Dwarfs versus Giants, Round Two

David and Goliath (detail): Lorenzo Ghiberti, Florence, 1452

If we want to understand how planets form, how their orbits change over time, and where to look for planets like Earth, then we need to look at systems of multiple planets. The higher the multiplicity, the better – because more planets in a single system means broader coverage of the parameter space for planet mass, composition, and orbital period.

Thanks to the confirmation of almost 1,000 extrasolar planet candidates with data collected by the Kepler Mission, we now have a reasonably well-constrained sample of 125 transiting systems with three or more planets. Most are located several hundred to a few thousand light years away. Two-thirds of these systems have exactly three confirmed planets. The remaining third have four or more, up to a maximum of seven, with Kepler-90 the current record holder.

This swarm of new worlds adds new dimensions to the data painstakingly collected by radial velocity (RV) observations of stars in the immediate Solar neighborhood (mostly within 100 parsecs/326 light years) over the past two decades. The smaller RV sample contains 27 systems with three or more planets. As with the transiting sample, about two-thirds have exactly three planets, and the rest have four or more, up to a maximum of six (with three systems so far identified as sextuplets: HD 10180, HD 40307, and GJ 667C).

What follows is an overview of the diverse population of 152 multiplanet systems revealed by transit searches and RV surveys, the two most productive methods. Five nifty charts in gumdrop colors encapsulate most of the message. The sample of planets is drawn from reasonably well-constrained objects listed in the Extrasolar Planets Encyclopaedia and the Kepler Discoveries Table in May 2014. The selection discussed here is both judicious and inclusive, but inevitably somewhat arbitrary.

two kinds of planets, three kinds of systems

Like previous posts (here and here), this one categorizes system architectures according to the kinds of planets they support, using the fundamental division of low-mass planets versus gas giants. The former have masses smaller than 55 times Earth (55 Mea) and radii smaller than 8 times Earth (8 Rea). Their bulk composition is dominated by elements heavier than helium (which astronomers call “metals”), but many also have hydrogen/helium (H/He) atmospheres. Prototypical low-mass planets in our Solar System (listed in order of ascending heft) are Mercury, Mars, Venus, Earth, Uranus, and Neptune. The local species can be subdivided into the terrestrial planets, which consist of rock and metal without H/He (Mercury, Venus, Earth, and Mars), and the gas dwarfs, which have H/He envelopes that account for more than a few percent, but less than half, of their mass (Uranus and Neptune, each about 15% H/He).

High-mass planets, or gas giants, are composed mostly of hydrogen and helium. Jupiter and Saturn are the classic examples in our Solar System; each is at least 85% H/He. Among extrasolar gas giants, the median mass is 50% larger than Jupiter’s (1.5 Mjup) and the median radius is 20% larger than Jupiter’s (1.2 Rjup). As giants go, then, ours are pretty small.

Using these two species, we get three architectural types: low-mass only, high-mass only, and a combination of the two. The relative proportions of these types in the combined RV and transiting sample of high-multiplicity systems provides important insight into formation processes. Among 152 systems with at least three planets, the vast majority – 84% of the sample – contain only low-mass planets. Systems with planets of both types represent 12%, while those with gas giants alone represent just 4%.

This lopsided distribution of planetary species is likely a reflection (distorted to some degree by detection limits) of their true ratio throughout our Galaxy. At all semimajor axes, giant planets are much easier to detect than low-mass planets, whether by transit or by RV, yet the present multiplanet census is dominated by low-mass planets.

Although high-mass systems were the earliest type to be confirmed (Upsilon Andromedae, the first three-giant architecture, was announced in 1999), only five similar systems have been identified in the fifteen years since. By contrast, the first low-mass system (HD 69830) was announced in 2006, and eight years later the low-mass sample has well over 100 members, most transiting. This ubiquitous population was just waiting for techniques sensitive enough to find it.

