The Kepler mission observed thousands of transiting exoplanet candidates around hundreds of thousands of FGK dwarf stars. He, Ford, & Ragozzine (2019) (arXiv:1907.07773) applied forward modeling to infer the distribution of intrinsic architectures of planetary systems, developed a clustered Poisson point process model for exoplanetary systems (SysSim) to reproduce the marginal distributions of the observed Kepler population, and they showed that orbital periods and planet radii are clustered within a given planetary system. Here, we extend the clustered model to explore correlations between planetary systems and their host star properties. We split the sample of Kepler FGK dwarfs into two halves and model the fraction of stars with planets (between 0.5-10 $R_\oplus$ and 3--300 days), $f_{\rm swpa}$, as a linear function of the Gaia DR2 color. We confirm previous findings that the occurrence of these planetary systems rises significantly toward later type (redder) stars. The fraction of stars with planets increases from $f_{\rm swpa} = 0.32_{-0.11}^{+0.12}$ for F2V dwarfs to $f_{\rm swpa} = 0.96_{-0.19}^{+0.04}$ for mid K-dwarfs. About half ($f_{\rm swpa} = 0.57_{-0.10}^{+0.14}$) of all solar-type (G2V) dwarfs harbor a planetary system between 3 and 300 days. This simple model can closely match the observed multiplicity distributions of both the bluer and redder halves in our sample, suggesting that the architectures of planetary systems around stars of different spectral types may be similar aside from a shift in the overall fraction of planet hosting stars.
Observations 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 model based on the observed 1D marginal distributions of orbital periods, period ratios, transit depths, transit depth rati…
Using our K2 Campaign 5 fully automated planet detection data set (43 planets), which has corresponding measures of completeness and reliability, we infer an underlying planet population model for the FGK dwarfs sample (9,257 stars). Implementing a broken power-law for both the period and radius distribution, we find an overall planet occurrence of $1.00^{+1.07}_{-0.51}$ planets per star within a period range of 0.5-38 days. Making similar cuts and running a comparable analysis on the Kepler sample (2,318 planets; 94,222 stars), we find an overall occurrence of $1.10\pm0.05$ planets per star. …
We present exoplanet occurrence rates estimated with approximate Bayesian computation for planets with radii between 0.5 and 16 $R_{\bigoplus}$ and orbital periods between 0.78 and 400 days, orbiting FGK dwarf stars. We base our results on an independent planet catalogue compiled from our search of all ~200,000 stars observed over the Kepler mission, with precise planetary radii supplemented by Gaia DR2-incorporated stellar radii. We take into account detection and vetting efficiency, planet radius uncertainty, and reliability against transit-like noise signals in the data. By analyzing our FG…
The presence of mean-motion resonances (MMRs) in exoplanetary systems is a new exciting field of celestial mechanics which motivates us to consider this work to study the dynamical behaviour of exoplanetary systems by time evolution of the orbital elements of the planets. Mainly, we study the influence of planetary perturbations on semimajor axis and eccentricity. We identify $(r+1):r$ MMR terms in the expression of disturbing function and obtain the perturbations from the truncated disturbing function. Using the expansion of the disturbing function of three-body problem and an analytical appr…
$\bf{Context}$. We investigate the validity of the claim that invokes two extreme exoplanetary system candidates around the pulsating B-type subdwarfs KIC 10001893 and KIC 5807616 from the primary $\it{Kepler}$ field. $\bf{Aims}$. Our goal was to find characteristics and the source of weak signals that are observed in these subdwarf light curves. $\bf{Methods}$. To achieve this, we analyzed short- and long-cadence $\it{Kepler}$ data of the two stars by means of a Fourier transform and compared the results to Fourier transforms of simulated light curves to which we added exoplanetary signals. T…
We characterize the occurrence rate of planets, ranging in size from 0.5-16 R$_\oplus$, orbiting FGK stars with orbital periods from 0.5-500 days. Our analysis is based on results from the "DR25" catalog of planet candidates produced by NASA's Kepler mission and stellar radii from Gaia "DR2". We incorporate additional Kepler data products to accurately characterize the efficiency of planets being recognized as a "threshold crossing events" (TCE) by Kepler's Transiting Planet Search pipeline and labeled as a planet candidate by the robovetter. Using a hierarchical Bayesian model, we derive plan…
Exoplanet Orbital Distribution around FGK Sun-like Host Stars I: planet occurrence rate derived from the Kepler Mission and theoretical interpretations from planet formation
