Friday, October 5, 2012

Mass Matters

Kepler-30: A very flat system. Credit: Sanchis-Ojeda et al. 2012

Scientists love data – the more the better. So the Kepler Mission gets a lot of love these days. Old data continue to yield new results, while the next data release, scheduled for October 28, should provide 13 quarters of transit light curves – enough, I hope, to identify plenty of small planets in the habitable zones of K-type and cooler G-type stars.

Given the abundance of multiplanet systems among the Kepler candidates, existing data have inspired an ever-growing number of analyses of system architectures. As Earth’s orbit carries us through the waning phases of the Harvest Moon, let’s take a look at this year’s crop.

architecture in a gravity well

When astronomers speak of system architecture, they are typically discussing which kinds of planets (mass, radius, composition) can be found on which kinds of orbits (period, semimajor axis, eccentricity, inclination). As we’ve already seen in some detail (How Weird Is Our Solar System? and Solar System Archaeology, Parts I and II), the distribution of the eight planets in our system is in no way typical of other systems in the general Solar neighborhood.

Instead, systems of Earth- to Neptune-mass planets, arranged on packed orbits that would fit inside the semimajor axis of Venus, seem to be among the commonest architectures. Within the next few years, thanks to Kepler and other programs, we should be able to quantify the true rarity or abundance of this and other architectural types.

hot jupiters make bad neighbors

For me, the first really exciting analysis of the Kepler architectural data appeared back in May: “Kepler constraints on planets near hot Jupiters,” by Jason Steffen and other members of the Kepler team. Their study examines transit data on Sun-like stars to assess the Galactic distribution of Hot Jupiters, a seemingly ubiquitous planetary species that dominates both radial velocity and transit searches.

Steffen and colleagues start by identifying three basic classes of objects in the Kepler database, all with orbital periods shorter than 16 days: Hot Jupiters (n = 63), which for study purposes they define as objects of 0.6 to 2.5 Jupiter radii (Rjup; this range is equivalent to 6.8-28 Earth radii or Rea), with periods between 19 hours and 6.3 days; Warm Jupiters (n = 31), which have the same radii, with periods between 6.3 and 15.8 days; and Hot Neptunes (n = 222), which have the same period range as Hot Jupiters, with radii of 0.126-0.6 Rjup (1.4-6.7 Rea). Note that the last category includes objects that are generally classified as Super Earths, since 2 Rea is the approximate upper limit for a low-mass, hydrogen-free planet.

The fact that Hot Neptunes (augmented by Hot Super Earths) outnumber Hot Jupiters by a factor of 3.5 to 1, even though the latter are much easier to detect in transit, confirms earlier findings that Hot Jupiters are “a relatively small population” (Steffen et al. 2012, Bayliss & Sacket 2011, Wright et al. 2012). Furthermore, using evidence of recorded transits and transit timing variations (TTV) to assess the presence of nearby companions in the same system, Steffen and colleagues were able to establish that none of their Hot Jupiters had any neighbors, while one-third of their Hot Neptunes and one-fifth of their Warm Jupiters did.

This definitive finding provides strong constraints on evolutionary scenarios. As the authors note, the relative frequency of these three planetary species – Hot Jupiters, Warm Jupiters, and Hot Neptunes – “indicates a mass dependence in system architecture.” They infer that Hot Jupiters typically form through planet scattering, rather than such alternative pathways as the Kozai mechanism or Type II migration. This inference agrees well with the conclusions of a newly published survey of transiting Hot Jupiters by Simon Albrecht and colleagues, who also rule out Type II migration and favor either planet scattering or Kozai cycles (or both) for their origin (Albrecht et al. 2012).

With specific reference to the overarching goal of the Kepler Mission – to determine the frequency of Earth-like planets in our Galactic neighborhood – Steffen and colleagues conclude: “Hot Jupiter systems where planet-planet scattering is important are unlikely to form or maintain terrestrial planets interior to or within the habitable zone of their parent star” (Steffen et al. 2012).

