THE STATISTICS OF MULTI-PLANET SYSTEMS

By S. Tremaine, S. Dong. 2011

135 citations recorded by the source corpus.

We describe statistical methods for measuring the exoplanet multiplicity function (the fraction of host stars containing a given number of planets) and inclination distribution from transit and radial-velocity (RV) surveys. The analysis is based on the approximation of separability—that the distribution of planetary parameters in an n-planet system is the product of identical 1-planet distributions. We review the evidence that separability is a valid approximation for exoplanets and conclude that it captures many, but not all, of the known characteristics of multi-planet systems. We show how to relate the observable multiplicity function in surveys with similar host-star populations but different sensitivities. We also show how to correct for geometrical selection effects to derive the multiplicity function from transit surveys if the distribution of relative inclinations is known. Applying these tools to the Kepler transit survey and to RV surveys, we find that (1) the Kepler data alone do not constrain the mean inclination of multi-planet systems; even spherical distributions are allowed by the data but only if a small fraction of host stars contain large planet populations (≳ 30); (2) comparing the Kepler and RV surveys shows that the mean inclination of multi-planet systems is less than 5°; and (3) the multiplicity function of the Kepler planets is not well determined by the present data.

Subfields: Astronomy and Astrophysics, Instrumentation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/451d592101fcb69c9407ca44caa75f48d5644ccb

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Citations in the corpus

The minimum-mass extrasolar nebula: in situ formation of close-in super-Earths (2012, background): “The super-Earth population is characterized by (i) orbital periods ranging from days to weeks, (ii) mass ratios M/M∗ ∼ 10−4.5, and (iii) orbits that are co-planar to within a few degrees (e.g., Fang & Margot 2012; Fabrycky et al. 2012; Tremaine & Dong 2012).”
The Occurrence and Architecture of Exoplanetary Systems (2014, background): “Figueira et al. (2012) performed such a study and concluded the compact systems of small planets ( <∼ 2 R⊕, <∼ 10 M⊕) have typical mutual inclinations smaller than a few degrees (see also Tremaine & Dong 2012).”
FRIENDS OF HOT JUPITERS. I. A RADIAL VELOCITY SEARCH FOR MASSIVE, LONG-PERIOD COMPANIONS TO CLOSE-IN GAS GIANT PLANETS (2013, background): “Tremaine & Dong (2012) perform a more detailed statistical analysis of the Kepler planet candidate sample and find a multiplicity rate ranging between 20%−50% depending on the distribution of mutual inclinations assumed in the calculation.”
Breaking the chains: hot super-Earth systems from migration and disruption of compact resonant chains (2017, methodology): “The orbital distribution of Kepler planets was derived in a series of statistical studies (Lissauer et al. 2011a; Figueira et al. 2012; Kane et al. 2012; Tremaine & Dong 2012; Fabrycky et al. 2014; Plavchan, Bilinski & Currie 2014; Van Eylen & Albrecht 2015; Ballard & Johnson 2016).”
TESTING IN SITU ASSEMBLY WITH THE KEPLER PLANET CANDIDATE SAMPLE (2013, methodology): “There is also a consistency of the observed ratios despite different sample selections by different authors (Lissauer et al. 2011b; Tremaine & Dong 2012; Fang & Margot 2012), suggesting that the comparison is also robust with respect to the particular observational cuts.”
Spacing of Kepler Planets: Sculpting by Dynamical Instability (2015, background): “Planets detected in these systems likely possess low mutual inclinations (e.g. Lissauer et al. 2011b; Tremaine & Dong 2012; Fang & Margot 2012; Fabrycky et al. 2014), and are spaced closely.”
About 30% of Sun-like Stars Have Kepler-like Planetary Systems: A Study of Their Intrinsic Architecture (2018, methodology): “Unlike Tremaine & Dong (2012) who used lmax = 50, we choose a much higher threshold, lmax = 3000, which is necessary in order to have the elements of G for flat and multi-planet systems (i.e., upper left corner of the left panel of Figure 10) converge.”
The Exoplanet Population Observation Simulator. I. The Inner Edges of Planetary Systems (2018, background): “The true multiplicity of planetary systems can only be constrained from the observed multiplicity and by making assumptions about their mutual inclination distribution (Tremaine & Dong 2012, see also Brakensiek & Ragozzine 2016).”
EXOPLANET POPULATION INFERENCE AND THE ABUNDANCE OF EARTH ANALOGS FROM NOISY, INCOMPLETE CATALOGS (2014, background): “…account: (1) making conservative cuts on the candidates and assuming that the resulting catalog is complete (Catanzarite & Shao 2011; Traub 2012; Tremaine & Dong 2012), (2) asserting an analytic form for the detection efficiency as a function of approximate signal-to-noise (Youdin 2011; Howard…”
HOW ROCKY ARE THEY? THE COMPOSITION DISTRIBUTION OF KEPLER’S SUB-NEPTUNE PLANET CANDIDATES WITHIN 0.15 AU (2014, background): “…transit surveys (Wolfgang & Laughlin 2012; Wright et al. 2012; Figueira et al. 2012), the Kepler eccentricity distribution (Moorhead et al. 2011; Kane et al. 2012; Wu & Lithwick 2013), and the frequency of multiple-planet systems (Lissauer et al. 2011; Tremaine & Dong 2012; Fabrycky et al. 2012).”
DENSITIES AND ECCENTRICITIES OF 139 KEPLER PLANETS FROM TRANSIT TIME VARIATIONS (2013, background): “The inclination dispersion is found to be very small– a few degrees (e.g., Lissauer et al. 2011a; Figueira et al. 2012; Tremaine & Dong 2012; Fang & Margot 2012; Johansen et al. 2012; Weissbein et al. 2012).”
DENSITY AND ECCENTRICITY OF KEPLER PLANETS (2012, background): “Relative inclinations in Kepler systems are inferred to be only a few degrees (e.g., Tremaine & Dong 2012; Fabrycky et al. 2012; Figueira et al. 2012).”
ARCHITECTURE OF PLANETARY SYSTEMS BASED ON KEPLER DATA: NUMBER OF PLANETS AND COPLANARITY (2012, methodology): “Similarly, other statistical studies have been performed to constrain multiplicity and/or inclinations using different methodologies or data sets (e.g., Lissauer et al. 2011b; Tremaine & Dong 2012; Figueira et al. 2012; Fabrycky et al. 2012; Weissbein et al. 2012; Johansen et al. 2012).”
The Habitability of Planets Orbiting M-dwarf Stars (2016, background): “For Kepler’s multi-planet systems, flat (mutual inclinations drawn from a Rayleigh distribution with σ < 3◦) and manifold models are apt descriptors (Lissauer et al., 2011; Tremaine & Dong, 2012; Fang & Margot, 2012; Fabrycky et al., 2014; Swift et al., 2013a).”
LOW FALSE POSITIVE RATE OF KEPLER CANDIDATES ESTIMATED FROM A COMBINATION OF SPITZER AND FOLLOW-UP OBSERVATIONS (2015, background): “This unprecedented sample of potential exoplanets has become an immense resource for statistical studies of the properties and distributions of planets around main-sequence stars (e.g.,Youdin 2011; Tremaine & Dong 2012; Wu & Lithwick 2013).”