Architectures of Exoplanetary Systems, Part One

architecture of planetary systems I

Possible architectures of planetary systems around Sun-like stars. Blue wavy lines represent the habitable or “liquid water” zone; the gray wavy line represents the ice line. Top to bottom: 1. Based on a simulation by Raymond et al. (2004), in which a Uranus analog of 10 Earth masses orbits at 5.2 AU and 7 terrestrial planets form. 2. Based on a simulation by Mandell et al. (2007), in which a gas giant migrates to 0.05 AU, a Saturn analog orbits at 9.5 AU, and 6 terrestrial planets form between them. 3. Based on the actual configuration of the HD 128311 system, in which two massive gas giants orbit between 1 and 2 AU and a debris belt occupies the outer system (the Mercury analog is speculative). 4. Based on the actual configuration of 55 Cancri.

Planets in powers of 10

Research into the architecture of planetary systems draws on evidence from diverse sources, including:

  • Radial velocity and photometric transit observations of individual exoplanets
  • Observational and analytic studies of systems with debris disks
  • Analytic studies of planetary accretion and orbital dynamics
  • Numerical simulations of planetary and orbital evolution
  • Adaptive optics searches for exoplanets in wide orbits

What follows is a layperson’s attempt to summarize current knowledge on system architectures, as derived from these fields of inquiry. The discussion is based on a review of recent scientific literature, with an emphasis on the following authors and their collaborators: Rory Barnes, John Chambers, Eric Ford, Jane Greaves, Shigeru Ida, John Johnson, Grant Kennedy, Scott Kenyon, Greg Laughlin, Harold Levison, Douglas Lin, Frederic Rasio, Sean Raymond, Kleomenis Tsiganis, Edward Thommes, and Mark Wyatt. For a full list of sources, click here.

1. Basic Concepts
System architecture defined
Architecture as evolutionary outcome
&nbsp a. Accretion in a gaseous nebula
&nbsp b. Accretion by collision after gas dispersal
&nbsp c. Planet-planet scattering
Ice line defined and discussed

2. Basic Data
Range of system parameters
Correlation between star metallicity and giant planets
Correlation between star mass and giant planets
Combined role of metallicity and mass

3. Inner System Architectures
Inner systems simulated by Levison & Agnor
Inner systems simulated by Raymond et al.
Effects of giant planet migration
Inner systems dominated by giants

4. Outer System Architectures
Evolution of the giant planets of the Solar System
Orbital relaxation and planet-planet scattering
Constraints on wide orbits

5. Packed Planetary Systems
Barnes et al. on the theory of packing
Predicted planets

More hypothetical systems

Evolution of planetary systems

basic concepts

When authors discuss the architecture of planetary systems, they are typically asking and answering questions about which kinds of objects, and how many, may be found in which kinds of orbits.

  • Objects are characterized in terms of mass and composition. Categories include asteroids and debris; terrestrial planets, both rocky and icy; ice giant planets; and gas giant planets.
  • Orbits are characterized in terms of period, semimajor axis, and eccentricity.

Data on planets and orbits are discussed in terms of likely scenarios for planet formation. These scenarios build on the observation that planetary systems evolve in some way out of primordial clouds of circumstellar gas and dust. The authors noted above subscribe to the theory of planetesimal accretion, in which planets form through the assembly or accretion of small solid particles. With substantial frequency, this process results in planetary cores that are massive enough to capture deep atmospheres of hydrogen and helium, and thus evolve into gas giant planets. Subsequently, if less often, the viscosity of the gas nebula may induce these giants to migrate into smaller orbits. Meanwhile, less massive icy and rocky planets assemble wherever the orbital dynamics of the gas giants permits. (See Ida & Lin 2004, Ida & Lin 2005, Alibert et al. 2005, Chambers 2006, Papaloizou & Terquem 2006.)

The overall process of accretion can be understood in two stages. The first coincides with the presence of the turbulent gas nebula. It begins when the parent star has reached its mature mass, and it involves a continuous dissipation of gases. Solid particles suspended in the nebula begin sticking together to form planetesimals that range in size from a meter to a kilometer. They may eventually combine into rocky or icy protoplanets with diameters that range from 1000 kilometers (620 miles) up to several times the size of the Earth. These nascent objects may be subject to aerodynamic drag or, at higher masses, to tidal interactions with the nebula, causing them to spiral inward to smaller orbits. This poorly understood and potentially catastrophic process is known as Type I migration (Ida & Lin 2008a). In disks with a sufficient mass in solids (metals, silicates, ices), such objects may instead coalesce into gas giant cores, which rapidly capture deep atmospheres from the ambient gas. Subsequently, the viscosity of the dissipating nebula may induce some of these giant planets to migrate near the central star in the process known as Type II migration. This first evolutionary stage concludes with the complete dispersal of the nebula.

