The Oort Cloud as a Gravitational Detector for Primordial Black Holes

Planetary systems can act as sensitive gravitational detectors for dark matter. We investigate the gravitational scattering of Oort cloud objects by primordial black holes (PBHs) as a potential component of the Galactic dark matter halo. Calculating the rates at which PBH encounters eject objects from the Oort cloud or inject them into Earth crossing orbits, we find a linear scaling $\mathrm{\Gamma }\propto m_{\mathrm{P}\mathrm{B}\mathrm{H}}$ for $m_{\mathrm{P}\mathrm{B}\mathrm{H}}\gtrsim {10}^{-10}{M}_{\odot }$. For $m_{\mathrm{P}\mathrm{B}\mathrm{H}}\sim {10}^3{M}_{\odot }$, PBHs constituting all local dark matter would eject $\sim 1.3\times {10}^{12}$ objects over the Solar System’s lifetime, comparable to the total Oort cloud population and inject $\sim 2.6\times {10}^{10}$ objects into Earth-crossing orbits. Comparing these rates with observational constraints from long period comet fluxes and terrestrial impact records, we derive upper limits on the PBH dark matter fraction $f_{\mathrm{P}\mathrm{B}\mathrm{H}}$. Our most stringent constraints exclude $f_{\mathrm{P}\mathrm{B}\mathrm{H}}=1$ for ${10}^2{M}_{\odot }\lesssim m_{\mathrm{P}\mathrm{B}\mathrm{H}}\lesssim {10}^5{M}_{\odot }$, with $f_{\mathrm{P}\mathrm{B}\mathrm{H}}\lesssim 0.002$ at $m_{\mathrm{P}\mathrm{B}\mathrm{H}}={10}^3{M}_{\odot }$. For the asteroid mass window (${10}^{17}$-${10}^{23}$ g), scattering rates are far too low to produce observable effects. These Solar System-based constraints complement existing astrophysical probes and demonstrate that planetary systems can serve as sensitive gravitational detectors for compact dark matter.