Kepler Dichotomy Research Articles

Orbital architectures of Kepler multis from dynamical instabilities

ABSTRACT The high-multiplicity exoplanet systems are generally more tightly packed when compared to the solar system. Such compact multiplanet systems are often susceptible to dynamical instability. We investigate the impact of dynamical instability on the final orbital architectures of multiplanet systems using N-body simulations. Our models initially consist of six to ten planets placed randomly according to a power-law distribution of mutual Hill separations. We find that almost all of our model planetary systems go through at least one phase of dynamical instability, losing at least one planet. The orbital architecture, including the distributions of mutual Hill separations, planetary masses, orbital periods, and period ratios, of the transit-detectable model planetary systems closely resemble those of the multiplanet systems detected by Kepler. We find that without any formation-dependent input, a dynamically active past can naturally reproduce important observed trends including multiplicity-dependent eccentricity distribution, smaller eccentricities for larger planets, and intra-system uniformity. On the other hand, our transit-detectable planet populations lack the observed sub-population of eccentric single-transiting planets, pointing towards the ‘Kepler dichotomy’. These findings indicate that dynamical instabilities may have played a vital role in the final assembly of sub-Jovian planets.

Migration Traps as the Root Cause of the Kepler Dichotomy

It is often assumed that the “Kepler dichotomy”—the apparent excess of planetary systems with a single detected transiting planet in the Kepler catalog—reflects an intrinsic bimodality in the mutual inclinations of planetary orbits. After conducting 600 simulations of planet formation followed by simulated Kepler observations, we instead propose that the apparent dichotomy reflects a divergence in the amount of migration and the separation of planetary semimajor axes into distinct “clusters.” We find that our simulated high-mass systems migrate rapidly, bringing more planets into orbital periods of less than 200 days. The outer planets are often caught in a migration trap—a range of planet masses and locations in which a dominant corotation torque prevents inward migration—which splits the system into two clusters. If clusters are sufficiently separated, the inner cluster remains dynamically cold, leading to low mutual inclinations and a higher probability of detecting multiple transiting planets. Conversely, our simulated low-mass systems typically bring fewer planets within 200 days, forming a single cluster that quickly becomes dynamically unstable, leading to collisions and high mutual inclinations. We propose an alternative explanation for the apparent Kepler dichotomy in which migration traps during formation lead to fewer planets within the Kepler detection window, and where mutual inclinations play only a secondary role. If our scenario is correct, then Kepler’s Systems with Tightly packed Inner Planets are a sample of planets that escaped capture by corotation traps, and their sizes may be a valuable probe into the structure of protoplanetary disks.

Evidence for a Nondichotomous Solution to the Kepler Dichotomy: Mutual Inclinations of Kepler Planetary Systems from Transit Duration Variations

Abstract Early analyses of exoplanet statistics from the Kepler mission revealed that a model population of multiplanet systems with low mutual inclinations (∼1°–2°) adequately describes the multiple-transiting systems but underpredicts the number of single-transiting systems. This so-called “Kepler dichotomy” signals the existence of a subpopulation of multiplanet systems possessing larger mutual inclinations. However, the details of these inclinations remain uncertain. In this work, we derive constraints on the intrinsic mutual inclination distribution by statistically exploiting transit duration variations (TDVs) of the Kepler planet population. When planetary orbits are mutually inclined, planet–planet interactions cause orbital precession, which can lead to detectable long-term changes in transit durations. These TDV signals are inclination sensitive and have been detected for roughly two dozen Kepler planets. We compare the properties of the Kepler-observed TDV detections to TDV detections of simulated planetary systems constructed from two population models with differing assumptions about the mutual inclination distribution. We find strong evidence for a continuous distribution of relatively low mutual inclinations that is well characterized by a power-law relationship between the median mutual inclination ( μ ˜ i , n ) and the intrinsic multiplicity (n): μ ˜ i , n = μ ˜ i , 5 ( n / 5 ) α , where μ ˜ i , 5 = 1.10 − 0.11 + 0.15 and α = − 1.73 − 0.08 + 0.09 . These results suggest that late-stage planet assembly and possibly stellar oblateness are the dominant physical origins for the excitation of Kepler planet mutual inclinations.