University of Oslo（奥斯陆大学）；Harvard University（哈佛大学）；Natural History Museum, University of Oslo（奥斯陆大学自然历史博物馆）；Konkoly Observatory, HUN-REN CSFK（孔科利天文台，匈牙利研究网络科学院）
In favourable conditions, the density of transiting planets in multiple systems can be determined from photometry data alone. Dynamical information can be extracted from light curves, providing modelling is done self-consistently, i.e. using a photodynamical model, which simulates the individual photometric observations instead of the more generally used transit times. We apply this methodology to the Kepler-138 planetary system. The derived planetary bulk densities are a factor of 2 more precise than previous determinations, and we find a discrepancy in the stellar bulk density with respect t…
The measurement of an exoplanet's oblateness and obliquity provides insights into the planet's internal structure and formation history. Previous work using small differences in the shape of the transit light curve has been moderately successful, but was hampered by the small signal and extreme photometric precision required. The measurement of changes in transit depth, caused by the spin precession of an oblate planet, was proposed as an alternative method. Here, we present the first attempt to measure these changes. Using Kepler photometry, we examined the brown dwarf Kepler-39b and the warm…
Architectures of Exoplanetary Systems. IV: A Multi-planet Model for Reproducing the Radius Valley and Intra-system Size Similarity of Planets around Kepler's FGK Dwarfs
The angle between the spin axis of the host star and the orbit of its planets (i.e., the stellar obliquity) is precious information about the formation and evolution of exoplanetary systems. Measurements of the Rossiter-McLaughlin effect revealed that many stars that host a hot-Jupiter have high obliquities, suggesting that hot-Jupiter formation involves excitation of orbital inclinations. In this contribution we show how the passage of the planet over starspots can be used to measure the obliquity of exoplanetary systems. This technique is used to obtain - for the first time - the obliquity o…
The true multiplicity distribution of transiting planet systems is obscured by strong observational biases, leading low-multiplicity systems to be overrepresented in the observed sample. Using the Kepler FGK planet hosts, we employ approximate Bayesian computation to infer the multiplicity distribution by comparing simulated catalogs to the observed one. After comparing a total of ten different multiplicity distributions, half of which were two-population models, to the observed data, we find that a single-population model following a Zipfian distribution is able to explain the Kepler data as …
We propose several descriptive measures to characterize the arrangements of planetary masses, periods, and mutual inclinations within exoplanetary systems. These measures are based in complexity theory and capture the global, system-level trends of each architecture. Our approach considers all planets in a system simultaneously, facilitating both intra-system and inter-system analysis. We find that based on these measures, Kepler's high-multiplicity ($N\geq3$) systems can be explained if most systems belong to a single intrinsic population, with a subset of high-multiplicity systems ($\sim20\%…
We study the effect of dynamical tides associated with the excitation of gravity waves in an interior radiative region of the central star on orbital evolution in observed systems containing Hot Jupiters. We consider WASP-43, Ogle-tr-113, WASP-12, and WASP-18 which contain stars on the main sequence (MS). For these systems there are observational estimates regarding the rate of change of the orbital period. We also investigate Kepler-91 which contains an evolved giant star. We adopt the formalism of Ivanov et al. for calculating the orbital evolution. For the MS stars we determine expected rat…
The field of exoplanetary science has experienced a recent surge of new systems that is largely due to the precision photometry provided by the Kepler mission. The latest discoveries have included compact planetary systems in which the orbits of the planets all lie relatively close to the host star, which presents interesting challenges in terms of formation and dynamical evolution. The compact exoplanetary systems are analogous to the moons orbiting the giant planets in our Solar System, in terms of their relative sizes and semi-major axes. We present a study that quantifies the scaled sizes …
