Distribution Of Planets Research Articles

Hints for a Turnover at the Snow Line in the Giant Planet Occurrence Rate

Abstract The orbital distribution of giant planets is crucial for understanding how terrestrial planets form and predicting yields of exoplanet surveys. Here, we derive giant planets occurrence rates as a function of orbital period by taking into account the detection efficiency of the Kepler and radial velocity (RV) surveys. The giant planet occurrence rates for Kepler and RV show the same rising trend with increasing distance from the star. We identify a break in the RV giant planet distribution between ∼2 and 3 au—close to the location of the snow line in the solar system—after which the occurrence rate decreases with distance from the star. Extrapolating a broken power-law distribution to larger semimajor axes, we find good agreement with the ∼1% planet occurrence rates from direct imaging surveys. Assuming a symmetric power law, we also estimate that the occurrence of giant planets between 0.1 and 100 au is for planets with masses 0.1–20 M J and decreases to for planets more massive than Jupiter. This implies that only a fraction of the structures detected in disks around young stars can be attributed to giant planets. Various planet population synthesis models show good agreement with the observed distribution, and we show how a quantitative comparison between model and data can be used to constrain planet formation and migration mechanisms.

OGLE-2014-BLG-0962 and a Comparison of Galactic Model Priors to Microlensing Data

Abstract OGLE-2014-BLG-0962 (OB140962) is a stellar binary microlensing event that was well covered by observations from the Spitzer satellite as well as ground-based surveys. Modeling yields a unique physical solution: a mid-M+M-dwarf binary with M prim = 0.20 ± 0.01 M ☉ and M sec = 0.16 ± 0.01 M ☉, with projected separation of 2.0 ± 0.3 au. The lens is only D LS = 0.41 ± 0.06 kpc in front of the source, making OB140962 a bulge lens and the most distant Spitzer binary lens to date. In contrast, because the Einstein radius (θ E = 0.143 ± 0.007 mas) is unusually small, a standard Bayesian analysis, conducted in the absence of parallax information, would predict a brown dwarf binary. We compare the results of Bayesian analysis using two commonly used Galactic model priors to the measured values for a set of Spitzer lenses. We find all models tested predict lens properties consistent with the Spitzer data. Furthermore, we illustrate the methodology for probing the Galactic distribution of planets by comparing the cumulative distance distribution of the Spitzer two-body lenses to that of the Spitzer single lenses.

3D simulations of planet trapping at disc–cavity boundaries

Abstract Inward migration of low-mass planets and embryos of giant planets can be stopped at the disc–cavity boundaries due to co-orbital corotation torque. We performed the first global three-dimensional (3D) simulations of planet migration at the disc–cavity boundary, and have shown that the boundary is a robust trap for low-mass planets and embryos. A protoplanetary disc may have several such trapping regions at various distances from the star, such as at the edge of the stellar magnetosphere, the inner edge of the dead zone, the dust-sublimation radius and the snow lines. Corotation traps located at different distances from a star, and moving outward during the disc dispersal phase, may possibly explain the observed homogeneous distribution of low-mass planets with distance from their host stars.

Spitzer Microlensing Parallax for OGLE-2016-BLG-1067: A Sub-Jupiter Orbiting an M Dwarf in the Disk

Abstract We report the discovery of a sub-Jupiter-mass planet orbiting beyond the snow line of an M dwarf most likely in the Galactic disk as part of the joint Spitzer and ground-based monitoring of planetary microlensing anomalies toward the Galactic bulge. Most of the microlensing parameters are strongly constrained by the light-curve modeling, and in particular there is a Spitzer-based measurement of the microlens parallax, π E. However, there are no caustic crossings, so the angular Einstein radius has only an upper limit based on the light-curve modeling alone. Additionally, the analysis leads us to identify eight degenerate configurations: the fourfold microlensing parallax degeneracy being doubled by a degeneracy in the caustic structure present at the level of the ground-based solutions. To calculate the physical parameters, and at the same time to break the parallax degeneracy, we make use of a series of arguments: the χ 2 hierarchy, the Rich argument (stating that the small-parallax solution is more likely), and a prior Galactic model. The preferred configuration, favored by a likelihood ratio of at least 4000, is for a host at with mass , orbited by a Saturn-like planet with at projected separation , about 2.1 times beyond the system snow line. Therefore, it adds to the growing population of sub-Jupiter planets orbiting beyond the snow line of M dwarfs discovered by microlensing. Based on the rules of the real-time protocol for the selection of events to be followed up with Spitzer, this planet will not enter the sample for measuring the Galactic distribution of planets.

