Inner System Architectures

Radial velocity data demonstrate that stable planetary orbits may be sustained at separations as small as 0.02 AU (less than 2 million miles) from the central star. This limit defines the inner boundary for the region of terrestrial planet formation. The outer boundary is provided by the ice line, which is determined by the host star’s mass and energy output. For a star of Solar mass and luminosity, the ice line is located at a radius of 2.7 AU. For a cooler M dwarf star like GJ 436 (0.47 MSOL), it will be located at about 0.6 AU, while for a hot F-type star like Upsilon Andromedae (1.32 MSOL), it will be located at about 4.7 AU (Ida & Lin 2005).

Exoplanet detections, along with the evidence of our own Solar System, establish that many stars are likely to support ensembles of 2 to 4 planets within their ice lines. These objects may range from rocky planets as small as Mercury (0.06 MEA) up to gas giants near the brown dwarf limit (13 MJUP).

Recent investigations generally agree that inner-system architectures are constrained by planet formation beyond the ice line, since this outer region is where a star’s most massive planets are likely to evolve, on time scales shorter than those required to assemble rocky planets at smaller radii.

simulations by Levison & Agnor

Harold Levison and Craig Agnor have conducted a series of simulations of terrestrial planet formation within a few AU of a Sun-like star by varying the properties of the outer system (Levison & Agnor 2003). Each set of simulations was based on one of six possible outer-system architectures: [1] no outer planets whatsoever (i.e., “giant free”); [2] four planets identical to the Solar System’s giants; [3] three gas giants in the range of 2-4 MJUP, plus one ice giant and one icy Super Earth; [4] four ice giants plus three Super Earths; [5] three Saturn-mass giants on moderately eccentric orbits; and [6] a single Jupiter-mass giant on a wide, eccentric orbit (a = 17.37 AU, e = 0.788).

Among the most striking results were those of the giant-free simulations. This configuration tended to produce systems of four to seven rocky planets within 2.5 AU, with planet masses ranging from that of Mercury to 1.5 times Earth (Levison & Agnor 2003). Without an external source of perturbations, planetesimal accretion proceeded more slowly than in the other configurations, such that collisions continued for a billion years of simulation time. Gravitational scattering produced a wide outer debris belt that steadily expanded to larger radii. These giant-free outcomes bear a strong resemblance to the debris-only systems postulated by Greaves and colleagues (Greaves et al. 2007).

Simulations involving outer Solar System analogs resulted in collections of rocky planets that were often surprisingly reminiscent of those in the giant-free configuration. Differences included much shorter accretion times and an absence of planets and debris beyond 1.5 AU.

The ice giant/Super Earth configuration also produced outcomes resembling those of the outer Solar System analogs (Levison & Agnor 2003). Notably, however, the innermost of the outer planets in this configuration, a Super Earth of 7 MEA, had a semimajor axis of only 4.08 AU and a periastron of only 3.44 AU, as compared to Jupiter’s semimajor axis of 5.2 AU.

Two of the three remaining sets of simulations also placed the nearest of the outer planets on an orbit tighter than Jupiter’s, and in all three this planet’s periastron was smaller than 3.7 AU. Planets in the resulting systems were always concentrated within 1 AU of the host star.

• Simulations based on three giant planets more massive than Jupiter produced fewer, more massive terrestrial planets on tighter orbits than the configurations described above, with individual runs resulting in one to three planets within 1.7 AU and no planets more massive than Venus beyond 1 AU.
  
  
• Simulations including three moderately eccentric Saturns were similar, insofar as they produced one to three planets concentrated within 1 AU, but the combined masses of these systems tended to be lower than those in the configuration dominated by large gas giants.
  
  
• The single highly eccentric gas giant resulted in the most distinctive outcomes, yielding low-mass inner systems containing only one or two planets within 0.9 AU. In these systems the total mass in rocky planets ranged from 0.7 MEA to 1.6 MEA , compared to a mass of 1.98 MEA in the Solar System.

A limitation of Levison & Agnor’s simulations is their decision to use idiosyncratic initial configurations rather than to systematically vary the mass, semimajor axis, and eccentricity of the outer-system planets. Nevertheless, their results support the general inference that more massive and eccentric giants traveling on orbits closer to the ice line favor fewer, more massive terrestrial planets on tighter orbits. Conversely, less massive giants on wider orbits encourage more and smaller terrestrial planets over an extended range of orbital radii.

simulations by Raymond & colleagues

Sean Raymond and colleagues have also conducted numerous simulations of inner system architectures, each focusing on rocky planet formation within ~5 AU of a Sun-like star. Like Levison & Agnor, they find that the evolution of inner planets will be strongly constrained by any giant planets orbiting in the vicinity of the ice line. However, Raymond’s group has focused on configurations in which a few basic parameters vary systematically. One key publication considered systems in which a gas giant or ice giant has already achieved a stable orbit between 4 and 7 AU, and no additional giant planets exist on interior orbits (Raymond et al. 2004). By varying the parameters of the giant planet as well as of the primordial disk itself, Raymond’s group produced dozens of simulated systems that might correspond to any of the first three defined above by Greaves and colleagues (excluding only the Hot Jupiter scenario).