Since planet scattering is more likely in systems of high-mass planets than low-mass planets (Thommes et al. 2008, Johansen et al. 2012), and since high-mass planets are more likely to orbit stars with high mass and metallicity (i.e., with Solar values or higher) than those with low mass and metallicity (Laughlin et al. 2004, Johnson et al. 2010), this “mass dependence” provides an important clue to the likely distribution of system architectures.

flat vs. bumpy systems

The study by Steffen and colleagues is distinguished from most analyses of Kepler system architectures by its emphasis on planet mass, for which radius is a rough but useful proxy. Several other studies have focused on such architectural features as multiplicity (what is the typical number of planets per system?), coplanarity (how often do multiple planets travel in a common orbital plane?), and inclination (what proportion of planets have orbits that are steeply inclined in relation to the invariable plane of their systems?). This work has been conducted both by researchers associated with Kepler (Lissauer et al. 2011, Fabrycky et al. 2012) and by others using publicly available data (Tremaine & Dong 2012, Figueira et al. 2012, Fang & Margot 2012, Johansen et al. 2012).

Johansen and colleagues frame the problem succinctly: “The relative numbers of systems with single and multiple transiting planets is a sensitive function of the intrinsic multiplicity of planetary systems and the relative inclinations between planet orbits, and thus holds important information about planetary system architectures.”

The Kepler data contain a surprising wealth of systems with multiple transiting planets. In such systems, the planets are necessarily coplanar, so that when their mutual inclinations can be measured, they turn out to be small. These systems are therefore described as “flat” and “well-aligned,” adjectives that also happen to apply to our Solar System. Of course, multiplanet systems that are especially “bumpy” or poorly aligned cannot be detected by photometric observations. Just one transiting planet would be observed in such cases – and as it turns out, most Kepler systems harbor just one observable planet.

yin & yang

Here it is worthwhile to point out that standard models of planetary evolution (see Solar System Archaeology) include two basic mechanisms: relatively smooth interactions between forming planets and the gases of the protoplanetary nebula (e.g., Type I and Type II migration), and relatively violent interactions between the planets themselves (e.g., planet scattering). The latter are most likely to occur after the dissipation of the nebula, whose presence damps orbital eccentricities and whose absence allows them to increase.

These two mechanisms may aptly be called the Yin and Yang of system evolution, since they have opposing tendencies, yet often coincide in a single system. Where smooth interactions prevail (Yin), we can expect flat configurations; where violent disruptions are uppermost (Yang), we will see bumps and misalignment. The architecture of the Solar System preserves clear traces of the interplay of both mechanisms during the Earth’s gestation and subsequent evolution. In our system, as in most of the Kepler multiplanet systems, smooth flow trumped violent instability. The Solar System is as flat as a long-playing vinyl record.

still as a mill pond or choppy as a typhoon?

One of the earliest studies of Kepler architectures, by Jack Lissauer and colleagues (2011), suggested that the Kepler light curve data may contain at least three types of configurations: coplanar systems of multiple planets (generally two or three) of Neptune mass or less on short-period orbits (corresponding to the majority of Kepler systems with at least two planets); a much rarer group of extremely compact multiplanet systems (with Kepler-11 as the principal example); and “bumpy” systems of multiple planets with high mutual inclinations, such that only one planet per system is detectable. Notably, the authors caution that “Kepler observations alone cannot put a strong limit on the true multiplicity of planetary systems” (Lissauer et al. 2011).

A nearly simultaneous study by Tremaine & Dong (2012) offered similar caution regarding the possibility of constraining planetary multiplicity. However, the authors included planets discovered by radial velocity searches in their analyses, to conclude – contrary to Lissauer et al. 2012 – that the most planetary systems are flat like our Solar System, with typical orbital inclinations in the range of 0 to 5 degrees.

Pedro Figueira and colleagues (2012) also undertook a combined analysis of Kepler and radial velocity planets, the latter pertaining specifically to the HARPS survey. They limited their study to the orbital inclinations of planets with radii of at least 2 Rea (corresponding to an approximate lower bound of m sin i = 7-10 Mea), thereby excluding terrestrial (AKA telluric) planets, among which are rocky Super Earths. Nor did they address the multiplicity function of planetary systems. Like Tremaine & Dong, they found that the transit data were consistent with the radial velocity data, and that both methods typically identify planetary systems with very low mutual inclinations, closer to 1 degree than to 5 degrees. From these findings they conclude that “most planetary systems evolve quietly without strong angular momentum exchanges,” such as those produced by planet scattering or the Kozai mechanism.

