Architectures of Exoplanetary Systems, Part Three: Outside the Ice Line

architecture of planetary systems III

Possible architectures of outer planetary systems around Sun-like stars. The gray wavy line represents the ice line. Top to bottom: 1. Based on Run 4a of a simulation series by Levison et al. (1998), with 3 Saturn-mass giants dominating the outer system. 2. Based on Run 3a of the simulations by Levison et al. (1998), with a chain of ice giants and Super Earths extending out to 40 AU. 3. Based on Run 25 of a simulation by Thommes et al. (2008a), modeling the evolution of the Solar System with the orbits of Jupiter and Saturn reversed. Only one ice giant survives amid a dense, extended debris belt.

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Planets in powers of 10

Outer System Architectures

Despite observational evidence on more than 300 exoplanets, we have little information on the outer reaches of extrasolar systems. Current data (March 2009), as posted online in the Extrasolar Planets Encyclopaedia and the Catalog of Nearby Exoplanets, reveal fewer than a dozen well-constrained exoplanets with semimajor axes larger than 4 AU. None have been reliably detected at separations wider than 6 AU. To explore the potential diversity of planets orbiting outside their systems’ ice lines, then, we must turn to observations of our own Solar System, as well as to the results of analytic studies and numerical simulations of our system’s formation and evolution.

All lines of evidence agree that the region of giant planet formation around a Sun-like star is quite limited. Its inner edge coincides with the ice line, and it outer boundary lies about 5 to 10 AU beyond. In all systems this is the principal “nursery,” the birthplace of its largest planets.

modeling the outer Solar System

Thus, according to the prevailing model of Solar System evolution – associated with Kleomenis Tsiganis and colleagues, and often dubbed the “Nice model” after the French city where Tsiganis works – our four giant planets originally assembled between 5 and 15 AU, and then underwent extensive orbital migration (Tsiganis et al. 2005, Gomes et al. 2005, Alibert et al. 2005, Desch 2007, Thommes et al. 2008). Once the primordial gases dissipated, ending the main phase of mass accretion, Saturn, Uranus, and Neptune were pushed and pulled outward to their present orbits by perturbations from Jupiter and gravitational scattering of objects in the Kuiper Belt. Some simulations suggest that a third ice giant originally formed along with Uranus and Neptune (Thommes et al. 2008). It was eventually ejected from the system, while the other two ice planets exchanged orbital positions as they spiraled away from Jupiter. Hence proto-Neptune orbited closer to the Sun than proto-Uranus (Desch 2007, Thommes et al. 2008).

Exoplanetary systems are expected to contain similar nurseries where young giants grow until they are massive enough to travel outward or inward to their mature orbits. As they accrete gases and migrate, they exercise strong perturbations on the rest of the system and thereby constrain its final architecture.

orbital relaxation & planet-planet scattering

While the first Hot Jupiters were the most surprising and unsettling discovery in the new era of exoplanetary studies, the simultaneous realization that most longer-period exoplanets follow eccentric orbits was equally puzzling. Several astronomers – including Stuart Weidenschilling, Francesco Marzari, Frederic Rasio, and Eric Ford – developed the theory of “planet-planet scattering” to explain these elongated orbits. Adams & Laughlin succinctly state its premise: “Planet formation can proceed – at least in principle – faster than dynamical relaxation of the newly formed system. The initial states for the planetary systems are not, in general, dynamically stable over much longer time intervals” (Adams & Laughlin 2003). In a system containing three or more massive planets, the outcome of such dynamic instabilities may be as follows: “Gravitational encounters among these planets can eject one from the system while placing the others into highly eccentric orbits both closer and farther from the star” (Weidenschilling & Marzari 1996). Thus, even if a system somehow produced ten gas giant planets orbiting between 3 AU and 30 AU, mutual dynamic interactions would likely reduce them to only two or three survivors (Juric & Tremaine 2008).

Several numerical simulations have established that the likelihood of ejection is closely correlated with planet mass, such that the most massive planet in a system is the least likely to be ejected, and vice versa (Adams & Laughlin 2003, Barnes & Quinn 2004, Ford & Rasio 2007). The most massive planet thus becomes a key determinant of system evolution.

Terms like “scattering” and “ejection” suggest astrophysical violence and extreme outcomes. But as the Nice model argues, even our own apparently sedate outer system, with its widely separated giants on circular orbits, has undergone extensive “orbital relaxation” and “spreading” (for these terms see Adams & Laughlin 2003) and probably a violent ejection also (Thommes et al. 2008). Thus similar processes of relaxation, spreading, and scattering, followed by partial or complete re-circularization of disrupted orbits, may be typical of outer systems generally, regardless of whether such systems currently contain eccentric planets.

