Planet Populations Across Five Orders of Magnitude in Mass

e x t r a s o l a r &nbsp &nbsp p l a n e t s

basic planetology : planets across 5 orders of magnitude in mass

Solar and extrasolar planets of various masses, from rocky terrestrial planets (Mars, Earth) through ice giants (Uranus) to gas giants (Saturn, HD 128311 c). Numbers above the red line indicate approximate mass in units of Earth mass (MEA); numbers below the red line indicate mass in units of Jupiter mass (MJUP). Planets are represented at their approximate relative sizes. HD 128311 c is assumed to have a diameter of 1.16 DJUP, given a mass of 3.22 MJUP, a semimajor axis of 1.76 AU, a system age of 300 million years, and a refractory core of 10 MEA.

Comparative sizes of nearby stars

Terrestrial planets and moons

Super Earth

Taxonomy refers to any orderly system of classification. Perhaps the most familiar example of a taxonomy is the assignment of genus and species names to biological organisms, such as Homo sapiens (people), Ursus maritimus (polar bears), or Triticum aestivum (wheat).

Although a universally accepted taxonomy of extrasolar planets does not yet exist, theory and observation have established its foundations. A few key factors are usually regarded as significant: planet mass, internal composition, and formation history.

The most reliable data on exoplanets derive from radial velocity and transit observations. When a system can be observed by using both methods, a wealth of evidence is available. More than 100 exoplanets have now been characterized in this way (Torres et al. 2008, Extrasolar Planets Encyclopaedia). They range in mass from CoRoT-7b at 0.015 MJUP (4.8 MEA) to XO3-b at 11.79 MJUP. For these planets, astronomers can determine radius as well as mass, and thus provide important constraints on composition.

In combination with evidence from the Solar System, whose planets we know best, radial velocity and transit data suggest a basic planetary taxonomy that includes at least three major species:

All three consist of the same basic ingredients mixed in different proportions: metals (mostly iron and nickel), silicate rocks, ices (water, methane, ammonia), and hydrogen (typically accompanied by a small proportion of helium). Together these three planetary species span at least five orders of magnitude in mass (see Fortney et al. 2007).

terrestrial planets

At the bottom of the mass distribution are the terrestrial planets. The Solar System has four, ranging from Mercury – a dense, airless, highly metallic world with only 6% of Earth’s mass – to the Earth itself, which has a substantial atmosphere and a very modest endowment of ice in addition to its metallic core and silicate mantle. The upper mass limit for such planets is poorly understood. Although 10 MEA is usually given as the boundary (e.g., Ida & Lin 2004), numerical simulations of planet formation typically yield smaller maximum masses (Raymond et al. 2004, Kenyon & Bromley 2006), in the range of 2 MEA to 4 MEA for planets composed primarily of refractory elements (i.e., metals and silicates).

The recent discovery of several “Super Earths” in short-period orbits around nearby G, K, and M dwarf stars invites a new perspective on this question. Although their host stars are often metal-poor, indicating a shortage of heavy elements in their native environments, the planets themselves have minimum masses ranging from about 2 MEA to 9 MEA. In many if not most cases, the likeliest explanation for their enhanced mass is a large endowment of volatiles (water, methane, ammonia).

Accordingly, several studies propose a subdivision of low-mass planets into two species: (1) rocky planets that resemble those in the inner Solar System and (2) icy planets that resemble scaled-up versions of Ganymede and Callisto, the two most massive and volatile-rich moons of Jupiter (Kuchner 2003, Leger et al. 2004, Sotin et al. 2007, Selsis et al. 2007). The latter are likely to be 50% refractory and 50% ice (Leger et al. 2004, Selsis et al. 2007).

