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 Earths 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.
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