In the second, gas-free stage, accretion of planetesimals continues wherever the system’s orbital dynamics permits. Likely regions for assembling solid protoplanets lie within a few AU of the central star (provided no gas giants are orbiting nearby), or in the distant belt of planetesimals scattered outward by giant planets that formed near the ice sublimation radius (see below). The second evolutionary stage concludes when the collisional process among planets and planetesimals switches over from increasing mass (accretion) to decreasing mass (shattering). By this point all planets and dwarf planets in the system have reached their mature masses.

The initial line-up of planets then begins an extended sorting period, often known as planet-planet scattering. Mutual interactions induce further orbital transformations, so that semimajor axes and eccentricities may become larger or smaller, and some planets may be ejected from the system or engulfed by the central star. (See Weidenschilling & Marzari 1996, Adams & Laughlin 2003, Ford 2005, Ford & Rasio 2007.)

A key concept in theories of core accretion, often used to characterize system architecture, is the ice line (also snow line or ice boundary or ice sublimation radius). This is generally understood as the distance from the central star where free-floating molecules of water and other volatiles condense into ice (Ida & Lin 2004, Mandell et al. 2007, Kennedy & Kenyon 2008a). Referring specifically to the evolution of protoplanetary disks, Kennedy and colleagues characterize the ice line as “the point in the disk that separates the inner region of rocky planet formation from the outer region of icy planet formation” (Kennedy et al. 2006). Most of these authors agree on a temperature of 170 K to define this boundary, corresponding to a distance of 2.7 AU from a Sun-like star. Thus the ice line provides a broadly applicable metric for characterizing system architecture, as it predictably divides systems into inner and outer regions.

Notably, not all researchers foreground this concept in discussing planet formation. For example, in an extensive and frequently cited review article, John Papaloizou & Caroline Terquem never even mention the ice line (Papaloizou & Terquem 2006). Other theorists nevertheless consider it a key variable, arguing that giant planets like those in the outer Solar System preferentially form just beyond the ice line, within 5 to 10 AU of the condensation radius, while rocky planets like Earth form in the far more limited region inside it (Ida & Lin 2004, Kennedy et al. 2006). The reasoning behind the ice line’s importance is simple: just beyond this point, the presence of ice particles increases the density of planet-forming materials by a factor of 3 or 4, enabling large protoplanets to assemble far more rapidly than they could at larger or smaller radii (Ida & Lin 2004, Kennedy & Kenyon 2008a).

One remaining uncertainty regarding the ice line is its location, which changes during the early stages of disk evolution, generally moving inward (Lecar et al. 2006, Garaud & Lin 2006, Kennedy et al. 2006, Kennedy & Kenyon 2008a). For example, if the Solar System’s ice line really is located at 2.7 AU, why did Jupiter originally assemble at 5.45 AU (Tsiganis et al. 2005) rather than 3 AU? Kennedy & Kenyon explain this apparent paradox by proposing that, when protoplanets began forming in the Solar System (about one million years after the Sun ignited), its ice line was actually at 6 AU (Kennedy & Kenyon 2008a). Hence the observed semimajor axis of Jupiter, attained after a brief phase of inward migration. The argument of Kennedy & Kenyon implies that we need to reconsider the location of the inner system/outer system boundary around stars of all masses and temperatures.

basic data

Until 1995, the single available example of a planetary system around a Sun-like star was our own. Such scarce data encouraged the notion that the Solar System is typical. Planetary systems around other stars were expected to contain rocky planets like Mars and Earth inside their ice lines – that is, between radii of 0.3 AU (the perihelion of Mercury) and 2.7 AU (the heart of the Asteroid Belt, which coincides with the Solar System’s ice line) – and a mix of gaseous and icy planets outside this region, perhaps in orbits as wide as, or wider than, 40 AU (the semimajor axis of the dwarf planet Pluto). Orbits were expected to be circular, like those of the eight major planets around our Sun.

The ensuing discoveries of large numbers of extrasolar planets – currently more than 350 planets orbiting more than 250 different stars (Extrasolar Planets Encyclopaedia) – demonstrated the naivete of such expectations. We now know that gas giants can be found both inside and outside their systems’ ice lines, as close to the central star as 0.02 AU. We know of numerous systems in which terrestrial planets like those in the Solar System (i.e., orbiting within a few AU of their host stars) are impossible. We know of many systems that contain debris fields like our Asteroid and Kuiper Belts, but no detectable gas giant planets. We know that planetary orbits can range from near-perfect circles to ellipses with eccentricities higher than 0.9, like the orbits of comets.