Earth and Super Earths. Comparative sizes and bulk compositions of three terrestrial-mass planets, all smaller than 2 Earth radii (Rea). Left: Earth, mass 1 Mea, diameter 7900 mi (12,755 km). Center: Rocky Super Earth, mass 3 Mea, diameter 10,665 mi (17,220 km). Right: Icy Super Earth, mass 6 Mea, diameter 15,010 mi (24,235 km). Mass-radius relationships follow Fortney et al. 2007.

Planets of GJ 581

Theories of planet formation typically conclude that rocky planets in the mass range of Super Earths will form inside the system’s ice line through a series of giant impacts among large protoplanets. Icy Super Earths (sometimes known as “mini-Neptunes”) will form outside the ice line and then, in many cases, migrate inward to smaller and hotter orbits by various mechanisms, including planet-planet scattering and Type I migration (Kuchner 2003, Leger 2004, Raymond et al. 2007, Mann et al. 2010). Their subsequent evolution will then depend on their final semimajor axes and on the luminosity of their host stars.

In the habitable zone, the outer layers of an icy planet would melt, resulting in an “Ocean Planet” with a rocky core surrounded by a thick layer of ice supporting a global ocean 100 kilometers deep. Starward of this region, water cannot be sustained in liquid form, so the result would be a “Steam Planet” or “Sauna World” in which a thick, hot atmosphere of water vapor is in direct contact with a high-pressure mantle of ice. Remarkably, a sufficiently massive Steam Planet is likely to maintain its volatile content even on a star-grazing orbit. Selsis and colleagues have found that a planet of 6 MEA whose composition is 50% ice and 50% rock and metal can maintain its reservoir of water for more than 5 billion years, even at a semimajor axis of 0.04 AU (Selsis et al. 2007).

Among stars, low-mass objects vastly outnumber high-mass objects. A similar relationship holds among the objects in our Solar System, which contains two gas giants, two ice giants, four terrestrial planets, well over 100 moons, and hundreds of thousands of meter-sized bits of debris. Although conclusive proof is still lacking, the same situation very likely prevails in extrasolar systems. Given the limitations of all current detection methods, announced gas giants outnumber all announced ice giants and Super Earths combined by a factor of 10 to 1. Nevertheless, Michel Mayor and colleagues have estimated that about 30% of G and K stars in the Solar neighborhood harbor ice giants or Super Earths with periods shorter than 50 days — in other words, closer to their host stars than Mercury is to our Sun (Mayor et al. 2009). This figure substantially exceeds the proposed population of nearby extrasolar gas giants. Andrew Cumming and colleagues have estimated that 17% of nearby Sun-like stars have gas giant planets orbiting within 20 AU, the approximate semimajor axis of Uranus (Cumming et al. 2008). A recent unbiased survey of Sun-like stars within 25 parsecs, led by Andrew Howard, supports these assessments, finding “a substantial increase in planet occurrence with decreasing planet mass” (Howard et al. 2010).

1183 Transiting Objects from the Kepler Mission
Diagram based on Table 5 of Borucki et al. 2011

Early results from the Kepler mission, a spaceborne search for transiting planets as small as Earth, provide compelling evidence for these estimates (Borucki et al. 2011). Data returned during the first four months of observations, representing exoplanets orbiting within 0.5 AU of their host stars, clearly demonstrate that gas giant planets are far less numerous than smaller objects even in the parameter space probed by radial velocity searches. Mission scientists consider the data on Neptune- to Jupiter-size objects to be relatively free of biases, suggesting that ice giants outnumber gas giants by a factor of 4 (see graph, above). The decline in the population of Super Earth- to Earth-size candidates, however, may be a selection effect stemming from the greater difficulty of detecting objects at the smallest observable radii.

