Planets have always been known in the plural. All of the Solar System's planets that are visible to the naked eye – Mercury, Venus, Mars, Jupiter, and Saturn – have been observed and probably discussed since prehistoric times. By about two thousand years ago, the idea of a planetary system, with lesser objects traveling in circles around a greater mass, was familiar to people in many civilizations – even if the central object was often assumed to be the Earth rather than the Sun.

As a consequence of this history, one of the most unsettling features of the recently discovered population of exoplanets is their isolation. Most known extrasolar planets appear to orbit their host stars without any detectable companions. These are lonely planets.

By March 2010, radial velocity data had characterized more than 300 exoplanetary systems, most of them located within 300 parsecs of our Sun (Extrasolar Planets Encyclopaedia, Catalog of Nearby Exoplanets, Wright et al. 2009). More than 85% contain just one detected planet, usually an object at least as massive as Uranus, and often more massive than Jupiter. Twenty-nine systems contain exactly two confirmed planets, and 143 systems contain three or more planets, making a total of 43 stars other than our Sun with two or more planetary companions. While these numbers demonstrate that less than 15% of all detected systems are multiple, they also reveal that about 25% of the known exoplanets reside in multiple systems.

    0-26 parsecs

1.   GJ 876 (3)
2.   GJ 581 (4)
3.   61 Virginis (3)
4.   55 Cancri (5)
5.   HD 69830 (3)
6.   HD 40307 (3)
7.   Upsilon Andromedae (3)
8.   47 Ursae Majoris (3)
9.   Mu Arae (4)
10. Gliese 777 (2)
11. HD 128311 (2)
12. HD 217107 (2)
13. HD 134987 (2)
14. HD 60532 (2)

    27-47 parsecs

15.   HD 181433 (3)
16.   HD 82943 (2)
17.   HD 45364 (2)
18.   HD 37124 (3)
19.   HD 11964 (2)
20.   HD 169830 (2)
21.   HD 12661 (2)
22.   HD 47186 (2)
23.   HD 168443 (2)
24.   HD 38529 (2)
25.   HD 155358 (2)
26.   HD 147018 (2)
27.   HD 215497 (2)
28.   BD -082823 (2)
29.   HD 202206 (2)

    47-362 parsecs

30.   HD 187123 (2)
31.   HD 125612 (3)
32.   HD 183263 (2)
33.   HIP 14810 (3)
34.   HD 9446 (2)
35.   HD 11506 (2)
36.   HD 68988 (2)
37.   HD 177830 (2)
38.   HD 74156 (3)
39.   HD 108874 (2)
40.   HD 73526 (2)
41.   CoRoT-7 (2)
42.   HAT-P-13 (2)
43.   HD 102272 (2)

This sample of 43 systems is clearly biased in favor of nearby stars. More than half of the systems with 3 or more planets are located within 16 parsecs, while the median distance of the entire sample is only 38 parsecs. Evidently the detection of multiple planetary companions requires robust, high-quality data collected over long periods of time. Such data, unfortunately, remain unavailable for most Sun-like stars located beyond a few tens of parsecs.

All these circumstances suggest that exoplanets are less lonely than they look. It seems a safe bet that many more await discovery in the known one- and two-planet systems.

The multiple systems span a broad range of spectral types (M, K, G, F) and include planets of most known species, from Super Earths to Super Jupiters. A minority even show evidence of debris fields like our own Asteroid and Kuiper Belts.

Insofar as these 43 are the only ones that can be described in the strictest sense as planetary systems – i.e., containing two or more planets that interact dynamically – this subset bears a closer resemblance to our Solar System than does the rest of the extrasolar catalog.

Yet these systems are quite unlike home in some important ways. If an exact duplicate of our Solar System were located 30 parsecs away, and astronomers on Earth had begun studying it in the early 1990s, they would only recently have confirmed that it harbors a single planet, a gas giant orbiting at 5.2 AU (i.e., Jupiter's imaginary twin). This detection would have required more than 12 years of regular radial velocity observations, since a planet cannot be confirmed until it completes at least one orbit. None of the terrestrial planets interior to this orbit would be detected because of their low mass, while the giant planets outside 5.2 AU would leave clues to their presence only in leftover data points. Therefore our nearby twin would not be included in the present discussion of multiple systems.

We recognize these systems as multiple only because all of them harbor at least one massive planet – either an ice giant like Uranus or Neptune, or a gas giant like Saturn or Jupiter, or a Super Earth like HD 40307 b, c, and d – at smaller radii than their ice lines. Several of them contain two or even three giants in this limited orbital space. Yet the corresponding region of the Solar System is the exclusive domain of lightweight rocky planets, from Mercury to Mars.