The Impact of Stellar Clustering on the Observed Multiplicity and Orbital Periods of Planetary Systems

Abstract It has recently been shown that stellar clustering plays an important role in shaping the properties of planetary systems. We investigate how the multiplicity distributions and orbital periods of planetary systems depend on the 6D phase space density of stars surrounding planet host systems. We find that stars in high stellar phase space density environments (overdensities) have a factor of 1.6–2.0 excess in the number of single-planet systems compared to stars in low stellar phase space density environments (the field). The multiplicity distribution of planets around field stars is much flatter (i.e., there is a greater fraction of multiplanet systems) than in overdensities. This result is primarily driven by the combined facts that (i) “hot Jupiters” (HJs) are almost exclusively found in overdensities and (ii) HJs are predominantly observed to be single-planet systems. Nevertheless, we find that the difference in multiplicity is even more pronounced when only considering planets in the Kepler sample, which contains few HJs. This suggests that the Kepler dichotomy—an apparent excess of systems with a single transiting planet—plausibly arises from environmental perturbations. In overdensities, the orbital periods of single-planet systems are smaller than orbital periods of multiple-planet systems. As this difference is more pronounced in overdensities, the mechanism responsible for this effect may be enhanced by stellar clustering. Taken together, the pronounced dependence of planetary multiplicity and orbital period distributions on stellar clustering provides a potentially powerful tool to diagnose the impact of environment on the formation and evolution of planetary systems.

Architectures of exoplanetary systems – I. A clustered forward model for exoplanetary systems around Kepler’s FGK stars

ABSTRACTObservations of exoplanetary systems provide clues about the intrinsic distribution of planetary systems, their architectures, and how they formed. We develop a forward modelling framework for generating populations of planetary systems and ‘observed’ catalogues by simulating the Kepler detection pipeline (SysSim). We compare our simulated catalogues to the Kepler DR25 catalogue of planet candidates, updated to include revised stellar radii from Gaia DR2. We constrain our models based on the observed 1D marginal distributions of orbital periods, period ratios, transit depths, transit depth ratios, transit durations, transit duration ratios, and transit multiplicities. Models assuming planets with independent periods and sizes do not adequately account for the properties of the multiplanet systems. Instead, a clustered point process model for exoplanet periods and sizes provides a significantly better description of the Kepler population, particularly the observed multiplicity and period ratio distributions. We find that $0.56^{+0.18}_{-0.15}$ of FGK stars have at least one planet larger than 0.5R⊕ between 3 and 300 d. Most of these planetary systems ($\sim 98{{\ \rm per\ cent}}$) consist of one or two clusters with a median of three planets per cluster. We find that the Kepler dichotomy is evidence for a population of highly inclined planetary systems and is unlikely to be solely due to a population of intrinsically single planet systems. We provide a large ensemble of simulated physical and observed catalogues of planetary systems from our models, as well as publicly available code for generating similar catalogues given user-defined parameters.

Accounting for incompleteness due to transit multiplicity inKeplerplanet occurrence rates

We investigate the role that planet detection order plays in the Kepler planet detection pipeline. The Kepler pipeline typically detects planets in order of descending signal strength (MES). We find that the detectability of transits experiences an additional $5.5\%$ and $15.9\%$ efficiency loss, for periods $<200$ days and $>200$ days respectively, when detected after the strongest signal transit in a multiple-planet system. We provide a method for determining the transit probability for multiple-planet systems by marginalizing over the empirical Kepler dataset. Furthermore, because detection efficiency appears to be a function of detection order, we discuss the sorting statistics that affect the radius and period distributions of each detection order. Our occurrence rate dataset includes radius measurement updates from the California Kepler Survey (CKS), Gaia DR2, and asteroseismology. Our population model is consistent with the results of Burke et al. (2015), but now includes an improved estimate of the multiplicity distribution. From our obtained model parameters, we find that only $4.0\pm4.6\%$ of solar-like GK dwarfs harbor one planet. This excess is smaller than prior studies and can be well modeled with a modified Poisson distribution, suggesting that the Kepler Dichotomy can be accounted for by including the effects of multiplicity on detection efficiency. Using our modified Poisson model we expect the average number of planets is $5.86\pm0.18$ planets per GK dwarf within the radius and period parameter space of Kepler.