Predictions for the Detection and Characterization of Galactic Disk Microlensing Events by LSST

Abstract The upcoming Large Synoptic Survey Telescope (LSST) survey will provide an unprecedented opportunity for studying populations of intrinsically faint objects using microlensing. The LSST’s large field of view and aperture allow effective time-series observations of many stars in the Galactic disk and bulge. Here, we combine Galactic models (for ) and simulations of LSST observations to study how observing strategies affect the number and properties of microlensing events detected by LSST. Generally, detectable microlensing events are (a little) longer than events observable with current surveys. In Galactic bulge fields, LSST should detect on the order of 600 microlensing events per square degree as compared to 19 in disk fields. Improving the cadence from 6 to 2 days approximately doubles the number of detectable microlensing events throughout the Galaxy. We develop an Operations Simulator (OpSim)–based simulation to predict the characteristics of detectable microlensing events in different OpSim strategies and compare them. Based on baseline_2018a, minion_1016, and colossus_2664 OpSim simulations, LSST will observe with either 900 or 170 epochs in different observing times and cadences. With worse cadences LSST will detect longer microlensing events of brighter stars with lower blending. Although increasing the observing time from 1 to 10 yr with a fixed number of epochs does not change the total number of microlensing events significantly, the longer observing time lets one discern artificial effects and measure baseline fluxes, parallax, etc. If LSST spends enough time observing near the Galactic plane, then the large number of microlensing events will allow studies of the Galactic distribution of planets and searches for isolated black holes among a wealth of other scientific cases.

The imprint of X-ray photoevaporation of planet-forming discs on the orbital distribution of giant planets

High energy radiation from a planet host star can have strong influence on the final habitability of a system through several mechanisms. In this context we have constructed a catalogue containing the X-ray luminosities, as well as basic stellar and planetary properties of all known stars hosting giant planets (> 0.1 Mjup) that have been observed by the Chandra X-ray Observatory, XMM-Newton and/or ROSAT. Specifically in this paper we present a first application of this catalogue to search for a possible imprint of X-ray photoevaporation of planet-forming discs on the present-day orbital distribution of the observed giant planets. We found a suggestive void in the semi-major axis, a, versus X-ray luminosity, Lx, plane, roughly located between a ~ 0.05-1 au and Lx ~10^27-10^29 erg/s, which would be expected if photoevaporation played a dominant role in the migration history of these systems. However, due to the small observational sample size, the statistical significance of this feature cannot be proven at this point.

The Effects of Stellar Companions on the Observed Transiting Exoplanet Radius Distribution

Abstract Understanding the distribution and occurrence rate of small planets was a fundamental goal of the Kepler transiting exoplanet mission, and could be improved with K2 and Transiting Exoplanet Survey Satellite (TESS). Deriving accurate exoplanetary radii requires accurate measurements of the host star radii and the planetary transit depths, including accounting for any “third light” in the system due to nearby bound companions or background stars. High-resolution imaging of Kepler and K2 planet candidate hosts to detect very close (within ∼0.″5) background or bound stellar companions has been crucial for both confirming the planetary nature of candidates, and the determination of accurate planetary radii and mean densities. Here we present an investigation of the effect of close companions, both detected and undetected, on the observed (raw count) exoplanet radius distribution. We demonstrate that the recently detected “gap” in the observed radius distribution (also seen in the completeness-corrected distribution) is fairly robust to undetected stellar companions, given that all of the systems in the sample have undergone some kind of vetting with high-resolution imaging. However, while the gap in the observed sample is not erased or shifted, it is partially filled in after accounting for possible undetected stellar companions. These findings have implications for the most likely core composition, and thus formation location, of super-Earth and sub-Neptune planets. Furthermore, we show that without high-resolution imaging of planet candidate host stars, the shape of the observed exoplanet radius distribution will be incorrectly inferred, for both Kepler- and TESS-detected systems.