This paper aims to derive a map of relative planet occurrence rates that can provide constraints on the overall distribution of terrestrial planets around FGK stars. Based on the planet candidates in the Kepler DR25 data release, I first generate a continuous density map of planet distribution using a Gaussian kernel model and correct the geometric factor that the discovery space of a transit event decreases along with the increase of planetary orbital distance. Then I fit two exponential decay functions of detection efficiency along with the increase of planetary orbital distance and the decr…
In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant configuration of the planets that exhibit a chain of mean-motion commensurabilities with the ratios 5:4:3. In the dynamical maps provided, the Shannon entropy is utilized to explore the general structure of the phase space, while, based on the time evolution of the entropy, we determine also the extent and rate of the chaotic diffusion as well as the characteristi…
Current spectroscopic surveys are producing large catalogs of chemical abundances for stars of all types. The yttrium to magnesium ratio, [Y/Mg], has emerged as a candidate age indicator for solar twins in the local stellar neighborhood. However, it is unclear whether it is a viable age diagnostic for more diverse stellar types, so we investigate [Y/Mg] as an age indicator for the FGK-type planet host stars observed by $Kepler$. We find that the [Y/Mg] "Clock" is most precise for solar twins, with a [Y/Mg]/Age slope of $m$ = $-$0.0370 $\pm$ 0.0071 dex/Gyr and $σ_{\mathrm{Age}}$ = 2.6 Gyr. We a…
New insights on stellar evolution and stellar interior physics are being made possible by asteroseismology, the study of stars by the observation of their natural, resonant oscillations. Asteroseismology is making significant contributions to our understanding of solar-type stars, in great part due to the exquisite data that have been made available by NASA's Kepler space telescope. Of particular interest is the synergy between asteroseismology and exoplanetary science. Herein I will review recent contributions from asteroseismology to the determination of fundamental properties of Kepler exop…
We investigate the origins of Kepler-419, a peculiar system hosting two nearly coplanar and highly eccentric gas giants with apsidal orientations librating around anti-alignment, and use this system to place constraints on the properties of their birth protoplanetary disk. We follow the proposal by Petrovich, Wu, & Ali-Dib (2019) that these planets have been placed on these orbits as a natural result of the precessional effects of a dissipating massive disk and extend it by using direct N-body simulations and models for the evolution of the gas disks, including photoevaporation. Based on a par…
Data from Kepler's first 136 days of operation are analyzed to determine the distribution of exoplanets with respect to radius, period, and host-star spectral type. The analysis is extrapolated to estimate the percentage of terrestrial, habitable-zone exoplanets. The Kepler census is assumed to be complete for bright stars (magnitude <14.0) having transiting planets >0.5 Earth radius and periods <42 days. It is also assumed that the size distribution of planets is independent of orbital period, and that there are no hidden biases in the data. Six significant statistical results are found: ther…
Precise exoplanet characterization requires precise classification of exoplanet host stars. The masses of host stars are commonly estimated by comparing their spectra to those predicted by stellar evolution models. However, spectroscopically determined properties are difficult to measure accurately for stars that are substantially different from the Sun, such as M-dwarfs and evolved stars. Here, we propose a new method to dynamically measure the masses of transiting planets near mean-motion resonances and their host stars by combining observations of transit timing variations with radial veloc…
The NASA Kepler mission has revolutionised time-domain astronomy and has massively expanded the number of known extrasolar planets. However, the effect of wide multiplicity on exoplanet occurrence has not been tested with this dataset. We present a sample of 401 wide multiple systems containing at least one Kepler target star. Our method uses Pan-STARRS1 and archival data to produce an accurate proper motion catalogue of the Kepler field. Combined with Pan-STARRS1 SED fits and archival proper motions for bright stars, we use a newly developed probabilistic algorithm to identify likely wide bin…
We examine how the fraction $f$ of stars for which rotational modulation has been detected in Kepler light curves depends on the stellar mass $M_\star$ and age $t_\star$. Our sample consists of $\approx 850$ FGK stars hosting transiting planet candidates detected from the prime Kepler mission. For these stars, atmospheric parameters have been derived using high-resolution spectra from the California-Kepler survey, and rotational modulation has been searched in Kepler light curves homogeneously. We fit stellar models to the atmospheric parameters, Gaia parallax, and 2MASS magnitude of these sta…
