits. The capture mechanism is driven by the Galactic tidal field, which can decelerate infalling objects to a degree where their binding energy becomes negative. Over time, trapped particles build a local overdensity – or halo'-- that reaches a steady state as the number of particles being captured equals that being tidally stripped. This paper uses classical stochastic techniques to calculate the capture rate and the phase-space distribution of particles trapped by a point-mass. In a steady state, bound particles generate a density enhancement that scales as $δ(r)\sim r^{-3/2}$ (a.k.a density spike’) and follow a velocity dispersion profile ${\sigma }_h(r)\sim r^{-1\mathrm{/}2}$. Collisionless $N$-body experiments show excellent agreement with these theoretical predictions within a distance range $r\gtrsim r_{\epsilon }$, where $r_{\epsilon }\simeq 0.8\exp [-V_{\star }^2\mathrm{/}(2{\sigma }^2)]G{m}_{\star }\mathrm{/}{\sigma }^2$ is the thermal critical radius of a point-mass $m_{\star }$ moving with a speed $V_{\star }$ through a sea of particles with a velocity dispersion $\sigma$. Preliminary estimates that ignore collisions with planets and Galactic substructures suggest that the solar system may be surrounded by a halo that contains the order of $N^{\mathrm{I}\mathrm{S}\mathrm{O}}(<0.1\mathrm{p}\mathrm{c})\sim {10}^7$ energetically-bound 'Oumuamua-like objects, and a dark matter mass of $M^{\mathrm{D}\mathrm{M}}(<0.1\mathrm{p}\mathrm{c})\sim {10}^{-13}{M}_{\odot }$. The presence of trapped interstellar matter in the solar system can affect current estimates on the size of the Oort Cloud, and leave a distinct signal in direct dark matter detection experiments.