Long-Term Changes in Vertical Geomagnetic Cutoff Rigidities of Cosmic Rays

Vertical geomagnetic cutoff rigidities are obtained for the worldwide network of neutron monitors via trajectory calculations for the International Geomagnetic Reference Field (IGRF) for the period of 1950–2020. The results of the calculations indicate a general decrease in the geomagnetic cutoff rigidity at most points due to an overall decrease in the geomagnetic field during the period under consideration. The planetary distribution of the geomagnetic cutoff rigidity until the 2050s is forecast.

The LEECH Exoplanet Imaging Survey: Limits on Planet Occurrence Rates under Conservative Assumptions

Abstract We present the results of the largest L′ (3.8 μm) direct imaging survey for exoplanets to date, the Large Binocular Telescope Interferometer Exozodi Exoplanet Common Hunt (LEECH). We observed 98 stars with spectral types from B to M. Cool planets emit a larger share of their flux in L′ compared to shorter wavelengths, affording LEECH an advantage in detecting low-mass, old, and cold-start giant planets. We emphasize proximity over youth in our target selection, probing physical separations smaller than other direct imaging surveys. For FGK stars, LEECH outperforms many previous studies, placing tighter constraints on the hot-start planet occurrence frequency interior to ∼20 au. For less luminous, cold-start planets, LEECH provides the best constraints on giant-planet frequency interior to ∼20 au around FGK stars. Direct imaging survey results depend sensitively on both the choice of evolutionary model (e.g., hot- or cold-start) and assumptions (explicit or implicit) about the shape of the underlying planet distribution, in particular its radial extent. Artificially low limits on the planet occurrence frequency can be derived when the shape of the planet distribution is assumed to extend to very large separations, well beyond typical protoplanetary dust-disk radii (≲50 au), and when hot-start models are used exclusively. We place a conservative upper limit on the planet occurrence frequency using cold-start models and planetary population distributions that do not extend beyond typical protoplanetary dust-disk radii. We find that ≲90% of FGK systems can host a 7–10 M Jup planet from 5 to 50 au. This limit leaves open the possibility that planets in this range are common.

The California-Kepler Survey. VII. Precise Planet Radii Leveraging Gaia DR2 Reveal the Stellar Mass Dependence of the Planet Radius Gap

Abstract The distribution of planet sizes encodes details of planet formation and evolution. We present the most precise planet size distribution to date based on Gaia parallaxes, Kepler photometry, and spectroscopic temperatures from the California-Kepler Survey. Previously, we measured stellar radii to 11% precision using high-resolution spectroscopy; by adding Gaia astrometry, the errors are now 3%. Planet radius measurements are, in turn, improved to 5% precision. With a catalog of ∼1000 planets with precise properties, we probed in fine detail the gap in the planet size distribution that separates two classes of small planets, rocky super-Earths and gas-dominated sub-Neptunes. Our previous study and others suggested that the gap may be observationally under-resolved and inherently flat-bottomed, with a band of forbidden planet sizes. Analysis based on our new catalog refutes this; the gap is partially filled in. Two other important factors that sculpt the distribution are a planet’s orbital distance and its host-star mass, both of which are related to a planet’s X-ray/UV irradiation history. For lower-mass stars, the bimodal planet distribution shifts to smaller sizes, consistent with smaller stars producing smaller planet cores. Details of the size distribution including the extent of the “sub-Neptune desert” and the width and slope of the gap support the view that photoevaporation of low-density atmospheres is the dominant evolutionary determinant of the planet size distribution.