Simulations in which the mass of the giant planet at 5.2-5.5 AU was variously set at 10 MEA , 0.33 MJUP, 1 MJUP, and 3 MJUP revealed significant constraints on the numbers, masses, and semimajor axes of rocky planets (see Raymond et al. 2004).

• The most massive gas giant (3 MJUP) produced fewer, more massive, closer-in terrestrial planets, with one simulation resulting in a single Super Earth of 3.85 MEA at 0.96 AU. This set of outcomes recalls the “three Jupiters” configuration of Levison & Agnor.
  
  
• The least massive ice giant (10 MEA , less than the mass of Uranus) produced more numerous and less massive planets, with one simulation resulting in seven Mars- to Earth-size objects, a handful of dwarf planets, and still larger numbers of leftover planetesimals, all distributed between 0.5 and 3.5 AU. This is very similar to the results of Levison & Agnor’s giant-free simulations, although it seems surprisingly at odds with their ice giant configurations.
  
  The mismatch between the two studies might stem from their different placement of the innermost of the outer planets (~4 AU vs. ~5 AU) or perhaps from more fundamental differences in their simulation code.

Variations in other parameters produced less spectacular but still significant results. Gas giants on wider orbits (7 AU) permit massive, volatile-rich “Super Earths” to form in the vicinity of the ice line at ~2.5 AU, whereas gas giants on tighter orbits (4 AU) sweep planetesimals from this region and restrict terrestrial planets to orbits close to the star. More eccentric giants (e = 0.2) produce fewer, more massive planets orbiting closer to the star (2 to 3 planets, most within 2 AU), while less eccentric giants (e = 0) permit more numerous planets at greater distances (4 to 8 planets within 3.5 AU).

The results of additional simulations focusing specifically on rocky planet formation in the circumstellar habitable zone have enabled Raymond to enunciate a general rule about the role of giant planets in terrestrial accretion (Raymond 2006). He finds that the presence of a Jupiter-mass planet at a semimajor axis smaller than 2.5 AU prohibits the formation of any planets of 0.3 Mea or more between 0.8 and 1.5 AU – that is, within the habitable zone of a Sun-like star (Raymond 2006, Mandell et al. 2007). Presumably, however, less massive planets might still assemble inside this region, while more massive planets could also form closer to the central star.

effects of giant planet migration

So far we have considered only systems where giant planets reside beyond the ice line. Yet this configuration represents a tiny minority of all extrasolar detections. In fact, the very earliest discoveries included several gas giants orbiting within 0.1 AU of their host stars, and this population has grown steadily over the years. It has always been clear that such giants must have formed at greater distances and then somehow traveled inward to their present orbits (Lin et al. 1996). Perhaps because they were so puzzling and unexpected, these planets were originally characterized in negative terms. For example, in remarks to the news media, Geoff Marcy sometimes called them “marauding Jupiters,” invoking visions of barbarian hordes blazing a path of destruction through otherwise well-behaved planetary systems (e.g., Hall 1999).

Even after the term Hot Jupiter replaced Marcy’s more colorful coinage, these objects were considered antithetical to terrestrial planets. As Charles Lineweaver and colleagues have expressed it, “Whether these planets slowly migrate in or are gravitationally perturbed into these close orbits, they may destroy Earth-mass planets as they pass through the circumstellar habitable zone” (Lineweaver et al. 2004). In their widely-discussed study Rare Earth (2000), Donald Brownlee and Peter Ward used the prevalence of Hot Jupiters to argue that Earth-like planets must be uncommon in the universe. Working from the fact that Hot Jupiters are found almost exclusively around highly metallic stars, Lineweaver and colleagues expanded on the “Rare Earth” argument to define a “Galactic habitable zone” in which metal abundances are just right for systems without Hot Jupiters to form (Lineweaver et al. 2004).

Several recent studies based on numerical simulations have attempted to refute these claims, with considerable success. One series of publications by Martyn Fogg and Richard Nelson (Fogg & Nelson 2005, 2006, 2007), and another by Sean Raymond and colleagues (Raymond 2006, Raymond et al. 2006b, Mandell et al. 2007), have shown that the passage of a migrating gas giant through the inner regions of the protoplanetary nebula need not preclude the formation and survival of rocky planets. For example, Fogg & Nelson found that, in systems where the migrating planet assumes a semimajor axis of 0.1 AU or less, “a large fraction of the disk mass survives the passage of the giant, either by accreting into massive terrestrial planets shepherded inward of the giant, or by being scattered into external orbits” (Fogg & Nelson 2005). Since giant planet migration necessarily occurs within the first few million years of the nebula’s lifetime, before gases completely disperse, the surviving refractory mass is still sufficient to form terrestrial planets.