Scattering may also occur in the inner regions of planetary systems as a result of the inward migration of gas giants. This scenario was proposed to explain the configuration of the Upsilon Andromedae system, which harbors a Hot Jupiter and two larger gas giants on moderately eccentric orbits inside the ice line. Ford and colleagues demonstrated that the two outer giants trade eccentricities over regular cycles, such that the eccentricity of planet c returns to zero every 6700 years. They further showed that such dynamical behavior can be explained only by an episode of planet-planet scattering early in the system’s history (Ford et al. 2005). Before the primordial nebula dissipated, a fourth planet must have circled Upsilon Andromedae. Its orbit was disrupted by planets c and d as they migrated inward from their nursery beyond the ice line. The fourth planet was ejected while the three surviving planets assumed their present orbits.

A similar study of the two-planet system of HD 128311 found compelling evidence of an analogous sequence of events there – inward migration, abrupt scattering, ejection of a third planet, and relaxation of the two surviving planets into their present configuration (Sandor & Kley 2006).

Weidenschilling & Marzari (1996) presented a classic simulation in which three Jupiter-mass planets formed in circular orbits with semimajor axes of 5, 7.25, and 9 AU, respectively. Over a period of 20,000 years, mutual interactions resulted in the ejection of the inner planet and the scattering of the other two into highly eccentric orbits, one with semimajor axis = 2 AU and e = 0.78, and the other with semimajor axis = 29 AU and e = 0.44. The presence of the eccentric giant at 2 AU suggests that some of the shorter-period gas giants discovered by radial velocity searches may have reached their present orbits not by Type II migration but by planet-planet scattering.

Nevertheless, the smallest and most circular orbits (i.e., classic Hot Jupiters) are unlikely to result from episodes of scattering. Adams & Laughlin (2003) conducted a very large ensemble of simulations showing how a variety of outer system configurations may result in the inward scattering of planets to semimajor axes as tight as 1 or 2 AU. Inside 1 AU, however, the probability that a scattered planet might achieve a stable orbit was vanishingly small, with such planets typically engulfed by the star.

More recent research by Nagasawa et al. (2008) finds that scattered planets may achieve highly eccentric orbits with small periastra and then undergo long-term tidal circularization. Thus a higher proportion of close-in planets than formerly expected may have reached their present orbits by scattering rather than by Type II migration. Nevertheless, Nagasawa’s group concedes that few Hot Jupiters will have this origin, and they suggest that one marker for scattered planets might be orbits that are misaligned with the spin axis of their host stars (Nagasawa et al. 2008). Information on alignment, unfortunately, is available only for the minority of exoplanets that transit their host stars.

In theory, scattering is much more successful at achieving wide orbits. Simulations by both Levison et al. (1998) and Adams & Laughlin (2003) showed that, even when the initial region of planet formation extends outward no farther than 30-40 AU, the final configuration may include semimajor axes larger than 100 AU. In fact, Adams & Laughlin produced several outcomes in which the outermost planet orbited near 150 AU (Adams & Laughlin 2003). They caution, however, that their simulations were integrated for only 1 million years, and that additional ejections were likely to occur among the outermost planets on longer time scales. They predict much less long-term evolution within 10 AU of the star, suggesting that systems generally stabilize from the inside out (Adams & Laughlin 2003). Their results hint that far-flung orbits are most likely to be found in young systems – that is, those younger than a few tens of millions of years.

constraints on wide orbits

Current theory also indicates that planets younger than 30-50 million years traveling on wide orbits are the most susceptible to direct telescopic detection (Apai et al. 2007). This enhanced visibility results from the intrinsic brightness of newly formed gas giants, which dim rapidly as they age (Lafreniere et al. 2007). Accordingly, several recent surveys have used state-of-the-art adaptive optics techniques to search for this hypothetical population of wide giants. All, however, reported null results.

The negative findings of the various studies are quite similar. Biller et al. (2007) conclude that “young massive extrasolar planets” must be rare beyond 5 AU. Nielsen et al. (2007) find that fewer than 20% of star systems might host planets more massive than 4 MJUP orbiting beyond 20 AU, while no systems will host any giant planets beyond 73 AU. Lafreniere et al. (2007) find that fewer than 24% of all stars host planets more massive than 2 MJUP beyond 25 AU. More forcefully, Apai et al. (2007) conclude, “The giant planet population does not extend beyond 30 AU,” while suggesting a likely “cut-off” at radii smaller than 15 AU.