Single site observations of TESS single transit detections

Context. The Transiting Exoplanet Survey Satellite (TESS) has been successfully launched and has begin data acquisition. To expedite the science that may be performed with the resulting data it is necessary to gain a good understanding of planetary yields. Given the observing strategy employed by TESS the probability of detecting single transits in long period systems is increased. These systems require careful consideration. Aims. We aim to simulate the number of TESS transit detections during its two-year mission with a particular emphasis on single transits. We also aim to determine the feasibility of ground-based follow-up observations from a single site. Methods. A distribution of planets was simulated around the approximately four million stars in the TESS candidate target list. These planets were tested for detectable transits and characterised. Based on simulated parameters the single transit detections were further analysed to determine which are amenable to ground-based follow-up. Results. TESS will discover an approximate lower bound of 4700 planets with around 460 being single transits. A large fraction of these will be observable from a single ground-based site. This paper finds that, in a single year, approximately 1000 transit events of around 320 unique TESS single transit detections are theoretically observable. Conclusions. As we consider longer period exoplanets, the need for exploring single transit detections increases. For periods ≳45 days the number of single transit detections outnumber multitransits by a factor of three (82 ± 18 and 25 ± 7, respectively) a factor which only grows as longer period detections are considered. Therefore, based on this paper, it is worth expending the extra effort required to follow-up these more challenging, but potentially very rewarding, discoveries. Additionally, we conclude that a large fraction of these targets can be theoretically observed from a single ground-based site. However, further work is required to determine whether these follow-up efforts are feasible when accounting for target specific criteria.

The Hot Jupiter Period–Mass Distribution as a Signature of in situ Formation

Abstract More than two decades after the widespread detection of Jovian-class planets on short-period orbits around other stars, their dynamical origins remain imperfectly understood. In the traditional narrative, these highly irradiated giant planets, like Jupiter and Saturn, are envisioned to have formed at large stello-centric distances and to have subsequently undergone large-scale orbital decay. Conversely, more recent models propose that a large fraction of hot Jupiters could have formed via rapid gas accretion in their current orbital neighborhood. In this study, we examine the period–mass distribution of close-in giant planets, and demonstrate that the inner boundary of this population conforms to the expectations of the in situ formation scenario. Specifically, we show that if conglomeration unfolds close to the disk’s inner edge, the semimajor axis–mass relation of the emergent planets should follow a power law a ∝ M −2/7—a trend clearly reflected in the data. We further discuss corrections to this relationship due to tidal decay of planetary orbits. Although our findings do not discount orbital migration as an active physical process, they suggest that the characteristic range of orbital migration experienced by giant planets is limited.

Super-Earth of 8M⊕in a 2.2-day orbit around the K5V star K2-216

Context.Although thousands of exoplanets have been discovered to date, far fewer have been fully characterised, in particular super-Earths. The KESPRINT consortium identified K2-216 as a planetary candidate host star in the K2 space mission Campaign 8 field with a transiting super-Earth. The planet has recently been validated as well.Aims.Our aim was to confirm the detection and derive the main physical characteristics of K2-216 b, including the mass.Methods.We performed a series of follow-up observations: high-resolution imaging with the FastCam camera at the TCS and the Infrared Camera and Spectrograph at Subaru, and high-resolution spectroscopy with HARPS (La Silla), HARPS-N (TNG), and FIES (NOT). The stellar spectra were analyzed with theSpecMatch-EmpandSMEcodes to derive the fundamental stellar properties. We analyzed the K2 light curve with thepyanetisoftware. The radial velocity measurements were modelled with both a Gaussian process (GP) regression and the so-called floating chunk offset (FCO) technique to simultaneously model the planetary signal and correlated noise associated with stellar activity.Results.Imaging confirms that K2-216 is a single star. Our analysis discloses that the star is a moderately active K5V star of mass 0.70 ± 0.03M⊙and radius 0.72 ± 0.03R⊙. Planet b is found to have a radius of 1.75−0.10+0.17R⊕and a 2.17-day orbit in agreement with previous results. We find consistent results for the planet mass from both models:Mp≈ 7.4 ± 2.2M⊕from the GP regression andMp≈ 8.0 ± 1.6M⊕from the FCO technique, which implies that this planet is a super-Earth. The incident stellar flux is 2.48−48+220F⊕.Conclusions.The planet parameters put planet b in the middle of, or just below, the gap of the radius distribution of small planets. The density is consistent with a rocky composition of primarily iron and magnesium silicate. In agreement with theoretical predictions, we find that the planet is a remnant core, stripped of its atmosphere, and is one of the largest planets found that has lost its atmosphere.

