Gravitational Scattering of Oort Cloud Objects by Dark Matter: Constraints on the Primordial Black Hole Fraction

Abstract

Planetary systems can act as long-term gravitational detectors for dark matter. We investigate the gravitational scattering of Oort cloud objects by primordial black holes (PBHs) using celestial kinematics in the impulsive approximation. By evaluating the energy transfer during these encounters, we compute the rates at which stellar-mass PBHs eject icy planetesimals or inject them into Earth-crossing orbits, demonstrating a linear scaling $\Gamma \propto m_{\mathrm{PBH}}$. Comparing these theoretical rates with four independent observables---Oort cloud survival limits, dynamically new long-period comet fluxes, and pristine terrestrial and lunar impact records---we derive stringent upper limits on the PBH dark matter fraction, $f_{\mathrm{PBH}}$. Our most robust combined constraint yields $f_{\mathrm{PBH}} \lesssim 0.65 (m_{\mathrm{PBH}}/M_\odot)^{-1}$, which excludes PBHs as the dominant dark matter component in the intermediate-to-high mass window of $10^2 M_\odot \lesssim m_{\mathrm{PBH}} \lesssim 10^5 M_\odot$. Furthermore, the solar motion through the Galactic halo induces a ``dark matter wind,'' generating a pronounced dipole anisotropy in the arrival directions of PBH-injected comets. This geometrical signature, manifesting as a $\sim 2.7:1$ hemispherical asymmetry (and a $\sim 40:1$ polar contrast) between the anti-apex and apex directions, provides a robust, testable discriminant against isotropic stellar perturbations. This distinct signature could be statistically detected with the discovery of $\mathcal{O}(10^2)$ new long-period comets by upcoming surveys such as the Legacy Survey of Space and Time (LSST) at the Rubin Observatory.