Figure 1. Twelve Low-Mass Multiplanet Systems Detected by RV

Semimajor axes are measured in astronomical units (AU), where 1 AU is the Earth-Sun separation; planet masses are indicated in Earth units (ME); star masses appear in Solar units at right.

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All twelve of the low-mass RV systems are located within 130 light years (40 parsecs), and all have been announced since 2006. Debate persists about the parameters of some of these systems, as discussed a few times in this blog (Year of the Signal, The Sun’s Back Yard, More Backyard Controversies). Nevertheless, most are likely to be giant-free, at least within a semimajor axis of about 2 AU or so. Only 25% have more than three detected planets.

The median stellar mass in this sample is 0.855 times Solar (0.855 Msol). The median metallicity is -0.14, similar to the median for stars in the immediate Solar neighborhood. Planetary orbits are extremely compact. The median semimajor axis is 0.17 AU, much smaller than the orbit of Mercury, and in two-thirds of systems, all known planets are contained within a semimajor axis of 0.7 AU. This would place them inside the orbit of Venus in our own system. While these compressed orbits may be, in part, an artifact of the RV bias toward objects on short orbital periods, the available data are nevertheless substantial enough to define a distinct, highly compact structural type. It has been detailed around a growing sample of nearby stars, from M dwarfs through K dwarfs to G dwarfs like our Sun.

Because the planets in Figure 1 are RV detections, only their minimum masses – m sin (i) – can be estimated. Nevertheless, the estimates are probably within a factor of a few of the true masses. Only the objects with the largest m sin (i) might be gas giants in disguise. The median m sin (i) across all twelve systems is 6.7 Mea. More than three-quarters of these planets are less massive than Uranus (14.5 Mea), while only 10% have m sin (i) below 3 Mea. This value is a generous upper limit for Earth-like planets without a H/He atmosphere. Still fewer planets (below 7%) have minimum masses in excess of 25 Mea.

Even though none of these systems supports a gas giant, most contain a significant quantity of mass within 1 AU. At the high end, HD 40307 contains a minimum of 36 Mea inside 0.6 AU, while HD 31527, HD 69830, and 61 Virginis contain more than 40 Mea each inside 0.9 AU. By comparison, the Solar System contains only 2 Mea inside a much wider radius of 5 AU.

Planets above 10 Mea tend to have semimajor axes wider than 0.1 AU, but the orbital distribution of planetary masses is relatively free: lower-mass planets may be flanked by higher-mass planets, and vice versa.

Although early data on compact systems suggested that tightly nested orbits must be circular to ensure long-term stability, recent additions to the sample are reported to have surprisingly high orbital eccentricities. In two-thirds of the systems in Figure 1, the outermost orbit has an eccentricity of 0.2 or more. In one-quarter, it exceeds 0.4. Just one system (the fascinating and controversial GJ 667C) has an orbital solution consistent with eccentricities smaller than 0.1 for all planets. Nevertheless, in many of the systems with large reported eccentricities, the reliability of the data is unclear; it is possible that additional, undetected planets are warping the results away from circularity.

RV methods are not yet sensitive enough to reveal Earth-mass planets, even around the diminutive M dwarfs that crowd the Sun’s back yard (Tuomi et al. 2014). The only planets in Figure 1 that might plausibly be Earth-like are GJ 667C e and f, according to the parameters provided by Anglada-Escude et al. (2013). They estimate a minimum mass of 2.7 Mea for each of these planets. Nevertheless, our understanding of the GJ 667C system is in a state of flux, and it may turn out that both of these planets (if they exist at all) exceed 5 Mea. Such a large mass would virtually guarantee a high-pressure H/He envelope, which in turn would produce surface conditions at least as hellish as those on Venus.

Figure 2. Selected Low-Mass Multiplanet Systems Detected by Kepler

Semimajor axes are measured in astronomical units (AU), where 1 AU is the Earth-Sun separation; planet radii are indicated in Earth units (RE); star masses appear in Solar units at right.