Star-planet interactions

Context. When planets are formed from the protoplanetary disk and after the disk has dissipated, the evolution of their orbits is governed by tidal interactions, friction, and gravitational drag, and also by changes in the mass of the star and planet. These interactions may change the initial distribution of the distances between the planets and their host star by expanding the original orbit, by contracting it (which may cause an engulfment of the planet by the star), or by destroying the planet. Aims. We study the evolution of the orbit of a planet orbiting its host star under the effects of equilibrium tides, dynamical tides, drag (frictional and gravitational), and stellar mass loss. Methods. We used the Geneva stellar evolution code to compute the evolution of stars with initial masses of 1 and 1.5 M⊙ with different rotation rates at solar metallicity. The star is evolved from the pre-main-sequence (PMS) up to the tip of the red giant branch. We used these models as input for computing the evolution of the planetary orbits. We explored the effects of changing the planet masses (of 1 Earth mass up to 20 Jupiter masses), the distance between the planet and the star (of 0.015 and more than 3 au), the mass, and the spin of the star. We present results when only the equilibrium tide was accounted for and when both equilibrium and dynamical tides were accounted for. The expression for the dynamical tide is a frequency-averaged dissipation of tidally excited inertial waves, obtained from a piecewise homogeneous two-layer stellar model. Gravity wave damping was neglected. Results. Dynamical tides in convective zones have a significant effect on planetary orbits only during the PMS phase and only for fast-rotating stars. They have no significant effects during the PMS phase for initially slow-rotating stars and during the red giant branch phase, regardless of the initial rotation. In the plots of initial orbital distance versus planetary mass, we show the regions that lead to engulfment or any significant changes in the orbit. As a result of orbital evolution, a region near the star can become devoid of planets after the PMS phase. We call this zone the planet desert, and its extent depends sensitively on stellar rotation. An examination of the planet distribution as a function of distance to the host star and mass can provide constraints on current computations.

Planet Formation: An Optimized Population-synthesis Approach

Abstract The physics of planet formation is investigated using a population synthesis approach. We develop a simple model for planetary growth including pebble and gas accretion, as well as orbital migration in an evolving protoplanetary disk. The model is run for a population of 2000 stars with a range of disk masses, disk radii, and initial protoplanet orbits. The resulting planetary distribution is compared with the observed population of extrasolar planets, and the model parameters are improved iteratively using a particle swarm optimization scheme. The characteristics of the final planetary systems are mainly controlled by the pebble isolation mass, which is the mass of a planet that perturbs nearby gas enough to halt the inward flux of drifting pebbles and stop growth. The pebble isolation mass increases with orbital distance such that giant planet cores can only form in the outer disk. Giants migrate inward, populating a wide range of final orbital distances. The best model fits have large initial protoplanet masses, short pebble drift timescales, low disk viscosities, and short atmospheric cooling times, all of which promote rapid growth. The model successfully reproduces the observed frequency and distribution of giant planets and brown dwarfs. The fit for super-Earths is poorer for single-planet systems, but improves steadily when more protoplanets are included. Although the study was designed to match the extrasolar planet distribution, analogs of the solar system form in 1–2% of systems that contain at least four protoplanets.

Evaporation of Low-mass Planet Atmospheres: Multidimensional Hydrodynamics with Consistent Thermochemistry

Abstract Direct and statistical observational evidence suggests that photoevaporation is important in eroding the atmosphere of sub-Neptune planets. We construct full hydrodynamic simulations, coupled with consistent thermochemistry and ray-tracing radiative transfer, to understand the physics of atmospheric photoevaporation caused by high-energy photons from the host star. We identify a region on the parameter space where a hydrostatic atmosphere cannot be balanced by any plausible interplanetary pressure, so that the atmosphere is particularly susceptible to loss by Parker wind. This region may lead to an absence of rich atmosphere (substantially H/He) for planets with low mass (M ≲ 3 M ⊕). Full numerical simulations of photoevaporative outflows show a typical outflow speed ∼ 30 km s − 1 and M ˙ ∼ 4 × 10 − 10 M ⊕ yr − 1 for a 5 M ⊕ fiducial model rocky-core planet with 10−2 of its mass in the atmosphere. The outflows modulated by strong stellar wind (ram pressure up to 5 times the total wind pressure) are collimated toward the nightside of the planet, while the mass-loss rate is only ∼25% lower than the fiducial model. By exploring the parameter space, we find that EUV photoionization is most important in launching photoevaporative wind; other energetic radiations have secondary importance. Based on simulation results we propose a semiempirical formula of photoevaporation rate (error ≲ 20%), which is a function of high-energy irradiation, planet mass, and envelope mass fraction (error ≲20%). We then reproduce the observed bimodal radius distribution of sub-Neptune Kepler planets semiquantitatively.