About 30% of Sun-like Stars Have Kepler-like Planetary Systems: A Study of Their Intrinsic Architecture

Abstract We constrain the intrinsic architecture of Kepler planetary systems by modeling the observed multiplicities of the transiting planets (tranets) and their transit timing variations (TTVs). We robustly determine that the fraction of Sun-like stars with Kepler-like planets, η Kepler, is 30 ± 3%. Here, Kepler-like planets are planets that have radii R p ≳ R ⊕ and orbital periods P &lt; 400 days. Our result thus significantly revises previous claims that more than 50% of Sun-like stars have such planets. Combined with the average number of Kepler planets per star (∼0.9), we obtain that on average each planetary system has 3.0 ± 0.3 planets within 400 days. We also find that the dispersion in orbital inclinations of planets within a given planetary system, σ i,k , is a steep function of its number of planets, k. This can be parameterized as and we find that −4 &lt; α &lt; −2 at the 2σ level. Such a distribution well describes the observed multiplicities of both transits and TTVs with no excess of single-tranet systems. Therefore we do not find evidence supporting the so-called “Kepler dichotomy.” Together with a previous study on orbital eccentricities, we now have a consistent picture: the fewer planets in a system, the hotter it is dynamically. We discuss briefly possible scenarios that lead to such a trend. Despite our solar system not belonging to the Kepler club, it is interesting to notice that the solar system also has three planets within 400 days and that the inclination dispersion is similar to Kepler systems of the same multiplicity.

The dynamical evolution of transiting planetary systems including a realistic collision prescription

Planet-planet collisions are a common outcome of instability in systems of transiting planets close to the star, as well as occurring during in-situ formation of such planets from embryos. Previous N-body studies of instability amongst transiting planets have assumed that collisions result in perfect merging. Here, we explore the effects of implementing a more realistic collision prescription on the outcomes of instability and in-situ formation at orbital radii of a few tenths of an au. There is a strong effect on the outcome of the growth of planetary embryos, so long as the debris thrown off in collisions is rapidly removed from the system (which happens by collisional processing to dust, and then removal by radiation forces) and embryos are small ($< 0.1\mathrm{\,M}_\oplus$). If this is the case, then systems form fewer detectable ($\gtrsim1\mathrm{\,M}_\oplus$) planets than systems evolved under the assumption of perfect merging in collisions. This provides some contribution to the "Kepler Dichotomy": the observed over-abundance of single-planet systems. The effects of changing the collision prescription on unstable mature systems of super-Earths are less pronounced. Perfect mergers only account for a minority of collision outcomes in such systems, but most collisions resulting in mass loss are grazing impacts in which only a few per cent. of mass is lost. As a result, there is little impact on the final masses and multiplicities of the systems after instability when compared to systems evolved under the assumption that collisions always result in perfect merging.

The Resilience of Kepler Systems to Stellar Obliquity

Abstract The Kepler mission and its successor K2 have brought forth a cascade of transiting planets. Many of these planetary systems exhibit multiple members, but a large fraction possess only a single transiting example. This overabundance of singles has led to the suggestion that up to half of Kepler systems might possess significant mutual inclinations between orbits, reducing the transiting number (the so-called “Kepler Dichotomy”). In a recent paper, Spalding &amp; Batygin demonstrated that the quadrupole moment arising from a young, oblate star is capable of misaligning the constituent orbits of a close-in planetary system enough to reduce their transit number, provided that the stellar spin axis is sufficiently misaligned with respect to the planetary orbital plane. Moreover, tightly packed planetary systems were shown to be susceptible to becoming destabilized during this process. Here, we investigate the ubiquity of the stellar obliquity-driven instability within systems with a range of multiplicities. We find that most planetary systems analyzed, including those possessing only two planets, underwent instability for stellar spin periods below ∼3 days and stellar tilts of order 30°. Moreover, we are able to place upper limits on the stellar obliquity in systems such as K2-38 (obliquity ≲20°), where other methods of measuring the spin–orbit misalignment are not currently available. Given the known parameters of T-Tauri stars, we predict that up to one-half of super-Earth-mass systems may encounter the instability, in general agreement with the fraction typically proposed to explain the observed abundance of single-transiting systems.