Super Earths, Ice Giants, Gas Giants
mass distribution of 123 exoplanets < 170 Mea (0.535 Mjup)
data from Extrasolar Planets Encyclopaedia as of 11 January 2011

Ice giant planet

Clouds over Neptune

ice giant planets

The defining criterion for an ice giant seems to be the accretion of enough frozen volatiles (water, methane, ammonia) around a heavy-element core to retain a hydrogen-helium atmosphere comprising about 10% of the object’s total mass. Theoretical studies indicate that about 10 MEA is the minimum mass needed to sustain such an atmosphere (Pollack et al. 1996). In the Solar System, this condition is satisfied by Uranus and Neptune, whose overall masses are 14.5 and 17.2 MEA, respectively. Each of these planets has an extensive rock/ice core enveloped by more than an Earth mass in gaseous hydrogen (Guillot 1999).

Among extrasolar planets, 4 similar objects have been studied by both radial velocimetry and transit photometry: Gliese 436 b, HAT-P-11b, Kepler-4b, and HAT-P-26b. Like most other transiting planets known to date, all orbit very close to their host stars, with periods ranging from 2.6 to 4.9 days. Their masses are well constrained: HAT-P-26b at 18.8 MEA, Gliese 436 b at 23.2 MEA, Kepler-4b at 24.5 MEA, and HAT-P-11b at 25.8 MEA (Torres et al. 2008, Kipping & Bakos 2010, Hartman et al. 2010). Precise data on their radii indicate that each contains at least 10% of its mass in gaseous hydrogen, enveloping a core of rock and ices comprising the remaining fraction (Gillon et al. 2007, Bakos et al. 2009, Kipping & Bakos 2010, Hartman et al. 2010). Thus these planets are plausibly described as Hot Neptunes.

Objects of this type must form outside their systems’ ice lines, where sufficient quantities of icy planetesimals are available to ensure the assembly of massive cores capable of retaining hydrogen atmospheres. Their upper mass limit remains uncertain. Ida & Lin predicted a “planet desert” between 10 and 100 MEA, on the grounds that gaseous accretion is so rapid once a planetary core reaches 10 MEA that it will quickly expand to the mass of Saturn (95 MEA), leaving few stragglers in the interval (Ida & Lin 2004).

Discoveries in the meantime have not supported this prediction, as illustrated by the graph above. It uses a sample of 123 exoplanets, representing all confirmed radial velocity discoveries with m sin i < 170 MEA (0.535 MJUP) listed in the Extrasolar Planets Encyclopaedia as of January 2011. This range was selected to highlight any potential boundary separating ice giants from gas giants. Although numbers are high between 10 and 20 MEA, coinciding with the mass range of Uranus and Neptune, no corresponding spike appears around the mass of Saturn. Instead, a number of “valleys” appear between 30 and 140 MEA, where we might expect to see overlapping populations of high-mass ice giants and low-mass gas giants.

Evidently rocky planets span almost three orders of magnitude, from less than 0.1 MEA to the vicinity of 10 MEA, whereas ice giants seem to be a transitional species. Their distribution begins around 10 MEA and then blends into the range of the gas giants, somewhere between 50 and 70 MEA.

Mass Distribution of 412 Exoplanets < 5.35 MJUP
in units of Earth and Jupiter mass (100 Mea = 0.314 Mjup)
data from Extrasolar Planets Encyclopaedia as of 11 January 2011

Gas giant with transiting moons

gas giant planets

Gas giants occupy the top of the planetary mass range, beginning at about 55 MEA (0.17 MJUP) and extending well beyond 1000 MEA (~3 MJUP). Their name reflects the assumption that their overall mass is about 75% to 95% hydrogen, like the bulk composition of Jupiter and Saturn.

A growing population of transiting planets probes the low-mass threshold for gas giants: Kepler-9c, HAT-P-18b, HAT-P-12b, and CoRoT-8b. Because these objects have been detected by radial velocity observations as well as by transit searches, their true masses have been determined and their internal compositions assessed. Their respective masses are 0.171 MJUP (54 MEA), 0.197 MJUP (63 MEA), 0.211 MJUP (67 MEA), and 0.22 MJUP (70 MEA), meaning that all of them are substantially less massive than Saturn (0.299 MJUP or 95 MEA). Their measured radii, however, seem at odds with their masses. HAT-P-18b, at 63 MEA, has almost the same radius as Jupiter, while HAT-P-12-b, which is slightly heavier, is also slightly more compact, at about 0.96 RJUP. The most lightweight member of this group, Kepler-9c, has a radius of 0.82 RJUP (similar to Saturn’s), while CoRoT-8b, the heaviest, is only 0.57 RJUP.