The study by Lafreniere and colleagues was also able to address the presence of brown dwarfs on wide orbits around Sun-like stars. Their results indicate that such objects are only a little more likely to be found than giant planets on analogous orbits. A maximum of 5% of stars might host low-mass brown dwarfs (13-40 MJUP) beyond 25 AU (Lafreniere et al. 2007). Moreover, as this group notes, the actual percentage may be much lower. Their findings speak to the enduring confusion over whether to classify objects of 13-20 MJUP, in planet-like orbits around Sun-like stars, as gas giant planets or as brown dwarf stars. Radial velocity searches have established that objects in this mass range are rare within 3 AU, while the recent adaptive optics searches demonstrate that they are also rare between 3 AU and 25 AU. The conclusions of Lafreniere and colleagues hint that, in terms of orbital configuration, these Super Jupiters resemble massive planets rather than lightweight brown dwarfs.

Notably, the unsuccessful surveys by the teams of Biller, Lafreniere, and Apai all shared the same limitation: they addressed stars of spectral types G, K, and M. Two subsequent searches around A-type stars have produced much more encouraging results. A team led by Paul Kalas, using the Hubble Space Telescope, has directly imaged a potential gas giant planet orbiting the nearby star Fomalhaut at a separation of at least 100 AU (Kalas et al. 2008, Chiang et al. 2009). Another team led by Christian Marois has imaged an astonishing three-planet system around the more distant HR 8799, with orbital separations ranging from 24 to 68 AU (Marois et al. 2008).

These preliminary results add further weight to the argument that system architectures vary by stellar mass and thus by spectral type. If we seek far-flung planets, Sun-like stars may simply be the wrong place to look.

Packed Planetary Systems

Along with eccentric orbits and gas giants at semimajor axes smaller than Mercury’s, the sample of multiple-planet exosystems also reveals an unexpected degree of crowding (see Crowded Orbits). Of the five planets so far detected in orbit around 55 Cancri, for example, the inner three are contained within a radius of only 0.24 AU – a little over half the distance of Mercury from the Sun. In order of increasing distance from the primary, these three planets have masses similar to those of Uranus, Jupiter, and Saturn. In our Solar System, by comparison, the three planets of corresponding mass occupy a region 14 AU in width. Even Mercury and Venus, the two Solar planets whose orbits most closely approach each other, are still separated by about 0.3 AU.

A similar pile-up has been observed around GJ 876, a nearby M dwarf whose three detected planets have a combined mass that exceeds the total of all planets, asteroids, and moons in the Solar System. Yet the three planets of GJ 876 orbit within 0.208 AU of the star. All available evidence suggests that the widely dispersed orbits of the Solar planets are the exception rather than the rule among planetary systems.

The configurations of the various multiple-exoplanet systems have led Rory Barnes and colleagues (e.g., Barnes & Raymond 2004, Barnes & Greenberg 2007) to formulate the hypothesis of packed planetary systems (PPS). This hypothesis suggests that “all planetary systems contain as many planets as they can support without becoming unstable,” so that “if a stable region exists within a planetary system, then it should contain an additional planet” (Raymond et al. 2006). Sean Raymond and colleagues have used the PPS hypothesis to test the possibility that additional terrestrial-mass planets may exist in known exoplanetary systems containing gas giants (Mandell et al. 2007). Meanwhile, Barnes & Greenberg have further refined this hypothesis in order to express the degree of stability of a given system with a single numerical value (Barnes & Greenberg 2007). According to their analysis, the system most likely to harbor an additional planet is that of the nearby yellow star HD 217107.

The PPS hypothesis achieved a notable success with its prediction of a third planet in the system of HD 74156. When only two gas giants were known in this system, Raymond and Barnes conducted numerical simulations demonstrating that an additional stable orbit was possible between 0.9 and 1.4 AU for a somewhat smaller gas giant (Raymond & Barnes 2005). Their prediction was borne out by the subsequent detection of HD 74156 d, a slightly sub-Jupiter mass planet orbiting at about 1 AU (Bean et al. 2008, Barnes et al. 2008). It will be very interesting to see whether Barnes’ analysis of HD 217107 proves equally prescient.

Last update March 2009

Index of exoplanetary topics
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Thommes EW, Nagasawa M, Lin DNC. (2008b) Dynamical shakeup of planetary systems II: N-body simulations of Solar System terrestrial planet formation induced by secular resonance sweeping. Astrophysical Journal, 676: 728-739. Abstract.
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All text is copyright Raymond Harris 2006-2009