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This chart of 14 systems is a non-random selection from the 116 systems with 3 or more low-mass planets confirmed by Kepler transit data. It is biased in favor of higher multiplicity and wider semimajor axes. In the full sample of transiting low-mass multiplanet systems, the median semimajor axis is just 0.10 AU, and only 30% of systems have more than three planets.

While the RV sample is biased in favor of low-mass stars, the transiting sample has the opposite problem. The Kepler Mission targeted bright stars that yield relatively high ratios of signal to noise across hundreds of parsecs. This criterion excluded most M dwarfs in the field of view. Nevertheless, the median stellar mass of the complete Kepler low-mass multiplanet sample is 0.91 Msol, less than 10% higher than the median for the RV sample in Figure 1. The median metallicity, though less reliably constrained, is about -0.11 – also just a little higher than that of the RV sample.

Planets in these systems have a median radius of 2.15 Rea. According to recent studies of the mass/radius relationship for transiting planets (Lopez & Fortney 2013, Weiss & Marcy 2014, Marcy et al 2014), this result implies that more than half the sample (i.e., the larger half, and some of the smaller half too) will have H/He envelopes. The same studies find that most planets smaller than 2 Rea are less massive than 10 Mea, as are most planets between 2 and 3 Rea. In fact, the only planet smaller than 3 Rea with a well-constrained mass above 10 Mea is Kepler-10c. This object has a radius of only 2.35 Rea, yet recent RV measurements determine a mass of about 17 Mea, similar to Neptune’s (Dumusque et al. 2014). According to the mass/radius relations published by Lissauer and colleagues (2013), these parameters are consistent with two different compositions: a rocky planet with a modest atmosphere containing a small fraction of H/He, or a mostly rocky planet with a substantial fraction of high-pressure ices (more than 10% but less than 50% of the total mass).

Only 7% of objects in the multiplanet sample are larger than 4 Rea (the approximate radius of Uranus and Neptune), while 25% are smaller than 1.5 Rea, the approximate theoretical threshold for rocky planets without H/He (Marcy et al 2014, Buchhave et al. 2014).

These statistics provide a snapshot of the overall population of compact systems: most have rocky planets several times as massive as Earth, and most of these planets have hydrogen atmospheres. Planets as big and heavy as Uranus are relatively uncommon on short orbits, but Super Earths and even Earth analogs lurk among their puffy siblings.

An analysis of Kepler data available in 2012 found that, in any pair of adjacent planets where one is larger than 4 Rea and the other is smaller than 3 Rea, the smaller planet is more likely to orbit interior to the larger planet (Ciardi et al. 2013). No such relationship obtains among planets pairs in which both are smaller than 3 Rea.

Although the architectures of the transiting and RV samples appear to overlap, the two populations still look distinct. Overall, transit searches appear to be more sensitive to low-mass planets than RV. Kepler multiplanet companions are generally less massive than their RV counterparts, and their orbital periods are generally shorter. They are also remarkably coplanar – in other words, each planet in these systems orbits in more or less the same plane, with minimal mutual inclinations (see Mass Matters).

Both samples have a similarly low percentage of systems with four or more planets, but the reasons underlying this trend toward reduced multiplicity may differ for each sample. In systems where just three planets are detected in transit, several more might be present, but their orbits are either wider than those of the observed planets, or slightly misaligned with them. Either situation would reduce their chances of detection in transit. In RV systems, however, planets may be missed simply because they aren’t massive enough, regardless of their alignment.

The relative insensitivity of RV observations makes transit searches the preferred method for finding habitable planets. RV techniques are not yet capable of detecting planets of 1-3 Earth masses in the habitable zones of K and G stars, nor have they yet returned a robust detection of such an object around an M dwarf. Space-based transit observations have identified two such planets, both of which appear in Figure 2: Kepler-62f, which orbits a K dwarf, and Kepler-186f, which orbits an M dwarf.

