Substructure evolution from protoplanetary to debris disks driven by mutually gravitating planetesimals and implications on Kepler resonances and free-floating planets

Abstract

Motivated by recent observations suggesting rings found in debris disks are wider than those in protoplanetary disks, we consider a picture in which planetesimals formed in radially narrow dust traps radially diffuse into debris rings via mutual scattering. Under this picture, evolving the fractional widths ($\Delta r/r$) of resolved debris rings back to a few Myr according to the theoretical $t^{1/5}$ evolutionary trajectory reproduces the protoplanetary ring distribution. We inferred the product of the ring mass and individual planetesimal mass required to reach the observed debris ring widths at their ages, finding that $M_\mathrm{disk}\times m$ ranges from $10^{-3}$ to $10^{3} \, M_\oplus^2$. The distribution of $M_\mathrm{disk} \times m$ appears to correlate with the stellar mass, peaking at 1.5 to 2 $M_\odot$, which resembles the stellar mass dependence of the giant exoplanet occurrence rate. The population of resolved debris rings lie close to the $\Delta r / r = 10 \, h$ equipartition relation expected of a planetesimal ring that formed narrow, with typical resolved debris disks still expected to be broadening radially and vertically at present. If sufficiently massive ($\sim$10 $M_\oplus$), this radial broadening can send a few Mercurys to the terrestrial region within 10 Myr, making debris disks a plausible source of planetesimals disrupting resonant chains among Kepler planets. Within Gyr timescales, outer planetesimal belts can also eject $\sim$1% of their mass into interstellar space if they consist of Moon-sized bodies or above, suggesting that the slow and steady intrinsic evolution of massive debris disks could contribute to the interstellar free-floating population of terrestrial-planet-sized bodies.