Capture of interstellar objects II: by the Solar system
  Capture of interstellar objects (ISOs) into the Solar system is dominated by
ISOs with asymptotic incoming speeds $v_\infty<4\,$km\,s$^{-1}$. The capture
rate is proportional to the ISO phase-space density in the Solar vicinity and
does not vary along the Sun's Galactic orbit, i.e.\ is not enhanced during a
passage through a cloud of ISOs (in contrast to previous suggestions). Most
bound orbits crossing those of Jupiter and Saturn are fully mixed with unbound
phase space, implying that they hold the same ISO phase-space density. Assuming
an interstellar number density $n_{iso}\sim0.1\,$au$^{-3}$, we estimate that in
1000 years the planets capture $\sim2$ ISOs (while $\sim17$ fall into the Sun),
resulting in a population of $\sim8$ captured ISOs within 5\,au of the Sun at
any time, less than the number of visiting ISOs passing through the same volume
on hyperbolic orbits. In terms of phase-space volume, capture onto and ejection
from the Solar system are equal, such that on average ISOs will not remain
captive at $a\lesssim2000\,$au for extensive periods.