Figure 3. Nine Mixed-Mass Multiplanet Systems Detected by RV

Semimajor axes are measured in astronomical units (AU), where 1 AU is the Earth-Sun separation; planet masses are indicated in Earth units (ME); and star masses appear in Solar units beneath each star name.

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Figure 3 features all RV systems that contain at least three planets, such that at least one has a minimum mass below 55 Mea and at least one has a minimum mass above 55 Mea. 55 Cancri is the oddball in this line-up, since the third and fourth planets (55 Cancri c and f) are right on the cusp between gas dwarfs and gas giants. Data on their bulk compositions would enable a more accurate classification, but so far this information is out of reach, as only the innermost planet in this system can be observed in transit.

All systems in this subsample are located within 175 light years (54 parsecs). The median star mass is 0.91 Msol, the same as the median for low-mass transiting systems and not much higher than the median for low-mass RV systems. The median stellar metallicity, however, is +0.23, much higher than the value for low-mass systems. This result is consistent with the widely supported observation that stars hosting gas giants tend to be enriched in metals.

The mixed-mass systems in Figure 3 bear little resemblance to their low-mass counterparts in Figures 1 and 2. Orbits are far more expansive, such that the outermost planet in more than three-quarters of these systems has a semimajor axis larger than 2 AU. For all planets in this subsample, the median semimajor axis is 0.33 AU.

Low-mass planets are a minority: three-quarters of these systems contain only one, and it is invariably the innermost planet. Yet even the low-mass planets aren’t particularly dainty; for this species, the median mass is 12.4 Mea, almost double the median for the low-mass planets in giant-free systems. However, the gas giants in this subsample are similar in mass to those in the complete exoplanetary census: the range is 0.2 Mjup to 7.2 Mjup, and the median is 1.7 Mjup.

Overall, we see low-mass planets orbiting inside 0.1 AU, high-mass planets orbiting outside 1 AU, and a mix of both between 0.1 and 1 AU. Three-quarters of these systems have planets with semimajor axes larger than Earth’s.

Even though our Solar System meets the basic criteria for this architectural type (at least one dwarf and one giant), none of the systems in Figure 3 seems to have room for an Earth analog. In many of them, a gas giant or large gas dwarf already occupies the habitable zone, while in others, a stable orbit in this region would be impossible because of perturbations by adjacent planets. Future research may identify Earth-like exoplanets in mixed-mass systems, but for now, all-dwarf architectures seem more hospitable to temperate rocky worlds.

Figure 4. Nine Potential Mixed-Mass Multiplanet Systems from Kepler

Semimajor axes are measured in astronomical units (AU), where 1 AU is the Earth-Sun separation; planet radii are indicated in Earth units (RE); and star masses appear in Solar units beneath each star name. Open circles indicate planets detected by RV observations but not in transit, so their radii are unknown. Nevertheless, all these RV objects have minimum masses above 55 Mea.

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Figure 4 depicts all high-multiplicity systems with at least one planet larger than 8 Rea and at least one planet smaller than 8 Rea. It also includes all such systems with at least one transiting planet smaller than 8 Rea and one massive planet of unknown radius detected by RV. However, not all planets with large radii are necessarily gas giants. For example, new analyses now indicate that neither of the large planets orbiting Kepler-9 is a gas giant (Dreizler & Ofir 2014), so that system is omitted from further discussion. In addition, the masses of the two large planets orbiting Kepler-90 remain unconstrained.

The figure suggests that transit searches are much less suited to finding mixed-mass systems than they are to finding low-mass systems. In the RV sample of high-multiplicity systems, the ratio of low-mass to mixed-mass systems is 4:3, while in the transiting sample, the ratio is about 14:1. One plausible explanation for this mismatch is that orbits in mixed-mass systems are often non-coplanar, so that only a subset of planets can be observed in transit. The RV method, on the other hand, can detect both “flat” (co-planar) and “bumpy” (non-coplanar) systems (see Mass Matters).