We confirm and characterize the exoplanetary systems Kepler-445 and Kepler-446: two mid-M dwarf stars, each with multiple, small, short-period transiting planets. Kepler-445 is a metal-rich ([Fe/H]=+0.25 $\pm$ 0.10) M4 dwarf with three transiting planets, and Kepler-446 is a metal-poor ([Fe/H]=-0.30 $\pm$ 0.10) M4 dwarf also with three transiting planets. Kepler-445c is similar to GJ 1214b: both in planetary radius and the properties of the host star. The Kepler-446 system is similar to the Kepler-42 system: both are metal-poor with large galactic space velocities and three short-period, likel…
Transmission spectra probe exoplanetary atmospheres, but they can also be strongly affected by heterogeneities in host star photospheres through the transit light source effect. Here we build upon our recent study of the effects of unocculted spots and faculae on M-dwarf transmission spectra, extending the analysis to FGK dwarfs. Using a suite of rotating model photospheres, we explore spot and facula covering fractions for varying activity levels and the associated stellar contamination spectra. Relative to M dwarfs, we find that the typical variabilities of FGK dwarfs imply lower spot coveri…
In the so-called "global polytropic model", we assume planetary systems in hydrostatic equilibrium and solve the Lane--Emden equation in the complex plane. We thus find polytropic spherical shells providing hosting orbits to planets. On the basis of this model, we develop a numerical method which has three versions. In its three-dimensional version, the method is effective for systems with substantial uncertainties in the observed host star radius, and in the orbit of a particular planet (compared to the uncertainties in the orbits of the other planets); the method uses as fixed entry values t…
JWST Exoplanetary Worlds and Elemental Survey (JEWELS) II: Condensation Temperature Trends and Galactic Chemical Evolution in JWST Planet-Hosting Stars
Tsung-Dao Lee Institute, School of Physics and Astronomy, & State Key Laboratory of Dark Matter Physics, Shanghai Jiao Tong University（上海交通大学物理与天文学院、汤川研究所、暗物质物理国家重点实验室）；Department of Physics, King’s College London（伦敦国王学院物理系）；Department of Astronomy, Tsinghua University（清华大学天文系）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
Aims. With the purpose of determining the orbital parameters of exoplanetary systems from observational data, we have developed a software, named TRADES (TRAnsits and Dynamics of Exoplanetary Systems), to simultaneously fit observed radial velocities and transit times data. Methods. We implemented a dynamical simulator for N-body systems, which also fits the available data during the orbital integration and determines the best combination of the orbital parameters using grid search, $χ^2$ minimization, genetic algorithms, particle swarm optimization, and bootstrap analysis. Results. To validat…
The lithium doublet at 6708 Å provides an age diagnostic for main sequence FGK dwarfs. We measured the abundance of lithium in 1305 stars with detected transiting planets from the Kepler Mission using high-resolution spectroscopy. Our catalog of lithium measurements from this sample have a range of abundance from A(Li) = 3.11 $\pm$ 0.07 to an upper limit of $-$0.84 dex. For a magnitude-limited sample that comprises 960 of the 1305 stars, our Keck-HIRES spectra have a median S/N = 45 per pixel at $\sim$6700 Å with spectral resolution $\fracλ{Δλ}$ = $R$ = 55,000. We identify 80 young stars that …
Knowledge of an exoplanet's oblateness and obliquity would give clues about its formation and internal structure. In principle, a light curve of a transiting planet bears information about the planet's shape, but previous work has shown that the oblateness-induced signal will be extremely difficult to detect. Here we investigate the potentially larger signals due to planetary spin precession. The most readily detectable effects are transit depth variations (T$δ$V) in a sequence of light curves. For a planet as oblate as Jupiter or Saturn, the transit depth will undergo fractional variations of…
We present a statistical study of the planet-metallicity (P-M) correlation, by comparing the 744 stars with candidate planets (SWPs) in the Kepler field which have been observed with LAMOST, and a sample of distance-independent, fake "twin" stars in the Kepler field with no planet reported (CKSNPs) yet. With the well-defined and carefully-selected large samples, we find for the first time a turn-off P-M correlation of Delta [Fe/H]_(SWPs-SNPs), which in average increases from ~0.00+-0.03 dex to 0.06+-0.03 dex, and to 0.12+-0.03 for stars with Earth, Neptune, Jupiter-sized planets successively, …