Therefore, all the known multiple systems preserve evidence of evolutionary processes that must have carried these massive planets from wider orbits to their present small semimajor axes. Current theory identifies the most likely mechanisms as (1) Type I or Type II migration through the primordial gas nebula; (2) planet-planet scattering after the nebula’s dissipation; or (3) some combination of these two processes (see, e.g., Nagasawa et al. 2008).

giant populations

Radial velocity data on some of the known single-planet systems hint at the presence of additional giant companions, usually traveling in wider orbits, but many other systems show no signs of additional giants, at least within the limits of current observations (Wright et al. 2007). It therefore seems reasonable to inquire into the likely maximum number of giant companions, whether gaseous or icy, that a Sun-like star might harbor.

Our own Solar System contains two gas giants and two ice giants, providing a point of comparison. Six extrasolar systems contain three gas giants each (Upsilon Andromedae, Mu Arae, HD 37124, HIP 14810, HD 74156, 47 Ursae MAjoris), but not even the systems known to harbor more than three planets (GJ 581, Mu Arae, 55 Cancri) contain more than three gas giants. The closest (d) of Mu Arae’s four companions is a likely ice planet in the mass range of Uranus, while 55 Cancri hosts two planets (c, f) half as massive as Saturn (representing a sort of transitional species between ice giants and gas giants) in addition to its two bona fide gas planets (b, d) and its innermost companion (e), a likely Super Earth. GJ 581 lacks gas giants entirely, harboring only ice giants and Super Earths.

One study of planet-planet interactions in multiple systems concludes:

Extrasolar systems with a single detected eccentric planet are likely to harbor at least one more planet of comparable mass. . . . However, a more stringent observational prediction is that such systems are also not likely to harbor more than one or two additional giant planets. (Juric & Tremaine 2007; emphasis in original)

Juric & Tremaine continue a line of argumentation proposed by several previous researchers (e.g., Weidenschilling & Marzari 1996, Rasio & Ford 1996, Ford 2005, Ford & Rasio 2007, Chatterjee et al. 2007). In this model, after gas accretion and orbital migration have resulted in the formation of two or more gas giants (see Evolution of Planetary Systems), a kind of sorting period ensues. Planet-planet scattering may excite orbital eccentricities and even eject one or more planets from the system. For example, Eric Ford and colleagues point to numerical simulations suggesting that, even if a planetary system begins with a very large number of gas giants, dynamic interactions over tens of millions of years lead to collisions and ejections that typically leave a minimum of one and a maximum of three surviving giants (Ford 2005).

Thus some percentage of the known exoplanetary systems may now be complete, at least with regard to gas giants. Of course, many of them may also host terrestrial-mass planets whose detection awaits the availability of sufficiently sensitive methods.

system architectures & evolutionary scenarios

The architectures of the rapidly growing sample of multi-planet systems presumably reflect their evolutionary histories. As noted above, all these systems contain at least one planet several times the mass of Earth orbiting within a few astronomical units of the central star.

Type I and Type II migration, sometimes in conjunction with shepherding of an interior object, are the most likely pathway by which planets attain tight orbits. Simulations of planet-planet scattering generally cannot produce semimajor axes smaller than 0.1 AU (Adams & Laughlin 2003, Nagasawa et al. 2008). Therefore, in the systems that contain 2 or more planets on relatively small, circular orbits, migration through the primordial nebula is the most likely formation process. This conclusion probably applies to at least 7 systems: GJ 876, GJ 581, 61 Virginis, 55 Cancri, HD 40307, HD 69830, and CoRoT-7.

In the two- and three-planet systems with wider and more eccentric orbits, on the other hand, we see evidence of planet-planet scattering – often in conjunction with migration. Such a history is likely for virtually every system containing at least one planet whose orbital eccentricity exceeds 0.3. Currently, this criterion is fulfilled by about 50% of the known multi-planet systems.

More specifically, among the systems with three or more planets, the most eccentric orbits have been observed in HD 74156 and HD 181433. Among the two-planet systems, high eccentricity is even more common, with HD 169830 and HD 183263 especially notable for their wide, eccentric orbits. In HD 169830, the two planets orbit at 0.82 AU and 3.62 AU, with eccentricities of 0.31 and 0.33, respectively. In HD 183263, they orbit at 1.51 AU and 4.25 AU, with eccentricities of 0.38 and 0.25.

mutual dynamic interactions

Substantial research has established that many adjacent planet pairs in these two- and multi-planet systems exhibit mutual dynamic interactions. Barnes and colleagues have outlined three kinds of interactions typical of such systems: mean motion resonance, near-separatrix behavior, and orbital isolation (Barnes & Quinn 2004, Barnes & Greenberg 2006a, Barnes & Greenberg 2006b).

