From: utzoo!decvax!harpo!seismo!hao!menlo70!nsc!rogers Newsgroups: net.physics Title: Re: Re: But Siriusly, Folks... Article-I.D.: nsc.279 Posted: Fri Apr 8 08:46:38 1983 Received: Mon Apr 11 00:54:27 1983 Expires: Fri Apr 22 08:46:38 1983 Subject: Multiple Star Solar Systems I received a request to post this article from a source whose address I could not decode. There was a remarkable(>5, more than I expected) number of requests for the article; so here it is. No flames about the length, please. A few years ago, an astronomy teacher gave me a copy of an article on the subject in answer to just that question. I have reprinted it without permission: >From MERCURY March/April 1978 pp 34-37 Can We Find A Place To Live Near A Multiple Star? Robert S. Harrington U.S. Naval Observatory and Betty J. Harrington As NASA begins a long-term effort to search for intelligent life else- where in space, the question of where other planetary systems might be found assumes new urgency. In this article Robert and Betty Harrington report on com- puter simulations which have given us new insight into the possibility of planets around multiple stars.(Introductory Blurb) Where, other than in our own solar system, might we hope to find planets? This question has acquired new significance in several ares of inquiry. First, the SETI(Search for Extraterrestrial Intelligence) project has achieved operational status, and one of the first questions that must be con- sidered is where to look. Further, we now have more plausible theories con- cerning the origin of our solar system and hopefully, planetary systems in general. We would like to find additional systems to test our theories, and thus to identify where such systems might still exist. Finally, there are future questions of interstellar spaceflight and exploration, and the selection of worthy target objects to examine. These efforts might ultimately lead to colonization, which necessitates not only planets, but hospitable ones. Thus, there is now a renewed need to examine the question of where planets might exist, and we must consider any promising objects or classes of objects. Of immediate concern is whether planets could exist in umltiple star systems, which appear to be quite common in the universe. In thses systems two or more stars move around each other, bound together by mutual gravitational attraction. Most common among such systems are the binary stars. There are two general types -- the very close binaries, with periods of revolution measured in days and the wide binaries, with periods measured in years. The first type is usually observed spectroscopically or photometrically, while the second type is observed micrometrically or photographically. Whether these are really two distinct types of systems(possibly with different origins), is still an open question. Besides the binary stars there are of higher multiplicity(triple,quad- ruple,etc.), though these are less common. A striking characteristic of these systems is that the members subgroup themselves, such that, at first glance, they can be treated as multiple binaries. Thus, in a triple system, two stars will be close together, with the third at a relatively great distance. A quadruple system can have two close binary pairs, separated by a comparatively large distance or it could have a close binary, a moderately distant third member, and a very distant fourth member. For systems of even higher multiplicity the number of possible combinations increases rapidly, but the same principle is followed. NEARBY MULTIPLE STARS SYSTEM DISTANCE PERIOD SEMI-MAJ ECCENTRICITY MIN DIST LIGHT-YR YRS AU AU AU -------------------------------------------------------------------------------- a-Centauri 4.3 80 23 0.5 11 L726.8 8.6 26 5 0.6 2 Sirius 8.7 50 20 0.6 8 61 Cygni 11.2 Possibly Parabolic 1 76 Procyon 11.4 41 16 0.4 10 Groombridge 34 11.6 3000 160 0.2 120 Kruger 60 12.8 44 9 0.4 6 Ross 614 13.1 16 4 0.4 2 Wolf 424 14.2 Orbit Not Known G208-44/45 15.5 Orbit Not Known 40 Eridani BC 15.6 250 34 0.4 2 40 Eridani A-BC Orbit Not Known 70 Ophiuchi 16.7 88 23 0.5 12 Stein 2051 17.0 Orbit Not Known FIGURE 1. A table fo nearby multiple stars. An examination of the list of the closest stars immediately shows the high frequency of multiple systems(See Figure 1). The nearest known star, Alpha Centauri, is actually a well-known binary, without even including the distant(probably nonbound) companion, Proxima. The next three nearest stars are not known to have companions, although two are suspected of having faint unseen ones. Next out is the faint binary, L726-8(long thought have the stars of lowest known masses), folowed by Sirius, with its white dwarf companion. Of the entire list of forty-seven stars within 17 light-years, fourteen are actually multiple systems(that is, 30 percent), with at least one of these being a triple system. These figures do not include any of the unseen dark companions(stars too dim for us to see) which have been detected or suspected. Other studies indicate the 30 percent retio continues for more distant stars, and, because of problems of detecting all binary or multiple systems, this figure has to be a lower limit. Some of the most optimistic estimates suggest that most, if not all, stars are associated with a multiple system of one form or another. In considering whether planets can exist in multiple stars, we will not concern ourselves with the initial formation of planets