A search for extrasolar planetary transits using the extended Kepler mission (K2) campaigns 9 and 11 revealed five new candidates towards the Galactic bulge. The stars EPIC 224439122, 224560837, 227560005, 230778501 and 231635524 are found to have low amplitude transits consistent with extrasolar planets, with periods P = 35.1695, 3.6390, 12.4224, 17.9856, and 5.8824 days, respectively. The K2 data and existing optical photometry are combined with the multi-band near-IR photometry of the VVV survey and 2MASS in order to measure accurate physical parameters for the host stars. We then measure t…
We present robust planet occurrence rates for Kepler planet candidates around M stars for planet radii $R_p = 0.5-4~\textrm{R}_\oplus$ and orbital periods $P = 0.5-256$ days using the approximate Bayesian computation (ABC) technique. This work incorporates the final Kepler DR25 planet candidate catalog and data products and augments them with updated stellar properties using Gaia DR2 and 2MASS PSC. We apply a set of selection criteria to select a sample of 1,746 Kepler M dwarf targets that host 89 associated planet candidates. These early M dwarfs and late K dwarfs were selected from cross-ref…
Our knowledge of planets' orbital dynamics, which was based on Solar System studies, has been challenged by the diversity of exoplanetary systems. Around cool and ultra cool dwarfs, the influence of tides on the orbital and spin evolution of planets can strongly affect their climate and their capacity to host surface liquid water. We illustrate the role of tides and dynamics with the extreme case of planets orbiting around brown dwarfs. In multiple planet systems, the eccentricity is excited by planet-planet interactions. Planets are therefore heated up from the inside by the tidally-induced f…
Inaccurate limb-darkening models can be a significant source of error in the analysis of the light curves for transiting exoplanet and eclipsing binary star systems. To test the accuracy of published limb-darkening models, I have compared limb-darkening profiles predicted by stellar atmosphere models to the limb-darkening profiles measured from high-quality light curves of 43 FGK-type stars in transiting exoplanet systems observed by the Kepler and TESS missions. The comparison is done using the parameters $h^{\prime}_1 = I_λ(\frac{2}{3})$ and $h^{\prime}_2 = h^{\prime}_1 - I_λ(\frac{1}{3})$, …
The angular momentum deficit (AMD) of a planetary system is a measure of its orbital excitation and a predictor of long-term stability. We adopt the AMD-stability criteria to constrain the orbital architectures for exoplanetary systems. Previously, He, Ford, & Ragozzine (2019) (arXiv:1907.07773v2) showed through forward modelling (SysSim) that the observed multiplicity distribution can be well reproduced by two populations consisting of a low and a high mutual inclination component. Here, we show that a broad distribution of mutual inclinations arising from systems at the AMD-stability limit c…
Trojans are small bodies in planetary Lagrangian points. In our solar system, Jupiter has the largest number of such companions. Their existence is assumed for exoplanetary systems as well, but none has been found so far. We present an analysis by super-stacking $\sim4\times10^4$ Kepler planets with a total of $\sim9\times10^5$ transits, searching for an average trojan transit dip. Our result gives an upper limit to the average Trojan transiting area (per planet) corresponding to one body of radius $<460$km at $2σ$ confidence. We find a significant Trojan-like signal in a sub-sample for planet…
The fields of astronomy and astrophysics are currently engaged in an unprecedented era of discovery as recent missions have revealed thousands of exoplanets orbiting other stars. While the Kepler Space Telescope mission has enabled most of these exoplanets to be detected by identifying transiting events, exoplanets often exhibit additional photometric effects that can be used to improve the characterization of exoplanets. The EXONEST Exoplanetary Explorer is a Bayesian exoplanet inference engine based on nested sampling and originally designed to analyze archived Kepler Space Telescope and CoR…
An important property of exoplanetary systems is the extent of the Habitable Zone (HZ), defined as that region where water can exist in a liquid state on the surface of a planet with sufficient atmospheric pressure. Both ground and space-based observations have revealed a plethora of confirmed exoplanets and exoplanetary candidates, most notably from the Kepler mission using the transit detection technique. Many of these detected planets lie within the predicted HZ of their host star. However, as is the case with the derived properties of the planets themselves, the HZ boundaries depend on how…
