CP-2156 Life In The Universe

 

Planetary Orbits in Multiple Star Systems

R. S. HARRINGTON

 

[119] If processes occurring during the formation of multiple star systems are not prohibitory, it appears quite likely that planets can exist in stable, roughly circular orbits around one or two members of common types of multiple star systems.

 

The Universe is full of multiple star systems. The most conservative estimates suggest that at least one-third of all apparently stellar objects are multiple systems, with some estimates going all the way from more than half to practically all. These are not just binary stars, since at least a third of all multiple systems have three or more components (arranged in hierarchies of spacing such that any stable multiple system may be thought of as a set of binaries). When it comes to selecting objects that might be capable of supporting a planetary system with potential life-bearing planets, however, it has been traditional to rule out these multiple systems immediately. It has been argued that planetary orbits would be unstable and that planets would be ejected from the system, or at least that the perturbations on the planetary orbits would be so great that the constancy of conditions required to support life would be impossible. Thus multiple systems (binaries in particular have not been considered as possible targets on many SETI lists. This question now needs to be examined more carefully.

Two questions must be considered. First, are planetary orbits in multiple systems sufficiently stable to allow life to develop? Second, could planets form in such systems in the first place? Considerable work has been don in the last few years on the first question. Before going further, we should clarify the definition of stability, since there are several in common use. Here we mean only what is usually referred to as orbital stability; that [120] is, an orbit is stable if there are no significant variations in its characteristic parameters (basically, the axes, or the major axis and eccentricity), and this must be true in particular for low-eccentricity orbits. Note that this is different from, and much weaker than, the more standard linear stability, but it is physically much more reasonable (after all, even the two-body problem is linearly unstable). Just what constitutes a significant variation is left somewhat vague, although in practice the transition from insignificance to significance is rather abrupt and easy to identify.

Szebehely (1977) and his students (Szebehely and Zare, 1977) examined the problem of stability from the point of view of the topology of Hill's zero-velocity surfaces. If a zero-velocity surface remains closed around the components of a binary system, a small mass cannot escape; if the surface remains closed around the entire body, an exterior body cannot get into the so-called region of interplay. If, however, the surface opens (Szebehely considers the first opening, the one at the neutral point between the components of the binary), then there is the possibility of exchange or escape, and the system is classified as unstable. Note that this is a sufficient condition for stability but only a necessary one for instability, in that a system need not actually be unstable just because a zero-velocity surface opens. Indeed, while many multiple stars are stable by this test, a planetary orbit in a binary (the case of a single small, but nonzero, mass) is unstable in general. This may be a bit too pessimistic.

An alternative approach is an experimental/statistical one. Here many multiple systems are integrated numerically on a computer, each system is evaluated for stability (usually qualitatively), and the pertinent parameters for stability are identified and quantified. The disadvantages of such an approach are that no system can be followed for anything like a cosmological length of time (because of error accumulation, if nothing else) and that, since we cannot consider all possible cases, the results are only empirical averages. Positive factors include a minimum of analytic assumptions, the fact that unstable systems do decay very quickly, and the fact that a statistical conclusion is all that is required now.

An extensive study of this nature was carried out by Harrington (1977), and the results will only be summarized here (see also Harrington and Harrington, 1978). Basically, a planet can stay in a stable orbit in a binary system if it stays close to one component (thus seeing the other star only as a distant perturbative influence) or well outside the system (thus seeing the two stars as approximately a single object). The first case would occur in the visual binary systems, the second in the spectroscopic systems. The actual limiting distance ratios depend on the eccentricity of the binary if the planet is close to one component, on the relative sense of revolution, and weakly on the mass ratio of the binary. A conservative all-inclusive statement is that a system will be stable if the distance ratios remain above 4:1.

[121] The above limit establishes a rather extensive region in a binary (and, by extension, in any multiple system) in which planetary orbits would be quite stable. if the so-called habitable zone is also within this region, then the system is capable of supporting a life-bearing planet and is a possible SETI candidate. Note that all the problems associated with identifying the habitable zone (temperature, variability, evolution, etc.) still exist with multiple stars and that, if a system does not qualify for other reasons, the considerations here are irrelevant. However, if we take the simplest definition of the habitable zone-a region where the total energy received is equal to that received from a 1symbol for solar massstar at 1 AU-then all of the popular nearby binaries qualify as possible SETI targets, with the exception of Sirius and possibly Procyon. Indeed, these are all cases in which the planet would have to orbit close to one component, which means that some of the nearby binaries might actually be potential multiple targets.