in such systems. Al- though there is some opinion that such formation would be very difficult, this is still an open question. Rather, our concern is whether if planets were formed in a multiple star, would their orbits be stable? By stability, we mean that the basic parameters describing the size and shape of the orbit(semi-major axis and eccentricity) do not change greatly over long periods of time. In par- ticular, the average separation of the stars should not grow or decay with time. Another characteristic of planetary orbits is that they are nearly circular(i.e. they have a low eccentricity), whereas binary stars can have quite noncircular orbits(high eccentricity). Low eccentricity is especially important in consdering the possibility of a planet sustaining life since there should not be large variations in distance from the primary source of energy over the course of one revolution. The question of stability thus becomes one of deter- mining whether there exist certain regions around a multiple star in which planetary orbits not change size or depart significantly from circularity. A second question in considering the possibility of life on such planets is whether these regions of stability are in what is known as the "zone of habitability." This is the region in which the total amount of energy received from all of the sources of energy(the various stars in the system) is consistent with the formation and maintenance of life. While not much can be said in detail about the size of such a region(which could depend on both the intrinsic brightnesses and the colors of the stars), we can assume it would include the space in which the total energy received is the same as that received by the Earth from the Sun. Thus we can adopt the following require- ment: for a multiple star to be "suitable," it must have a zone of stable planetary orbits which would include the region in which the total energy received is equal to that received from one solar-type star at the mean distance of the Earth from the Sun(this distance is known as an Astronomical Unit, ab- breviated AU).[Footnote: Of course it is possible that alien life can adapt to conditions Earth life would find unbearable. However, in our discussion we will for the sake of simplicity restrict ourselves to considering zones in which con- ditions are suitable to terrestial-type life.] There are other considerations that might affect the suitability of particular systems. For instance, if we know that the stars are rotating very rapidly, we might conclude that they absorbed all of the material that otherwise might have gone into forming planets. Further, if we know tht one of the stars has gone through the explosive evolutionary changes, we would eliminate that as a star capable of have a nearby planet, since it probably would have destroyed any planets in the explosive process. There is also the question of whether a planet near a red dwarf would have to be so close, to be warm enough, that its rotation rate would be locked to its revolution rate, thus eliminating a normal day-night cycle. However, the mechanism of tidal locking is not well enough understood to make this argument conclusive. In addition many red dwarfs are flare stars, but we can not now predict which ones, or whether they all are. Therefore, we will not consider any of these additional factors as defining suitability of a multiple system for having planets. We now must consider the problem of determining whether multiple stars can indeed have regions in which planetary orbits are stable, and what their limitations are. By comparison with the known multiple star systems, a hierar- chical arrangement is expected to be stable, with a planet being close to one star or distant from a binary pair. However, because the mass of a typical planet is very small compared to the mass of a typical star, the limits of the stable regions may be different for planets than for stars. Let us first examine the case of the planet in a simple binary star system(the situation for systems of higher complexity will then become fairly obvious). Planetary motion around a binary star is one example of the classical celestial mechanics three-body problem. The two-body problem(e.g. a binary star or a planet around a single star) can be solved very simply, with the result being the elliptic motion which Kepler first found centuries ago. No such simple solution exists for the three-body problem. However progess can be made by making certain assumptions or focusing on certain specific cases. Unfortun- ately, the use of such assumptions, may also mask important features of the problem. This is especially true in stability analysis,, where often the con- ditions for breakdown fo the assumptions are being sought. With modern high-speed computers, it is possible to approach the problem statistically, by means of numerical experiments. It is possible to follow the motion within a specific system on a computer long enough to determine whether the system is indeed stable. If this is done for a large number of cases, with certain parameters being varied for each one, one can determine statistically what the key factors for stability might be and what the limits on these factors should be to maintain the stability. The drawbacks to such an approach are: 1) that a system cannot be followed for an indefinite amount of time and 2) that all possible configurations can be tried. Therefore, the results