Stable Planetary Orbits in Exosolar Systems

Research project P 14375 Stabile Planetary Orbits in Exosolar Systems Rudolf DVORAK 26.6.2000 This project is concerned with the stability of the new discovered planetary systems on the one hand, and the long term stability of planets in binary systems on the other hand. The first planet outside the Solar System has been found in 1994 around the pulsar PSR 1257+12; this discovery was a first answer to the interesting question if there are other planets beyond our Solar System. Already in 1995 the indirect observation of the first planet orbiting a sun-like star - 51 Pegasi - was reported and now we know about 27 systems with one or more planets. We know, mainly from recent results in celestial mechanics, that the planets in the Solar System are moving around the sun in more or less the same orbits for some 10` years and we deduce from numerical and analytical investigations that there will be no significant changes of the orbits within the next several 109 years. Besides the question of the formation of such systems the long-term dynamical stability is of major interest, because only then - under certain further conditions - a biosphere develops. Therefore, in this project, we want to deal with the problem of the dynamical stability of all the known planetary systems with special emphasis on habitable zones. As a second task we also want to determine the possible orbits of planets in double stars, because most of the stars are not single but are in double star systems or even in multiple star systems. We want to reach the scientific aims with different techniques: with straightforward numerical integrations of the orbits known through observations and with statistical methods for a whole bundle of different initial conditions close to the "real" orbit of the planets. Additionally we plan to use as well qualitative methods using simplified analytical models, especially the three dimensional circular and elliptic restricted three body problem. Furthermore we will investigate planetary orbits in double stars, where the theoretical models of the double star will consist of two massive bodies in different orbits covering a wide range of eccentricity (0.0 < e < 0.6) and mass ratio (1 < m 1 /m2 < 10) of the stars involved. The massless body (which is a good approximation for the planet compared to the masses of the stars) in these theoretical investigations should move on different inclined orbits (0 < i < 90). These second part will be devoted to both types of planetary orbits, the so-called P-types, orbiting both primary bodies, and the so called S-types, staying always in the vicinity of one of the stars. In the framework of the project "Stable Planetary Orbits in Exosolar Systems" we should be able to answer most of the questions of the dynamical lifetime of the known planetary systems and of the stability limits of motions of planets in double stars in connection with possible favorable regions for the development of biospheres.

Since the first discovery of exosolar planets more than 10 years ago many groups are investigating the dynamics of such systems. Today we know more than 100 planets, all approximately of the size of Jupiter, which are moving in systems of quite a different structure than our own planetary system: some of these giant planets are orbiting their host star in distances smaller than our innermost planet Mercury; the ones which are farer away have quite eccentric orbits. The goal of the project was to find stable orbits in dynamical models, where quite often the mass of the planet was not taken into account. In these models - according to the "category" of the systems in question, planets in double stars, terrestrial planets in systems with only one planet or multiplanetary system -- we were able to characterize the stability of the planets` orbits. We also have taken into account the massratio of the doublestar, or the hoststar and the gasplanet, as well as the orbital parameters of these primary bodies. With the aid of these dynamical models we were able - in a first analysis - to determine whether the parameters derived from observations are such that the orbits are stable, but also whether an additional terrestrial planet may move in the so-called habitable zone, where water could be present in liquid form. The study was accomplished with the aid of extensive long-term numerical integrations, where we used different methods of integration as well as different methods of analyzing the data with respect to the stability of the orbits. Finally we investigated real exosolar planetary systems in detail, where special emphasis was given to the possibility of the existence of terrestrial planets in stable orbits. In two double star systems Gamma Cephei and Gliese 86) as well as in the multiplanetary systems (HD 38529) and HD 74156 it is likely that terrestrial planets may move on stable orbits in habitable zones.