The Effects of a Stellar Encounter on a Planetesimal Disk

Abstract

We investigate the effects of a passing stellar encounter on a planetesimal disk through analytical calculations and numerical simulations, and derive the boundary radius ( a planet) outside which planet formation is inhibited by disruptive collisions with high relative velocities. S. Ida, J. Larwood, and A. Burkert (2000, Astrophys. J. 528, 1013–1025) suggested that a stellar encounter caused inhibition of planet formation in the outer part of a protoplanetary disk. We study orbital eccentricity ( e) and inclination ( i) of planetesimals pumped up by perturbations of a passing single star. We also study the degree of alignment of longitude of pericenter and ascending node to estimate relative velocities between the planetesimals. We model a protoplanetary system as a disk of massless particles circularly orbiting a host star, following S. Ida, J. Laywood, and A. Burkert (2000, Astrophys. J. 528, 1013–1025). The massless particles represent planetesimals. A single star as massive as the host star encounters the protoplanetary system. Numerical orbital simulations show that in the inner region at semimajor axis a≲0.2 D where D is the pericenter distance of the encounter, e and i have power-law dependence on ( a/ D) as e∝( a/ D) 5/2 and i∝( a/ D) 3/2, and the longitudes are aligned, independent of the encounter parameters. In the outer region a≳0.2 D, and the radial gradient is steeper and is not expressed by a single power law. The longitudes are not aligned. Since planet accretion is inhibited by e as small as 0.01, we focus on the weakly perturbed inner region. We analytically reproduce the power-law dependence and explicitly give numerical factors of the power-law dependence as functions of encounter parameters. We derive the boundar y radius ( a planet) of the planet-forming region as a function of dynamical parameters of a stellar cluster, assuming the protoplanetary system belongs to the stellar cluster. The radial gradient of e is so steep that the boundary is sharply determined. Planetesimal orbits are significantly modified beyond the boundary, while they are almost intact inside the boundary. This tendency is strengthened by reduction of relative velocity due to the longitude alignment in the inner region. We find a planet ∼ 40–60 AU in the case of D ∼ 150–200 AU. D ∼ 200 AU may be likely to occur in a relatively dense cluster. We point out that the size of planetary systems ( a planet) born in a dense cluster may be necessarily restricted to that comparable to the size of a planet region (∼30–40 AU) of our SolarSystem.