only permit statements of probability, not certainty. However, various validity tests, plus comparisons with observed condidions, give some confidence in the final results. Such computer experiments have now been carried out for the case of a planet in a binary star system, and the results are pretty much what we ex- pected: The two general classes of stable planetary orbits are shown schemat- ically in Figures 2 and 3(the systems are being viewed from a point 30 degrees above the assumed common plane of motion of stars and planets, although the conclusions hold up even if the motion is not all in the same plane). The first figure shows an example of a planet orbiting close to one of the stars, while the second figure shows the planet quite distant from the stellar binary. Note that the planetary orbits are circular, whereas the stellar orbits are definitely not. Somewhat surprising, however, is the extent of the regions of stability. For the first case, the planetary orbit is stable as long as the distant star newver gets nearer than approximately three-and-a-half times the distance of the planet from the close star. In the second, the orbit is stable as long as the planet is outside approximately three-and-a-half times the mean separation of the stars in the binary. Thus, the stability regions are quite extensive, being limited only by the distances just mentioned on the one hand,, and by the cases of hitting the surface of a star or being affected by other stars in the galaxy on the other. For a specific example, consider what might happen to our own solar sys- tem if it were suddenly to become part of a binary star system. Numerical simulations like the ones just described can be carried out for our planetary system. Indeed, this is one procedure which is actively used to study the mo- tions of our planets. To illustrate what might happen we can replace the planet Jupiter with a star having the same mass as the Sun. Of the inner planets, Mars gets perturbed very quickly, wandering erratically from practically the Earth's orbit out to well beyond the asteroid belt, and presumably ultimately escaping from the system. However, if our results above are right, the Earth's orbit should be stable, since Jupiter's orbit has a mean distance 5.2 AU. This is just what happens in the simulation, in that the Earth's orbit varies only slightly from what it is in the present solar system. For the second case, we can replace the Sun by a close pair of stars having a mean separation of 0.2 AU(such a binary would have a revolution period of just under 33 days). In this example Mercury is immediately thrown out of the system and Venus, while keeping an orbit similar to its present one, shows somewhat greater variations in distance from the center of the binary. We would again predict the Earth's orbit to be stable, since its distance from the binary is five times the mean binary separation. Once again the prediction holds up, in that the Earth's orbit varies only slightly from that observed in our solar system. Let us now examine nearby multiple stars, to see if any of them might possess habitable planets. As has been mentioned, the nearest sellar system is Alpha Centauri. This system contains a G-type* star that is quite similar to the Sun(though probably older and therefore possibly evolved), plus a K-type main-sequence# star. The mean separation of this pair is 24 AU, with a revolu- tion period of 80 years. Thus, a planet in the habitable zone(which is close to one AU from the primary) would always be well within the distance limits given above, and therefore would be quite stable to perturbations. In addition, the secondary has a habitable zone around 0.6 AU, making it possible to have an interesting planet close to this component as well. Thus, there is no dynamical reason why there could not be at least one planet in system at the right distance to support life. This system should definitely be examined as part of the SETI project. *[Footnote: These letters refer to a system of classifying stars according to a system of classifying stars according to their temperature. The letters used are O,B,A,F,G,K, and M(in order from hot to cool).] #[Footnote: Main-sequence stars are those which are in the longest stage of their normal evolution, converting hydrogen to helium as their primary source of energy.] The next nearest binary is L726-8, consisting of two very faint red dwarfs(one of which is a known flare star) for which the habitability zone would probably be so close to the stars that the orbits would be unstable. Next is the Sirius system, the only one among the very nearby stars that is clearly not suitable for a habitable planet(unless you consider a sometimes suggested but never confirmed distant THIRD[italics] companion). This system consists of a bright A-type main-sequence star and a white dwarf, with a mean separation of 20 AU and a period of 50 years. The habitable zone for the primary is out around 4.5 AU, but the orbit of secondary is very eccentric, bringing it in to as close as 10 AU every revolution. At this distance the planet would be perturbed out of the system and thus could not support the formation of life. And the secondary, having already gone through the nova stage, could no longer have any planet capable of carrying active life forms. Next outward is the binary 61 Cygni, often suspected of having one or more planetary components. Since the mean separation