The Kepler mission has discovered a plethora of multiple transiting planet candidate exosystems, many of which feature putative pairs of planets near mean motion resonance commensurabilities. Identifying potentially resonant systems could help guide future observations and enhance our understanding of planetary formation scenarios. We develop and apply an algebraic method to determine which Kepler 2-planet systems cannot be in a 1st-4th order resonance, given the current, publicly available data. This method identifies when any potentially resonant angle of a system must circulate. We identify…
NASA's Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called CORBITS which, given a collection of conjectured exoplanets orbiting a star…
We present new radial velocities from Keck Observatory and both Newtonian and Keplerian solutions for the triple-planet system orbiting HD 37124. The orbital solution for this system has improved dramatically since the third planet was first reported in Vogt et al. 2005 with an ambiguous orbital period. We have resolved this ambiguity, and the outer two planets have an apparent period commensurability of 2:1. A dynamical analysis finds both resonant and non-resonant configurations consistent with the radial velocity data, and constrains the mutual inclinations of the planets to be less than ab…
The population of exoplanetary systems detected by Kepler provides opportunities to refine our understanding of planet formation. Unraveling the conditions needed to produce the observed exoplanets will sallow us to make informed predictions as to where habitable worlds exist within the galaxy. In this paper, we examine using N-body simulations how the properties of planetary systems are determined during the final stages of assembly. While accretion is a chaotic process, trends in the ensemble properties of planetary systems provide a memory of the initial distribution of solid mass around a …
Here we describe a story behind the discovery of Kepler-46, which was the first exoplanetary system detected and characterized from a method known as the transit timing variations (TTVs). The TTV method relies on the gravitational interaction between planets orbiting the same star. If transits of at least one of the planets are detected, precise measurements of its transit times can be used, at least in principle, to detect and characterize other non-transiting planets in the system. Kepler-46 was the first case for which this method was shown to work in practice. Other detections and characte…
An exoplanet's structure and composition are first-order controls of the planet's habitability. We explore which aspects of bulk terrestrial planet composition and interior structure affect the chief observables of an exoplanet: its mass and radius. We apply these perturbations to the Earth, the planet we know best. Using the mineral physics toolkit BurnMan to self-consistently calculate mass-radius models, we find that core radius, presence of light elements in the core and an upper-mantle consisting of low-pressure silicates have the largest effect on the final calculated mass at a given rad…
In this paper we investigate the detectability of a habitable-zone exomoon around various configurations of exoplanetary systems with the Kepler Mission or photometry of approximately equal quality. We calculate both the predicted transit timing signal amplitudes and the estimated uncertainty on such measurements in order to calculate the confidence in detecting such bodies across a broad spectrum of orbital arrangements. The effects of stellar variability, instrument noise and photon noise are all accounted for in the analysis. We validate our methodology by simulating synthetic lightcurves a…
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 dataset is consistent with no host star mass dependence. These models are then applied to the \tex…
The Kepler mission has recently discovered a number of exoplanetary systems, such as Kepler-11 and Kepler-32, in which ensembles of several planets are found in very closely packed orbits (often within a few percent of an AU of one another). These compact configurations present a challenge for traditional planet formation and migration scenarios. We present a dynamical study of the assembly of these systems, using an N-body method which incorporates a parametrized model of planet migration in a turbulent protoplanetary disc. We explore a wide parameter space, and find that under suitable condi…
Context. With the detection of thousands of exoplanets, characterising their dynamical evolution in detail represents a key step in the understanding of their formation. Studying the dissipation of tides occurring both in the host star and in the planets is of great relevance in order to investigate the distribution of the angular momentum occurring among the objects populating the system and to studying the evolution of the orbital parameters. From a theoretical point of view, the dissipation of tides throughout a body may be studied by relying on the so-called phase or time-lag equilibrium t…
