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| 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:
- 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.
- 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.
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.
 |
| 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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