To illustrate: in three of the systems in Figure 4 (Kepler-25, Kepler-48, and Kepler-68), the candidate gas giant is not observed in transit, indicating that the giant’s orbit is inclined with respect to the orbital plane of the low-mass planets. RV observations detected those three giants while missing the associated low-mass planets.

Compared to the mixed-mass RV systems, mixed-mass Kepler systems have more compact orbits. Only one-third of systems have planets outside 1 AU. However, this limitation is directly related to the duration of the Kepler Mission, which ended after less than four years. Several more years of space-based observations would be needed to explore the orbital space beyond 1 AU. Nevertheless, we still see a similar distribution of species in both RV and transiting systems: low-mass planets inside 0.1 AU, gas giants outside 1 AU, and a mix of both between 0.1 and 1 AU. 

Figure 5. Six High-Mass Multiplanet Systems

Semimajor axes are measured in astronomical units (AU), where 1 AU is the Earth-Sun separation; planet masses are indicated in Jupiter units (Mj); and star masses appear in Solar units beneath each star name.

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All the systems shown in Figure 5 were detected by RV surveys. Systems with three or more gas giants have yet to be observed in transit. The explanation for this mismatch is likely the same as the one for the mixed-mass sample: These planets have non-coplanar orbits, so for any given observer, only a subset of the ensemble can be seen crossing the face of the star.

To date, high-mass, high multiplicity systems have been identified only by RV measurements or direct imaging. The latter method has detected exactly one such multi-giant system, HR 8799, which remains exceedingly mysterious. All the systems in Figure 5 are located within 175 light years (54 parsecs) – in other words, the same volume of space as the mixed-mass RV sample. The median star mass is about 1.1 Msol, and the median star metallicity is +0.14. The first value is higher than in the mixed-mass systems, while the second is lower. In these systems, perhaps, stellar mass was as important as metallicity in building an ensemble of giants (Johnson et al. 2010).

Like the mixed-mass RV systems, the planets in all-giant systems tend to have wide orbits. The median semimajor axis is 1.8 AU, by far the largest median among the five subsamples discussed in this post. Just two systems (one-third of the tiny sample) have planets inside 0.1 AU: Upsilon Andromedae b and HIP 14810 b. Although both planets meet the standard criteria for Hot Jupiters (i.e., a gas giant with a semimajor axis smaller than 0.1 AU and an orbital period shorter than 10 days), both are outliers within the Hot Jupiter sample, which exhibits a distinctive pile-up of orbital periods around 3 days. Ups And b has a period of 4.6 days, and HIP 14810 b has 6.7 days.

As the discovery team for HD 141399 recently observed, systems with several giants are intrinsically scarce (Voigt et al. 2014). One widely endorsed explanation proceeds like a chronicle of dynastic strife. If a protoplanetary disk manages to precipitate three or more gas giant planets, they are likely to perturb each other’s orbits after the cushioning cocoon of hydrogen dissipates (Matsumura et al. 2013). Through ejections and mergers, the number of contenders will usually be reduced by one or more, leaving the kind of configuration we see in Figure 5.

how did they get that way?

The most widely accepted theory of planet formation is core accretion, according to which solid particles suspended in the primordial gas nebula surrounding a young star coalesce to form the solid cores of protoplanets. These protoplanets then interact and collide to build larger planets, and if they become massive enough before the primordial nebula dissipates, they also accrete H/He atmospheres.

However, no general theory of core accretion has managed to explain all the system architectures pictured in Figures 1 through 5, let alone all these architectures plus the peculiar configuration of our own Solar System. A future blog post will explore the current state of the art in planet formation theory, bearing in mind the necessity for any such theory to account for all architectures, and not just a convenient subset.

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