rogers (04/05/83)
I have an article on the possibility of multiple stars having planets if anyone is interested. Just send me your address and I will send it to you. If enough interest is shown, I'll post it. Nessus
rogers (04/08/83)
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