Perhaps more serious is the second question, that of whether planets could ever form in multiple star systems. The currently accepted mode of planet formation-condensation in the protostar nebula-is appealing in that it makes planetary formation a common phenomenon; it is therefore assumed that what could happen around single stars could also happen around components of a multiple system. However, when Heppenheimer (1974, 1978) studied the problem in detail, his conclusions were pessimistic. The basic mechanism assumed involves a cloud of particles orbiting a newly formed star and undergoing collisions reasonably often. If the relative collisional velocities are below a certain limiting value, the collision is inelastic and the particles stick together, eventually building up to planet-sized bodies. If the relative velocities are above the limit, the particles fragment, preventing formation by accretion.

For a single star, with all the planetesimals in essentially circular orbits, the mechanism works well. For a binary, the particles orbiting one component suffer perturbations by the other component. These perturbations will, in particular, produce secular increases in the eccentricities of the planetesimal orbits, which in turn produce increases in the velocity dispersion. With a set of reasonable assumptions about conditions within the cloud of particles and the nature of the particles themselves, this increased velocity dispersion may raise the relative collision velocities above the limiting velocity for accretion. Heppenheimer concludes that, since the semimajor axis of the binary needs to be greater than 50 AU, most nearby binaries are indeed unsuitable for planet formation. (Note that the case of a spectroscopic system with a planet orbiting the full system has not been treated.)

Several considerations may make the prospect seem less bleak. First, as Heppenheimer points out, the actual physical situation is more complicated. The protostar nebula is not a cloud of massless particles orbiting a point mass. The nebula has mass and its perturbations should be considered. More [122] significantly, the nebula will produce aerodynamic drag on the particles, and this tends to decrease eccentricity, offsetting the effects of the other component. Unfortunately, the nebula has to be quite massive for either of these effects to be significant in the binaries under consideration, probably more massive than can be reasonably justified.

Another possibility is that the planets are created about the components before the final binaries are formed. It now seems quite reasonable that stars form out of fairly large clouds initially into loose clusters and associations. These unstable configurations undergo dynamical decay, leaving behind the observed distribution of single and multiple stars (Harrington, 1975). The escape energies for the decay are taken from the binding energies of the remaining multiple systems, so that these systems close up as the decay proceeds. If the nebulae around the stars contracted and formed planets before the decay of the system (Larson, 1978; Kobrick and Kaula, 1979), there would be no significant perturbations to increase the velocity dispersion within the nebula. The major drawback to this idea is that the time scales for decay (relaxation) of typical stellar systems are short compared to the time scales usually assumed for planet formation, making it difficult for planets to form before the system decays.

Finally, there is always the possibility that we do not yet fully understand the process (or processes) of planet formation. Indeed, this is the major area of uncertainty. If the Goldreich and Ward (1973) picture of the formation of planets is basically correct, and if the various assumptions concerning nebular conditions employed by Heppenheimer are correct, then it is difficult to reconcile the existence of planets in multiple stars. However, there are considerable uncertainties in these assumptions, which would make it premature to rule out multiple systems as possible locations of planets. Indeed, an observational determination of the relative numbers of planets around single and multiple stars would do much to place empirical limits on the possible mechanisms for planet formation. Multiple systems should remain possible targets for any SETI strategy, with the understanding that there are added uncertainties about the possibilities for such systems.

 

REFERENCES

 

- Goldreich, P.; and Ward, W. R.: The Formation of Planetesimals. Astrophys. J., vol. 183,1973, pp. 1051 -1061.

- Harrington, R. S.: Production of Triple Stars by Dynamical Decay of Small Stellar Systems. Astronom. J., vol.80, 1975, pp. 1081-1086.

[123] - Harrington, R. S.: Planetary Orbits in Binary Stars. Astronom. J., vol. 82, 1977, pp. 753-756.

- Harrington, R. S.; and Harrington, B. J.: Can We Find a Place to Live Near a Multiple Star. Mercury, vol. 7,1978, pp. 34-37.

- Heppenheimer, T. A.: Outline of a Theory of Planet Formation in Binary Systems. Icarus, vol. 22,1974, pp. 436-447.

- Heppenheimer, T. A.: On the Formation of Planets in Binary Star Systems. Astron. Astrophys., vol. 65,1978, pp. 421-426.

- Kobrick, M.; and Kaula, W. M.: Tidal Theory for the Origin of the Solar Nebula. Moon and Planets, vol. 20,1979, pp. 61 -101.

- Larson, R. B.: Calculations of 3-Dimensional Collapse and Fragmentation. Monthly Notices Royal Astronom. Soc., vol. 184, 1978, pp. 69-85.

- Szebehely, V.: Analytical Determination of the Measure of Stability of Triple Stellar Systems. Celestial Mech., vol. 15, 1977, pp. 107-110.

- Szebehely, V.; and Zare, K.: Stability of Classical Triplets and of Their Hierarchy. Astron. Astrophys., vol. 58,1977, pp.145-15.


previousindexnext