These values indicate a substantial variation in bulk composition, illustrating the diversity of gas giant structures. HAT-P-18b may be almost 100% hydrogen/helium (Hartman et al. 2010), while Kepler-9c and HAT-P-12b are about 80-90% hydrogen/helium and no more than 15% rock, metal, and ice (Holman et al. 2010, Hartman et al. 2009). Given their inflated radii, these 3 objects have analogs among more massive gas giants in short-period orbits. CoRoT-8b, however, has 66-90% of its mass in heavy elements and only 10–33% in hydrogen/helium (Borde et al. 2010). Its classification as a gas giant may thus be dubious, since its internal structure is more reminiscent of Neptune or GJ 436 b than of Saturn or HAT-P-12b. Among transiting planets, the closest analog of CoRoT-8b is HD 149026 b, which has a mass of 0.359 MJUP, a radius of 0.725 RJUP, and a bulk composition that is 60% heavy elements (Nutzman et al. 2009).

Recent data on more than 500 extrasolar planets, as posted in the Extrasolar Planets Encyclopaedia, place the median mass of the gas giant population at about 510 MEA (1.6 MJUP), assuming a range of 0.17-20.0 MJUP in minimum mass. Nevertheless, the upper limit for this planetary species remains imprecise. Uncertainty stems from the fact that any substellar object above 13 MJUP may be classified as a brown dwarf: a minimally luminous object that forms like a star through the collapse of a molecular hydrogen cloud. Although gas giants become progressively scarcer above 5 MJUP, a population of massive objects on planet-like orbits (more than 20 so far) has been reported between 10 and 25 MJUP, coinciding with the brown dwarf range. For this group of “super planets,” data on mass and composition may be insufficient to establish their true nature; we may need to know their formation histories, which so far remain out of reach. See also Super Jupiter or Brown Dwarf?

Mass Distribution of 475 Exoplanets < 15 MJUP
data from Extrasolar Planets Encyclopaedia as of 11 January 2011

Index of exoplanetary topics

With regard to size, both theory and observation indicate that a gas giant’s radius is determined primarily by its temperature and bulk composition rather than its mass. Fortney and colleagues (2007) provide theoretical tables of planetary radii for various combinations of age, semimajor axis, mass, and internal structure. All gas giant planets with similar ages and bulk compositions have very similar diameters, regardless of their variation in mass. Also, as Fortney and colleagues demonstrate, gas giants are systematically larger when their cores are less massive, and smaller when their cores are more massive (Fortney et al. 2007).

According to these models, if we consider all gas giants at all ages, masses, core masses, and semimajor axes, the potential range in radii extends from 1.656 RJUP for the youngest, hottest, least massive, and least dense, down to 0.558 RJUP for the oldest, coldest, least massive, and most dense (Fortney et al. 2007). Note that, somewhat counterintuitively, the least massive gas giants present both the largest and the smallest radii.

The observed population of transiting gas giants presents an ever-growing body of evidence against which astronomers can test the predictions of Fortney and others. Currently, the planet with the largest measured radius is TrES-4, a gas giant less massive than Jupiter orbiting a hot F-type star in a period of less than 4 days. This planet’s radius is a remarkable 1.78 RJUP, substantially exceeding predictions (Sozzetti et al. 2009). No widely accepted scenario has yet emerged to explain this bloated object. Gas giants with unexpectedly small radii, such as CoRoT-8b and HD 149026 b, present fewer theoretical challenges.

Last revised February 2011

All text is copyright Raymond Harris 2006-2011