Giant Planets Can Act as Stabilizing Agents on Debris Disks

Abstract

We have explored the evolution of a cold debris disk under the gravitational influence of dwarf planet sized objects (DPs), both in the presence and absence of an interior giant planet. Through detailed long-term numerical simulations, we demonstrate that, when the giant planet is not present, DPs can stir the eccentricities and inclinations of disk particles, in linear proportion to the total mass of the DPs; on the other hand, when the giant planet is included in the simulations, the stirring is approximately proportional to the mass squared. This creates two regimes: below a disk mass threshold (defined by the total mass of DPs), the giant planet acts as a stabilizing agent of the orbits of cometary nucleii, diminishing the effect of the scatterers; above the threshold, the giant contributes to the dispersion of the particles.

The Contribution of Dwarf Planets to the Origin of Low-inclination Comets by the Replenishment of Mean Motion Resonances in Debris Disks

“…In Muñoz-Gutiérrez et al (2017) we demonstrated that the excitation levels of the disk particles are weakly dependent on the index of the DP differential mass distribution (dMD), α. For a differential size distribution (dSD) of the form dN/dD ∝ D −q , a dMD will be given by: dN/dM ∝ M −α , where α is related to the index of the dSD, q, as α = (2 + q)/3; since, for a constant density, D ∝ M 1/3 .…”

“…Regarding the orbital distribution, all eccentricities and inclinations are randomly assigned between 0 and 0.1 and 0 • and 5 • , respectively, while the three angles, ω, Ω, and M , are randomly assigned between 0 • and 360 • . The simulations shown in this work included some of those presented previously in Muñoz-Gutiérrez et al (2017), plus several new cases.…”

“…The radius of the DPs are calculated from their assigned random masses and densities. As we described in Muñoz-Gutiérrez et al (2017), the mass of each DP, m n , is assigned using the formula:…”

“…Panels 7e and 7f correspond to disks with masses where the giant planet no longer acts as stabilizer (Muñoz-Gutiérrez et al 2017), therefore the dispersion observed in those panels grows significantly when compared to the first four panels, with particles which come from region 1 being rapidly sent either to the scattered population or to the inner planetary system system. In Fig.…”

“…In Figure 11 we compare the results of both of the 0.05M ⊕ disk simulations. Our new simulation was done with 2000 particles; in Muñoz-Gutiérrez et al (2017) we checked that simulations with that number of particles are statistically equivalent. Panel 11a shows the fractional number of particles evolution for all the regions described earlier, where the broad curves represent results from our standard simulation, while the thin curves are result from the modified simulation.…”