Host Star Dependence of Small Planet Mass–Radius Distributions

Abstract The planet formation environment around M dwarf stars is different than around G dwarf stars. The longer hot protostellar phase, activity levels and lower protoplanetary disk mass of M dwarfs all may leave imprints on the composition distribution of planets. We use hierarchical Bayesian modeling conditioned on the sample of transiting planets with radial velocity mass measurements to explore small planet mass–radius distributions that depend on host star mass. We find that the current mass–radius data set is consistent with no host star mass dependence. These models are then applied to the Kepler planet radius distribution to calculate the mass distribution of close-orbiting planets and how it varies with host star mass. We find that the average heavy element mass per star at short orbits is higher for M dwarfs compared to FGK dwarfs, in agreement with previous studies. This work will facilitate comparisons between microlensing planet surveys and Kepler, and will provide an analysis framework that can readily be updated as more M dwarf planets are discovered by ongoing and future surveys such as K2 and the Transiting Exoplanet Survey Satellite.

Stability and self-organization of planetary systems.

We show that stability of planetary systems is intimately connected with their internal order. An arbitrary initial distribution of planets is susceptible to catastrophic events in which planets either collide or are ejected from the planetary system. These instabilities are a fundamental consequence of chaotic dynamics and of Arnold diffusion characteristic of many body gravitational interactions. To ensure stability over astronomical time scale of a realistic planetary system-in which planets have masses comparable to those of planets in the solar system-the motion must be quasiperiodic. A dynamical mechanism is proposed which naturally evolves a planetary system to a quasiperiodic state from an arbitrary initial condition. A planetary self-organization predicted by the theory is similar to the one found in our solar system.

M-dwarf exoplanet surface density distribution

Aims. We fit a log-normal function to the M-dwarf orbital surface density distribution of gas giant planets, over the mass range 1–10 times that of Jupiter, from 0.07 to 400 AU. Methods. We used a Markov chain Monte Carlo approach to explore the likelihoods of various parameter values consistent with point estimates of the data given our assumed functional form. Results. This fit is consistent with radial velocity, microlensing, and direct-imaging observations, is well-motivated from theoretical and phenomenological points of view, and predicts results of future surveys. We present probability distributions for each parameter and a maximum likelihood estimate solution. Conclusions. We suggest that this function makes more physical sense than other widely used functions, and we explore the implications of our results on the design of future exoplanet surveys.

Photoevaporation Does Not Create a Pileup of Giant Planets at 1 au

Abstract The semimajor axis distribution of giant exoplanets appears to have a pileup near 1 au. Photoevaporation opens a gap in the inner few au of gaseous disks before dissipating them. Here, we investigate if photoevaporation can significantly affect the final distribution of giant planets by modifying gas surface density and hence Type II migration rates near the photoevaporation gap. We first use an analytic disk model to demonstrate that newly formed giant planets have a long migration epoch before photoevaporation can significantly alter their migration rates. Next, we present new 2D hydrodynamic simulations of planets migrating in photoevaporating disks, in which each are paired with a control simulation of migration in an otherwise identical disk without photoevaporation. We show that in disks with surface densities near the minimum threshold for forming giant planets, photoevaporation alters the final semimajor axis of a migrating gas giant by at most 5% over the course of 0.1 Myr of migration. Once the disk mass has become low enough for photoevaporation to carve a sharp gap, migration has almost completely stalled due to the low surface density of gas at the Lindblad resonances. We find that photoevaporation modifies migration rates so little that it is unlikely to leave a significant signature on the distribution of giant exoplanets.