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The Effects of a Stellar Encounter on a Planetesimal Disk
We investigate the effects of a passing stellar encounter on aplanetesimal disk through analytical calculations and numericalsimulations, and derive the boundary radius (aplanet) outsidewhich planet formation is inhibited by disruptive collisions with highrelative velocities. S. Ida, J. Larwood, and A. Burkert (2000,Astrophys. J. 528, 1013-1025) suggested that a stellar encounter causedinhibition of planet formation in the outer part of a protoplanetarydisk. We study orbital eccentricity (e) and inclination (i) ofplanetesimals pumped up by perturbations of a passing single star. Wealso study the degree of alignment of longitude of pericenter andascending node to estimate relative velocities between theplanetesimals. We model a protoplanetary system as a disk of masslessparticles circularly orbiting a host star, following S. Ida, J. Laywood,and A. Burkert (2000, Astrophys. J. 528, 1013-1025). The masslessparticles represent planetesimals. A single star as massive as the hoststar encounters the protoplanetary system. Numerical orbital simulationsshow that in the inner region at semimajor axis a<~0.2 D where D isthe pericenter distance of the encounter, e and i have power-lawdependence 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 andis 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 onthe weakly perturbed inner region. We analytically reproduce thepower-law dependence and explicitly give numerical factors of thepower-law dependence as functions of encounter parameters. We derive theboundar y radius (aplanet) of the planet-forming region as afunction of dynamical parameters of a stellar cluster, assuming theprotoplanetary system belongs to the stellar cluster. The radialgradient 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 isstrengthened by reduction of relative velocity due to the longitudealignment in the inner region. We find aplanet ~ 40-60 AU inthe case of D ~ 150-200 AU. D ~ 200 AU may be likely to occur in arelatively dense cluster. We point out that the size of planetarysystems (aplanet) born in a dense cluster may be necessarilyrestricted to that comparable to the size of a planet region (~30-40 AU)of our SolarSystem.
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