of this system is around 80 AU any planet at typical habitable distance would be very stable dynamically. While both components are fainter and cooler than the Sun(K dwarfs around an absolute magnitude of 8), they are still energetic enough to support comfortable planets well outside distances at which the planets would encounter the atmospheres of the stars; hence, this system should also not be ruled out as a possible candidate for examination. Beyond this system, we come to Procyon, another system with a bright primary and a white dwarf secondary. This system works out to be marginally suitable, but not very promising, and therefore not a good candidate for examination. Then there is a series of red dwarf pairs, such as Struve 298, GR 34, Kruger 60, Ross 614, Wolf 424, and G208-44/45, all of which are formally suitable for planets by the definitions we have considered but are not prime candidates, since the stars are faint and cool. There are also two triples that contain white dwarfs and therefore may be less than suitable. However, this region also has the very suitable binary, 70 Ophiuchi. This system contains an early K and a mid K-type main-sequence star, the primary being almost as massive as the Sun and less than a magnitude fainter. With a mean separation of 23 AU and a period of 88 years, the habitable zones are well within the stable regions for both components, and the primary, at least, is sufficiently sun-like to be an attractive candidate. Of the multiple stars closer than 20 light years, the most attractive (of those with fairly well-known orbits) as a place to look for planets is Eta Cassiopeia. This system, 19.2 light years away, consists of a G0 main- sequence star, almost identical to the Sun in mass, temperature, and brightness (ignoring, for the moment, the possibility that it might be a very close spectroscopic binary), and a 7th magnitude M0 red dwarf. These stars orbit each other in a period of about 480 years with a mean separation of 70 AU and an eccentricity of 0.5. This means the minimum separation is still 35 AU(somewhat greater than the present distance from the Sun to Pluto). While the secondary is still a good candidate for a planet, the primary is almost ideal(and could potentially produce conditions similar to those on the Earth). Furthermore, the orbit of a planet a 1 AU from the primary would be extremely stable. From an Earth-type planet orbiting Eta Cas A, the secondary would appear as an orange point of light(its apparent diameter even at closest approach would be only a third that of Jupiter's in our system), varying in magnitude& from -14 to -16 over a period of 480 years. Since the full moon has a magnitude of about -12.5, the star would range in brightness from 4 to 25 times as bright as the full moon. Further, it would appear relatively stationary in the sky, especially when it was farthest and thus faintest, when it would move only 0.3 degrees per year(approximately half a solar diameter). Even at closest approach it would move just 2.6 degrees per year, just 5 solar diameters. Thus, for much of its 480-year period it would be an almost permanent fixture in the sky, casting enough light to produce a faint orange twilight at night and being visible, but not obvious, during the part of the year it was in the daytime sky. For periods of many years every 480 years, however, it would be bright enough to keep it from ever getting dark at night for a portion of the year, and it would be quite conspicuous in the daytime sky during the rest of the year. It is interesting to speculate what this might mean for the development of a species with interest in astronomy and space travel, to say nothing of the evolution of commerce, exploration, colonization, and even religion. Remember that the entire period since the invention of the telescope and the beginning of serious colonization on the Earth is less than the period of one cycle of revolution of this system. &[Footnote: The magnitude system is defined backwards, so that -16 is brighter than -14. A difference of 5 magnitudes means that two stars differ in brightness by a factor of 100.] As we go outward to even greater distances, the number of binaries with sufficient separations to permit stable planetary orbits within the zone of habitability increases dramatically. There are dozens of good candidates for the search for life or a place to live, even if we restrict our attention to those systems with at least one component similar to our Sun. Thus, to leave out binaries in any SETI observing list certainly runs the risk of overlooking potentially good candidates, especially since some of the very best nearby prospects, astrophysically, are members of multiple systems. Multiple stars are very common, and possibly even the rule, rather than the exception; they may very well be the best place to look for interesting planetary systems. For Further Reading Abt, H.: "The Companions of Sunlike Stars" in Scientific American, April 1977 Herbig, G.: "A Universe Teeming With Planetary Systems -- Perhaps" in Mercury[Magazine] March/April 1976 * * * * Editor's Note: In this connection, science fiction fans may recall Isaac Asimov's award-winning short story "Nightfall"(see the Fawcett paperback with the same title) about a planet in a multiple star system where night comes only once every 2000 years. There are a couple of graphics in the article that could not be duplicated on a terminal. Nessus