No Metallicity Correlation Associated with the Kepler Dichotomy

Abstract NASA’s Kepler mission has discovered thousands of planetary systems, ∼20% of which are found to host multiple transiting planets. This relative paucity (compared to the high fraction of single transiting systems) is postulated to result from a distinction in the architecture between multi-transiting systems and those hosting a single transiting planet: a phenomenon usually referred to as the Kepler dichotomy. In this paper, we investigate the hypothesis that external giant planets are the main cause behind the over-abundance of single- relative to multi-transiting systems, which would be signaled by higher metallicities in the former sample. To this end, we perform a statistical analysis on the stellar metallicity distribution with respect to planet multiplicity in the Kepler data. We perform our analysis on a variety of samples taken from a population of 1166 Kepler main-sequence planetary hosts, using precisely determined metallicities from the California-Kepler survey and Swift et al. Contrary to some predictions, we do not find a significant difference between the stellar metallicities of the single- and multiple-transiting planet systems. However, we do find a 55% upper bound for systems with a single non-giant planet that could also host a hidden giant planet, based on metallicity considerations. While the presence of external giant planets might be one factor behind the Kepler dichotomy, our results also favor alternative explanations. We suggest that additional radial velocity and direct imaging measurements are necessary to constrain the presence of gas giants in systems with a single transiting planet.

The signatures of the parental cluster on field planetary systems

Due to the high stellar densities in young clusters, planetary systems formed in these environments are likely to have experienced perturbations from encounters with other stars. We carry out direct $N$-body simulations of multi-planet systems in star clusters to study the combined effects of stellar encounters and internal planetary dynamics. These planetary systems eventually become part of the Galactic field population the parental cluster dissolves, which is where most presently-known exoplanets are observed. We show that perturbations induced by stellar encounters lead to distinct signatures in the field planetary systems, most prominently, the excited orbital inclinations and eccentricities. Planetary systems that form within the cluster's half-mass radius are more prone to such perturbations. The orbital elements are most strongly excited in the outermost orbit, but the effect propagates to the entire planetary system through secular evolution. Planet ejections may occur long after a stellar encounter. The surviving planets in these reduced systems tend to have, on average, higher inclinations and larger eccentricities compared to systems that were perturbed less strongly. As soon as the parental star cluster dissolves, external perturbations stop affecting the escaped planetary systems, and further evolution proceeds on a relaxation time scale. The outer regions of these ejected planetary systems tend to relax so slowly that their state carries the memory of their last strong encounter in the star cluster. Regardless of the stellar density, we observe a robust anticorrelation between multiplicity and mean inclination/eccentricity. We speculate that the "Kepler dichotomy" observed in field planetary systems is a natural consequence of their early evolution in the parental cluster.

Transit probabilities in secularly evolving planetary systems

This paper considers whether the population of known transiting exoplanets provides evidence for additional outer planets on inclined orbits, due to the perturbing effect of such planets on the orbits of inner planets. As such, we develop a semi-analytical method for calculating the probability that two mutually inclined planets are observed to transit. We subsequently derive a simplified analytical form to describe how the mutual inclination between two planets evolves due to secular interactions with a wide orbit inclined planet and use this to determine the mean probability that the two inner planets are observed to transit. From application to Kepler-48 and HD-106315, we constrain the inclinations of the outer planets in these systems (known from radial velocity). We also apply this work to the so-called Kepler Dichotomy, which describes the excess of single transiting systems observed by Kepler. We find three different ways of explaining this dichotomy: Some systems could be inherently single, some multiplanet systems could have inherently large mutual inclinations, while some multiplanet systems could cyclically attain large mutual inclinations through interaction with an inclined outer planet. We show how the different mechanisms can be combined to fit the observed populations of Kepler systems with one and two transiting planets. We also show how the distribution of mutual inclinations of transiting two-planet systems constrains the fraction of two-planet systems that have perturbing outer planets, since such systems should be preferentially discovered by Kepler when the inner planets are coplanar due to an increased transit probability.