1. The most obvious and extensively discussed of these relationships is mean motion resonance, in which the orbital periods of two planets can be expressed as a ratio between two small integers. According to recent calculations, at least five exoplanetary systems contain planet pairs in resonant orbits (Barnes & Greenberg 2006b, Fischer et al. 2007; Correia et al. 2009; see also Gozdziewski et al. 2006). In four out of five systems, the relationship is a 2:1 mean motion resonance. In order of increasing distance from the Sun, these are the three-planet system GJ 876 and the two-planet systems HD 128311, HD 82943, and HD 73526. The two planets in the fifth system (HD 45364) are believed to orbit in a 3:2 mean motion resonance.
   
   
2. Many other planet pairs reveal orbital dynamics that lie “near a secular separatrix,” that is, near the boundary between the alternative regimes of libration and circulation (Barnes & Greenberg 2006a). Another way of expressing this relationship is to say that such systems lie on the brink of instability, since slight changes in their elements would result in disruption (Barnes & Quinn 2004). Proposed examples of near-separatrix behavior occur in most of the known multi-planet systems, as well as in the two-planet systems 47 Ursae Majoris, HD 169830, HD 12661, HD 168443, and HD 38529 (Barnes & Greenberg 2006b). Notably, the four giant planets of the Solar System exhibit this behavior, in particular Jupiter and Saturn, the most massive of the Solar planets.
   
   A characteristic of both mean motion resonances and near-separatrix behavior is that the eccentricities of the adjacent planets oscillate on secular time scales, such that the eccentricity of one planet periodically approaches zero (Greenberg & Barnes 2007). These cycles have been calculated for the systems of Upsilon Andromedae (Ford et al. 2005), GJ 876 (Laughlin et al. 2005), and HD 128311 (Sandor & Kley 2006).
   
   
3. Many systems also present instances of orbital isolation through tidal circularization. In this case, one planet orbits extremely close to the host star, with an eccentricity approaching zero. The planet’s originally elliptical orbit has been circularized by the tidal drag of the star, so that their separation varies only slightly over the course of each period. Meanwhile, an adjacent planet orbits at a larger semimajor axis, in a configuration that isolates it from perturbations involving the inner planet. The overwhelming drag of the host star effectively shields the inner planet from any interactions with the outer planet. Orbital isolation occurs in most of the two- and multi-planet systems containing semimajor axes smaller than 0.1 AU.

super jupiters & brown dwarfs

A minority of proposed two-planet systems contain objects in the mass range of brown dwarfs. In each case (HD 168443 c, HD 38529 c, HD 202206 b, HAT-P-13c) this "Super Jupiter" seems more likely to be a high-mass planet than a low-mass star.

1. Both theory and observation agree that brown dwarfs occur most frequently as single objects, and are much less common than gas giants within about 50 AU of a Sun-like star (Jiang et al. 2004, Lafreniere et al. 2007, Liu et al. 2008). Thus an object between 10 and 20 MJUP in orbit within a few AU of such a star is probably a planet.
   
   
2. The planets around HD 168433 and HD 38529 display near-separatrix behavior, which is typical of planetary systems rather than binary stars (Barnes & Quinn 2004).
   
   
3. The observed physical configurations of HD 168433, HD 38529, and HAT-P-13 could not have evolved if the brown dwarf-mass objects had formed like stars through gravitational collapse, and then subsequently passed through the expected phase of star-like temperatures of about 3000 K (see L. Neill Reid 2002). A star-like object within 5 AU of the primary would severely truncate the primordial gas disk, and truncation would prevent any gas giant planets from forming on interior orbits. Yet all three systems contain a brown dwarf-mass object orbiting at or inside the presumed ice line, plus a gas giant planet at a smaller semimajor axis. Presumably both planets in each system formed at larger radii and then migrated into their present orbits.

Whether the planetesimal accretion model can adequately account for the evolution of these four systems remains to be established. A stepwise accretion of kilometer-sized planetesimals, followed by runaway gas capture, seems incapable of yielding such enormous bodies within the time constraints imposed by gas dispersal. Nevertheless, the theory of planet-planet scattering proposed by Ford and colleagues predicts planetary collisions as well as ejections. It may be that the extremely massive objects observed in these systems formed by collisional accretion of two already enormous gas giant planets. Alternatively, as suggested by the discovery team for HD 168433, perhaps these brown-dwarf sized bodies are the result of a merger between two protoplanetary disks in the high-density environment of a star-forming nebula (Marcy et al. 2001). See also Super Jupiter or Brown Dwarf?.

Last update March 2010