  A new physical phenomenon is identified: volumetric stellar emission into
gravitationally bound orbits of weakly coupled particles such as axions,
moduli, hidden photons, and neutrinos. While only a tiny fraction of the
instantaneous luminosity of a star (the vast majority of the emission is into
relativistic modes), the continual injection of these particles into a small
part of phase space causes them to accumulate over astrophysically long time
scales, forming what I call a "stellar basin", in analogy with the geologic
kind. The energy density of the Solar basin will surpass that of the
relativistic Solar flux at Earth's location after only a million years, for any
sufficiently long-lived particle produced through an emission process whose
matrix elements are unsuppressed at low momentum. This observation has
immediate and striking consequences for direct detection
experiments---including new limits on axion parameter space independent of dark
matter assumptions---and may also increase the prospects for indirect detection
of weakly interacting particles around compact stars.