Collisions of Terrestrial Worlds: The Occurrence of Extreme Mid-infrared Excesses around Low-mass Field Stars

Abstract We present the results of an investigation into the occurrence and properties (stellar age and mass trends) of low-mass field stars exhibiting extreme mid-infrared (MIR) excesses ( ). Stars for the analysis were initially selected from the Motion Verified Red Stars (MoVeRS) catalog of photometric stars with Sloan Digital Sky Survey, 2MASS, and WISE photometry and significant proper motions. We identify 584 stars exhibiting extreme MIR excesses, selected based on an empirical relationship for main-sequence colors. For a small subset of the sample, we show, using spectroscopic tracers of stellar age (Hα and Li i) and luminosity class, that the parent sample is most likely comprised of field dwarfs ( Gyr). We also develop the Low-mass Kinematics (LoKi) galactic model to estimate the completeness of the extreme MIR excess sample. Using Galactic height as a proxy for stellar age, the completeness-corrected analysis indicates a distinct age dependence for field stars exhibiting extreme MIR excesses. We also find a trend with stellar mass (using r − z color as a proxy). Our findings are consistent with the detected extreme MIR excesses originating from dust created in a short-lived collisional cascade (≲100,000 years) during a giant impact between two large planetismals or terrestrial planets. These stars with extreme MIR excesses also provide support for planetary collisions being the dominant mechanism in creating the observed Kepler dichotomy (the need for more than a single mode, typically two, to explain the variety of planetary system architectures Kepler has observed), rather than different formation mechanisms.

A flat inner disc model as an alternative to the Kepler dichotomy in the Q1–Q16 planet population

We use simulated planetary systems to model the planet multiplicity of Kepler stars. Previous studies have underproduced single planet systems and invoked the so called Kepler dichotomy, where the planet forming ability of a Kepler star is dichotomous, producing either few or many transiting planets. In this paper we show that the Kepler dichotomy is only required when the inner part of planetary disks are just assumed to be flared. When the inner part of planetary disks are flat, we reproduce the observed planet multiplicity of Kepler stars without the need to invoke a dichotomy. We find that independent of the disk model assumed, the mean number of planets per star is approximately 2 for orbital periods between 3 and 200 days, and for planetary radii between 1 and 5 Earth radii. This contrasts with the Solar System where no planets occupy the same parameter space.

HIDING PLANETS BEHIND A BIG FRIEND: MUTUAL INCLINATIONS OF MULTI-PLANET SYSTEMS WITH EXTERNAL COMPANIONS

ABSTRACT The Kepler mission has detected thousands of planetary systems with one to seven transiting planets packed within 0.7 au from their host stars. There is an apparent excess of single-transit planet systems that cannot be explained by transit geometries alone, when a single planetary mutual inclination dispersion is assumed. This suggests that the observed compact planetary systems have at least two different architectures. We present a scenario where the “Kepler dichotomy” may be explained by the action of an external giant planet or stellar companion misaligned with the inner multi-planet system. The external companion excites mutual inclinations of the inner planets, causing such systems to appear as “Kepler singles” in transit surveys. We derive approximate analytic expressions (in various limiting regimes), calibrated with numerical calculations, for the mutual inclination excitations for various planetary systems and perturber properties (mass m p , semimajor axis a p , and inclination ). In general, the excited mutual inclination increases with and , though secular resonances may lead to large mutual inclinations even for small . We discuss the implications of our results for understanding the dynamical history of transiting planet systems with known external perturbers.