Julia Fang & Jean-Luc Margot (2012) relied solely on Kepler data, but again reached similar results. They found that more than 85% of planets with periods of 200 days or less have inclinations smaller than 3 degrees relative to the common orbital plane – a situation that implies, as they note, “a high degree of coplanarity.” Unlike Tremaine & Dong and Figueira et al., they also provided an estimate of the multiplicity of systems with short- to medium-period planets, finding that about 80% of planetary systems have either one or two planets in this period range. However, they made no prediction about the overall percentage of stars with planetary systems. Their main conclusion about system evolution favors flat over bumpy ensembles: most systems evolve “without any strong perturbative force that could have caused a significant and lasting impact on inclinations” (Fang & Margot 2012).

mass matters

The study by Johansen and colleagues followed a different path from most of the others cited, with conclusions that seem most compatible with those of Lissauer et al. (2011). Johansen’s group limited their analyses to Kepler data and focused on finding the set of underlying system architectures that best reproduces the observed patterns of transits. Given the constraints of available data, their results apply only to planets with periods shorter than 240 days – similar to the sample surveyed by Fang & Margot.

Johansen’s group began by highlighting a fundamental dichotomy in the data: the divide between single-transit and multi-transit systems. Single-transit systems may contain either large planets (like Jupiter) or small planets (Earth to Uranus). Multi-transit systems, the vast majority of which contain two or three transiting objects, are typically limited to planets smaller than Uranus (4 Rea). Not observed are packed systems containing two or more short-period gas giants, even though many possible configurations of these objects could achieve orbital stability.

Two competing explanations for the dichotomy are explored:

  1. Both populations originated in the same architecture: packed systems of low-mass, short-period planets. After formation, many of these systems experienced episodes of greater or lesser dynamical instability, producing a range of outcomes. Two or more objects might collide to form a single massive planet; one or more objects might be lost through ejection or engulfment by the host star, leaving a single low-mass survivor; or if the instability were relatively weak, most or all planets might survive, but their orbits would be misaligned by mutual perturbations, such that only one can be observed in transit.

  2. Each population had a separate origin. In systems where no gas giants formed, or where giants were confined to wide orbits beyond the system ice line, one or more low-mass planets might achieve short-period orbits, either through in situ formation or through smooth migration through the primordial nebula. Depending on the number of planets and their mutual inclinations, these systems might be observed as singly or multiply transiting, with all planets of small radii. On the other hand, in systems where gas giants formed and found orbits small enough to perturb objects inside the system ice line, no low-mass planets could survive. In such systems, any giant that achieved an orbit shorter than 240 days might potentially appear in the transit data. 
Although the first explanation is sensible and attractive, Johansen’s group concluded that it cannot explain the observed reality. Packed systems of low-mass planets are remarkably stable; instability ensues only if the masses of the original planets are boosted substantially. Yet a mass-boost scenario, it turns out, produces too many systems with singly-transiting giant planets, and too few with singly-transiting dwarfs. It also produces too many systems with more than one short-period giant.

Johansen and colleagues therefore conclude that the two populations have two different origins. Systems with several small planets on short-period orbits will lack nearby gas giants, while systems with a single giant on a short-period orbit will typically lack nearby Super Earths.

It’s all a matter of mass. As they say, “The formation or migration of a massive gas giant in a system suppresses the formation of additional (small and large) planets” (Johansen et al. 2012). The giant chases away the pygmies, in somewhat the same way that a cat scares away the mice from your home.
Fur or fat? Scary either way.
Naturally we can find exceptions. Earlier this year, the flattest system yet discovered (even flatter than ours) was reported in the pages of Nature (Sanchis-Ojeda et al. 2012). This marvel is Kepler-30, which harbors three planets within a semimajor axis of 0.5 AU (tighter than the orbit of Venus). The innermost planet, Kepler-30b, has a radius of 3.7 Rea (just below Neptune’s) and a period of 29 days, while its outer companions, Kepler-30c and Kepler-30d, are much larger planets with periods of 60 and 143 days, respectively. Kepler-30c is evidently a gas giant, while Kepler-30d may be a highly inflated gas dwarf with a mass closer to Neptune’s than to Saturn’s. As the discovery team concludes, “the coplanarity of the planetary orbits suggests a quiescent history without disruptive dynamical interactions” (Sanchis-Ojeda et al. 2012). Potentially similar systems identified by the radial velocity method include GJ 876 and HIP 57274.

Nevertheless, considering the results of Steffen et al. alongside those of Johansen et al., it still seems safe to conclude that system architecture is largely a function of planet mass. And that’s a topic I want to explore in more detail very soon.


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