The theory of planet formation by accretion has been continuously refined to accommodate these unexpected discoveries, potentially offering an ever more nuanced understanding of system architectures. Nevertheless, the most successful detection methods – radial velocity measurements, supplemented wherever possible by photometric transit observations – have so far illuminated only the inner regions of exoplanetary systems. Our picture of the diversity of outer systems is quite limited, informed primarily by simulation studies, analytical arguments, the imperfect evidence of our own Solar System, and the potentially ambiguous results of adaptive optics surveys. (See Biller et al. 2007, Lafreniere et al. 2007, Nielsen et al. 2007, Apai et al. 2007.)

Index of exoplanetary topics

metallicity and mass

  1. The first robust generalization to be made about exoplanetary systems was that gas giant planets orbiting within a few AU of their host stars (the vast majority of all exoplanet detections so far) are much more likely to be found around metal-rich stars than metal-poor stars (Marcy et al. 2005). In specific terms, this means that stars whose metallicity is lower than -0.2 rarely host giant planets (Sozzetti et al. 2008), while at least 25% of Sun-like stars (spectral types F, G, K) with metallicities greater than +0.3 regularly host gas giants, often in short-period orbits (Marcy 2005). Metallicity is understood as the ratio of heavy elements (collectively termed metals) to hydrogen in the composition of a star and, by inference, its primordial accretion disk.

  2. The key importance of the overall mass contained in the primordial disk has also been evident for some time. Kokubo & Ida (2002) conducted simulations showing that low-mass disks (~0.0015 MSOL) cannot form gas giant planets at all, because primordial gases disperse before protoplanets have time to accrete enough solids to capture deep atmospheres. Disks similar to the primordial Solar nebula (0.015-0.075 MSOL) are more successful, producing one or more gas giants immediately beyond their ice lines. High-mass disks (~0.15 MSOL) are the most productive, as they yield numerous gas giants, possibly including a few formed in situ as close as 1 AU to the central star (Kokubo & Ida 2002). Many other researchers have reached analogous, if not identical, conclusions (e.g., Thommes et al. 2003, Chambers 2006, Brunini & Benvenuto 2008).

    Although two stars of the same mass and spectral type may harbor disks of widely different masses, disk mass in general scales with star mass and thus with spectral type. Low-mass M dwarfs are far less likely to host detectable planets than are more massive stars of types F and A (Laughlin et al. 2004; Johnson et al. 2007a, 2007b, 2008). This trend has been succinctly expressed by Kennedy and Kenyon, who predict, “The probability that a given star has at least one gas giant increases linearly with stellar mass from 0.4 MSOL to 3 MSOL(Kennedy & Kenyon 2008a).

the hydrogen game

A number of recent studies have attempted to combine these robust generalizations into a coherent model of planetary system formation (e.g., Greaves et al. 2007, Garaud 2007, Thommes et al. 2008, Matsumura et al. 2009). Among them the work of Edward Thommes and colleagues stands out as an especially comprehensive treatment of this process, which the authors demonstrate in a series of animated simulations. Their primary goal is to model the formation of gas giant planets, whose absence or presence (and whose key attributes, if present) determines the ultimate configuration of a given system. In their approach, all outcomes depend on two key parameters: the viscosity (rate of gas flow onto the central star) and the mass of the dusty protoplanetary nebula. Enhancement in metals is treated as an increase in the ratio of solids (metals and silicates) to gaseous hydrogen within the overall nebular mass. Thus, as Jane Greaves and colleagues have observed, “a massive low-metal disk and a low-mass metal-rich disk could both lead to the same outcome” (Greaves et al. 2007).

What emerges from the work of Thommes and colleagues is a kind of game in which “planets must compete with each other for gas,” within a narrow window of opportunity defined by the nebula’s dissipation timescale (Thommes et al. 2008, Supporting Material). The outcome of this hydrogen game constrains each system’s architecture – for example, the number and masses of the planets, the shapes of their orbits (circular vs. elliptical), and their location in relation to the ice line.

In protoplanetary disks of low mass and low metallicity, no gas giants form, whereas rocky and icy planets in the range of Mars to Neptune are common. Conversely, massive disks that are enriched in metals produce an abundance of giants, but their very success leads to impoverishment: high mass and metallicity also promote rapid Type II migration, which destroys successive generations of giants by delivering them to the interior of the central star. Furthermore, once the gas dissipates, any surviving objects fall prey to planet-planet interactions, resulting in ejections and leaving perhaps a single giant at the end of the game.

The intermediate or Goldilocks regime of protoplanetary nebulae – not too massive, not too metallic – yields the kind of systems that planet searches have been reporting for the past 15 years. These have retained one or more gas giants, often at intermediate semimajor axes that reflect a moderate degree of migration: enough to shrink orbits but not enough to incinerate planets.

Last update July 2009

NEXT: Inner System Architectures

All text is copyright Raymond Harris 2006-2008