Simulations by Raymond and colleagues are in excellent agreement with those of Fogg & Nelson. Raymond’s group concludes that giant planets migrating to within 0.5 AU of their host stars may actually encourage the formation of terrestrial planets, as long as their final orbits have low eccentricity. A giant planet’s passage brings large quantities of planetesimals and debris in its wake, encouraging the assembly of rocky worlds containing a high percentage of volatiles (Raymond et al. 2006b, Mandell et al. 2007). At the same time, materials shepherded inside the giant’s orbit may accrete into Hot Super Earths or Hot Neptunes like the ones observed around GJ 876, 55 Cancri, and Mu Arae.

Of course, systems containing gas giants that have crossed inside their ice lines remain sensitive to the dynamical influences of the outer system. If a system hosts a Hot Jupiter but no additional giant planets at larger radii, the outcome may be a chain of massive terrestrial planets extending well beyond the ice line, as it might be in systems entirely lacking gas giants. However, if another gas giant orbits in the outer system, whether at 3, 5, or 10 AU, it will affect inner-system evolution just as it would in the absence of a Hot Jupiter. Mandell, Raymond, and Sigurdsson (2007) performed several sets of simulations, some including only a Hot Jupiter and others adding a Saturn-mass giant at 9.5 AU. In simulations without the outer giant, numerous massive, volatile-rich terrestrial planets formed between 0.2 AU and 10 AU. In simulations with the Saturn analog included, terrestrial planets were less massive and remained confined within 5 AU of the host star (Mandell et al. 2007).

domination by giants

Under certain conditions, then, giant planet migration into the inner system can encourage the formation of rocky planets inside the ice line. But migration can also result in configurations that drastically curtail or entirely prohibit the assembly of terrestrial planets. For example, the single known companion of the G4 star 70 Virginis has a minimum mass of 7.49 MJUP, a semimajor axis of 0.484 AU, and an eccentricity of 0.4. These parameters correspond to a periastron of 0.29 AU (similar to the periastron of Mercury) and an apastron of 0.68 AU (similar to the semimajor axis of Venus). The planet’s wide radial excursions and large mass guarantee that the inner system of 70 Virginis has been cleared of any competing planets or planetoids. Thus, despite its resemblance to our Sun, this nearby star is highly unlikely to host terrestrial planets.

In a recent paper announcing the discovery of two gas giants traveling in Earth-like orbits, Sarah Robinson and colleagues note, “Many giant planets are being found on terrestrial planet-like orbits, in or near the habitable zone” (Robinson et al. 2007). Data published in the Extrasolar Planets Encyclopaedia (4/25/2008) indicate that 31% of exoplanets (84/271) so far detected by radial velocity measurements are either gas giants (minimum mass 0.2 MJUP) or brown dwarf candidates (more massive than 13 MJUP) orbiting between 0.5 and 2.0 AU. This range of semimajor axes either encompasses or overlaps with the habitable zones of most Sun-like stars – that is, virtually all main sequence G-type stars, most early K stars, and many late F stars. As Robinson and colleagues conclude, “Planetary systems often have habitable zones dominated by gas giants.” It appears that true Solar System analogs, comprising star systems that contain only terrestrial planets within their ice lines, may be even rarer than inner systems in which the giants have swept away the dwarfs.

The evident frequency of these giant-dominated configurations places strong limits on the population of rocky planets in our Galaxy, and thereby on the likelihood of discovering Earthlike exoplanets. A small subset of such giant-dominated inner systems may nevertheless sustain numerous massive rocky objects in the form of moons rather than planets. According to the mass scaling relationship proposed by Canup & Ward (2006), a gas giant of 3 MJUP may host one or more co-formed satellites as massive as Mars (0.11 MEA), while a Super Jupiter of 8 MJUP or more might even host a potentially habitable world of 0.3 MEA (note that 0.3 MEA is widely considered to be the minimum mass for a habitable planet; see, e.g., Raymond et al. 2007; see also Potential Exomoons). Such massive satellite systems – in effect, scaled-up versions of Jupiter’s Galilean moons – might qualify as analogs of our inner Solar System.

At least two potential hosts for such configurations can be identified in current data:

• HD 92788 b, a giant of 3.68 MJUP traveling on a moderately eccentric orbit (e = 0.33) around a G5 star at a semimajor axis of 0.97 AU, implying a periastron of 0.65 AU and an apastron of 1.29 AU
  
  
• HD 28185 b, a giant of 5.72 MJUP also accompanying a G5 star on a circular orbit with a semimajor axis almost identical to the Earth’s

Also quite intriguing is the system of HD 168443, which hosts two extremely massive planets. The inner has a minimum mass of about 8 MJUP, indicating the potential for large moons, but the planet’s semimajor axis of 0.3 AU and eccentricity of 0.53 (corresponding to a periastron of only 0.14 AU) argue against the retention any satellites. The system’s outer planet is a colossus of 18 MJUP, raising the suspicion that it might be a brown dwarf instead of a gas giant. Regardless of the precise nature of this object, its semimajor axis of 2.91 AU and its moderate eccentricity of 0.22 (corresponding to a periastron of 2.27 AU and an apastron of 3.54 AU) mean that it probably crisscrosses the host system’s ice line. If so, it travels through fertile territory for the growth of Mars- to Venus-size companions.

Last update April 2008

NEXT: Outer System Architectures