Lunar and Planetary Science XXXI
1096.pdf
THE EFFECTS OF CHAOS ON PLANETESIMAL INTERACTIONS WITHIN PROTOPLANETARY DISKS. Bruce Lindsay and Truell Hyde, Center for Astrophysics, Space Physics and Engineering Research, Baylor University, Waco, TX 76798-7316, USA, phone: 254-710-2511 (email:
[email protected] [email protected]). Introduction: Protoplanetary formation models have primarily focused on one of two areas, corresponding to the two basic types of planets observed in our own solar system. The simulations either concentrate on Earth-like planets forming under the influence of a gas giant that is already assumed to exist[1], or they study the outer planets exclusively with no regard as to what happened in areas closer to the central star[2]. Researchers have yet to find a comprehensive model that produces the terrestrial planets as well as the gas giants using the same physical processes. A research area, which might well provide at least a partial solution to the above problem, deals with the study of chaos within the protoplanetary disk. Chaotic interactions between planetesimals yield a much higher probability of dramatic change over the course of a planetary system’s evolution. This is primarily due to the overlap of mean motion resonances between the planetesimals as they orbit the protostar, an effect that can be seen in the outer planets[3] as well as the asteroid belt[4]. If this chaotic influence can be so easily noticed in a fully developed planetary system, it is reasonable to assume that chaos would have a significant impact on a protoplanetary disk in its early developmental stages. One possible impetus for such chaotic behavior in the early protoplanetary disk is the formation of protoplanets around a forming binary star. Through tidal interactions, energy and angular momentum are transferred between the disk and the protostellar or protoplanetary companion leading to significant modifications of the disk’s structure. Recent discoveries of planetesimal disks around binary T Tauri stars[5] have renewed interest in exactly what form this diskcompanion tidal interaction might take regarding the formation of planets, either in circumstellar orbits or circumbinary ones. A solid understanding of the physics involved would provide important constraints on both the origin of binary stars as well as the exact nature of the disk companion tidal interaction. (Studies have in fact already been done to determine the boundaries of the regions in which forming protoplanets can remain in a stable state[6].) Computer Model: The computer model discussed in this work examines the motion and conglomeration of five hundred planetesimals as they orbit either a single central protostar or one with a binary companion. The program uses a fifth-order Runge-Kutta algorithm to calculate the trajectories of the planetesimals within the forming protoplanetary system[7]. Collisions between the planetesimals are taken into account as either
elastic or inelastic. The planetesimals initially start out with one of two densities, corresponding to either a rock or ice compositional structure. These densities and compositional structures are allowed to dynamically evolve during the course of the simulation as the result of either inelastic collision processes or the planetesimal moving within the “snow line” of the star and its subsequent thermal ablation. Only mutual gravitational forces are accounted for, since the bodies are considered large enough to ignore any sort of gas drag from the solar nebula. The initial conditions for all of the above as well as simulation run times are user defined. At the end of the simulation, the number of surviving planetesimals along with the total mass of the system is recorded, as are the masses, densities, and orbital elements for individual bodies in any predetermined group. Simulation Results: As the planetesimals collide and form protoplanets, smaller rocky bodies are found within the “snow line” of the star, while larger cores of mixed rock and ice survive at larger distances. If these intermediate-density bodies form rapidly enough, then they may be able to accrete sufficient amounts of gas from the solar nebula in order to form Jovian-type planets[8]. Initial simulations of this scenario are currently being run and the results will be shown. There have recently been examples of extrasolar gas giants being discovered in unusual situations, such as orbiting their parent stars with very small semimajor axes or high eccentricities. One possible explanation involves multiple planets of roughly the same size in similar orbits with the resulting perturbations on the system. This possibility is under investigation to determine if the resulting N-body interaction is able to eject some of the planets while at the same time bringing the remaining into tighter orbits. If so, this could serve as a theoretical basis for the discoveries of “hot Jupiters” such as 51 Pegasi B and 70 Virginis B[9]. References: [1] Chambers J. C. and Wetherill G. W. (1998) Icarus, 136, 304-327. [2] Brunini A. and Fernandez J. A. (1999) Planet. Space Sci., 47, 591-605. [3] Murray N. and Holman, M. (1999) Science, 283, 1877-1881. [4] Murray N. et al. (1998) Astro. J, 116, 2583-2589 [5] Boss A. P. (1998) Nature, 395, 320-321. [6] Holman M. J. and Wiegert P. A. (1999) Astro. J., 117, 621-628. [7] Nazzario R. (2000) Ph.D. Dissertation, Baylor University. [8] Wetherill, G. W. (1995) Nature 373, 490 [9] Weidenschilling, S. J. and Marzari, F. (1996) Nature 384, 619-621.