THE KEPLER DICHOTOMY IN PLANETARY DISKS: LINKING KEPLER OBSERVABLES TO SIMULATIONS OF LATE-STAGE PLANET FORMATION

ABSTRACT NASA’s Kepler Mission uncovered a wealth of planetary systems, many with planets on short-period orbits. These short-period systems reside around 50% of Sun-like stars and are similarly prevalent around M dwarfs. Their formation and subsequent evolution is the subject of active debate. In this paper, we simulate late-stage, in situ planet formation across a grid of planetesimal disks with varying surface density profiles and total mass. We compare simulation results with observable characteristics of the Kepler sample. We identify mixture models with different primordial planetesimal disk properties that self-consistently recover the multiplicity, radius, period and period ratio, and duration ratio distributions of the Kepler planets. We draw three main conclusions. (1) We favor a “frozen-in” narrative for systems of short-period planets, in which they are stable over long timescales, as opposed to metastable. (2) The “Kepler dichotomy,” an observed phenomenon of the Kepler sample wherein the architectures of planetary systems appear to either vary significantly or have multiple modes, can naturally be explained by formation within planetesimal disks with varying surface density profiles. Finally, (3) we quantify the nature of the “Kepler dichotomy” for both GK stars and M dwarfs, and find that it varies with stellar type. While the mode of planet formation that accounts for high multiplicity systems occurs in 24% ± 7% of planetary systems orbiting GK stars, it occurs in 63% ± 16% of planetary systems orbiting M dwarfs.

SPIN–ORBIT MISALIGNMENT AS A DRIVER OF THE KEPLER DICHOTOMY

ABSTRACT During its five-year mission, the Kepler spacecraft has uncovered a diverse population of planetary systems with orbital configurations ranging from single-transiting planets to systems of multiple planets co-transiting the parent star. By comparing the relative occurrences of multiple to single-transiting systems, recent analyses have revealed a significant over-abundance of singles. Dubbed the “Kepler Dichotomy,” this feature has been interpreted as evidence for two separate populations of planetary systems: one where all orbits are confined to a single plane, and a second where the constituent planetary orbits possess significant mutual inclinations, allowing only a single member to be observed in transit at a given epoch. In this work, we demonstrate that stellar obliquity, excited within the disk-hosting stage, can explain this dichotomy. Young stars rotate rapidly, generating a significant quadrupole moment, which torques the planetary orbits, with inner planets influenced more strongly. Given nominal parameters, this torque is sufficiently strong to excite significant mutual inclinations between planets, enhancing the number of single-transiting planets, sometimes through a dynamical instability. Furthermore, as hot stars appear to possess systematically higher obliquities, we predict that single-transiting systems should be relatively more prevalent around more massive stars. We analyze the Kepler data and confirm this signal to be present.

THE KEPLER DICHOTOMY AMONG THE M DWARFS: HALF OF SYSTEMS CONTAIN FIVE OR MORE COPLANAR PLANETS

ABSTRACT We present a statistical analysis of the Kepler M dwarf planet hosts, with a particular focus on the fractional number of systems hosting multiple transiting planets. We manufacture synthetic planetary systems within a range of planet multiplicity and mutual inclination for comparison to the Kepler yield. Similarly to studies of Kepler exoplanetary systems around more massive stars, we report that the number of singly transiting planets found by Kepler is too high to be consistent with a single population of multi-planet systems, a finding that cannot be attributed to selection biases. To account for the excess singleton planetary systems we adopt a mixture model and find that 53 ± 10% of planetary systems are either single or contain multiple planets with large mutual inclinations. The other 47 ± 10% of systems contain 7.5 &minus; 1.5 &plus; 0.5 ?> planets with mutual inclinations of 2.°0 ± 1.°3. This mutual inclination range is consistent with studies of transit durations within multiply transiting systems. The mixture model is preferred 8:1 to a model with only one architecture. Thus, we find that the so-called “Kepler dichotomy” holds for planets orbiting M dwarfs as well as Sun-like stars.

An artificial Kepler dichotomy? Implications for the coplanarity of planetary systems

AbstractWe challenge the assumptions present in previous efforts to model the ensemble of detected Kepler systems, which require a dichotomous stellar population of ‘fertile’ and ‘sterile’ planet producing stars. We remove the assumption of Rayleigh distributed mutual inclinations between planets and show that the need for two distinct stellar populations disappears when the inner part of planetary disks are assumed to be flat, rather than flared.