We investigate whether certain extra-solar multi-planet systems simultaneously follow the scaling and spacing rules of the angular-momentum-deficit model. The masses and semi-major axes of exoplanets in ten multi-planet systems are considered. It is found that GJ 667C, HD 215152, HD 40307, and Kepler-79 systems are currently close to configurations of the angular-momentum-deficit model. In a gas-poor scenario, GJ 3293, HD 141399, and HD 34445 systems are those which had a configuration of the angular-momentum-deficit model in the past and get scattered away due to post gaseous effects. In addition, no matter in gas-free or gas-poor scenario, 55 Cnc, GJ 876, and WASP-47 systems do not follow the angular-momentum-deficit model. Therefore, our results reveal important formation histories of these multi-planet systems.
We study the orbital architecture of multi-planet systems detected by the Kepler transit mission using N-body simulations, focusing on the orbital spacing between adjacent planets in systems showing four or more transiting planets. We find that the observed spacings are tightly clustered around 12 mutual Hill radii, when transit geometry and sensitivity limits are accounted for. In comparison, dynamical integrations reveal that the minimum spacing required for systems of similar masses to survive dynamical instability for as long as a billion years is, ~10 if all orbits are circular and coplan…
The Kepler space mission has detected a large number of exoplanets in multiple transiting planet systems. Previous studies found that these Kepler multiple planet systems exhibit an intra-system uniformity, namely planets in the same system have similar sizes and correlated orbital spacings. However, it is important to consider the possible role of selection effects due to observational biases. In this paper, we revisit the orbital spacing aspect of the pattern after taking observational biases into account using a forward modeling method. We find that orbital spacings, in terms of period rati…
We used a sample of Kepler candidate planets with orbital periods less than 200 days and radii between 1.5 and 30 Earth radii to determine the typical dynamical spacing of neighboring planets. To derive the intrinsic (i.e., free of observational bias) dynamical spacing of neighboring planets, we generated populations of planetary systems following various dynamical spacing distributions, subjected them to synthetic observations by the Kepler spacecraft, and compared the properties of observed planets in our simulations with actual Kepler detections. We found that, on average, neighboring plane…
The giant impact phase of terrestrial planet formation establishes connections between super-Earths' orbital properties (semimajor axis spacings, eccentricities, mutual inclinations) and interior compositions (the presence or absence of gaseous envelopes). Using N-body simulations and analytic arguments, we show that spacings derive not only from eccentricities, but also from inclinations. Flatter systems attain tighter spacings, a consequence of an eccentricity equilibrium between gravitational scatterings, which increase eccentricities, and mergers, which damp them. Dynamical friction by res…
We have established precise planet radii, semimajor axes, incident stellar fluxes, and stellar masses for 909 planets in 355 multi-planet systems discovered by Kepler. In this sample, we find that planets within a single multi-planet system have correlated sizes: each planet is more likely to be the size of its neighbor than a size drawn at random from the distribution of observed planet sizes. In systems with three or more planets, the planets tend to have a regular spacing: the orbital period ratios of adjacent pairs of planets are correlated. Furthermore, the orbital period ratios are small…
Many of the multi-planet systems discovered to date have been notable for their compactness, with neighbouring planets closer together than any in the Solar System. Interestingly, planet-hosting stars have a wide range of ages, suggesting that such compact systems can survive for extended periods of time. We have used numerical simulations to investigate how quickly systems go unstable in relation to the spacing between planets, focusing on hypothetical systems of Earth-mass planets on evenly-spaced orbits (in mutual Hill radii). In general, the further apart the planets are initially, the lon…
We perform long-term simulations, up to ten billion years, of closely-spaced configurations of 2 -- 6 planets, each as massive as the Earth, traveling on nested orbits about either stellar component in $α$ Centauri AB. The innermost planet initially orbits at either the inner edge of its star's empirical habitable zone (HZ) or the inner edge of its star's conservative HZ. Although individual planets on low inclination, low eccentricity, orbits can survive throughout the habitable zones of both stars, perturbations from the companion star require that the minimum spacing of planets in multi-pla…
The basic geometry of the Solar System -- the shapes, spacings, and orientations of the planetary orbits -- has long been a subject of fascination as well as inspiration for planet formation theories. For exoplanetary systems, those same properties have only recently come into focus. Here we review our current knowledge of the occurrence of planets around other stars, their orbital distances and eccentricities, the orbital spacings and mutual inclinations in multiplanet systems, the orientation of the host star's rotation axis, and the properties of planets in binary-star systems.
Closely-packed multi-planet systems are known to experience dynamical instability if the spacings between the planets are too small. Such instability can be tempered by the frictional forces acting on the planets from gaseous discs. A similar situation applies to stellar-mass black holes embedded in AGN discs around supermassive black holes. In this paper, we use $N$-body integrations to evaluate how the frictional damping of orbital eccentricity affects the growth of dynamical instability for a wide range of planetary spacing and planet-to-star mass ratios. We find that the stability of a sys…
We present the results of a search for additional exoplanets in all multiplanetary systems discovered to date, employing a logarithmic spacing between planets in our Solar System known as the Titius-Bode (TB) relation. We use the Markov Chain Monte Carlo method and separately analyse 229 multiplanetary systems that house at least three or more confirmed planets. We find that the planets in $\sim53\%$ of these systems adhere to a logarithmic spacing relation remarkably better than the Solar System planets. Using the TB relation, we predict the presence of 426 additional exoplanets in 229 multip…
ALMA has found multiple dust gaps and rings in a number of protoplanetary disks in continuum emission at millimeter wavelengths. The origin of such structures is in debate. Recently, we documented how one super-Earth planet can open multiple (up to five) dust gaps in a disk with low viscosity ($α\lesssim10^{-4}$). In this paper, we examine how the positions, depths, and total number of gaps opened by one planet depend on input parameters, and apply our results to real systems. Gap locations (equivalently, spacings) are the easiest metric to use when making comparisons between theory and observ…
The dynamical stability of tightly packed exoplanetary systems remains poorly understood. While for a two-planet system a sharp stability boundary exists, numerical simulations of three and more planet systems show that they can experience instability on timescales up to billions of years. Moreover, an exponential trend between the planet orbital separation measured in units of Hill radii and the survival time has been reported. While these findings have been observed in numerous numerical simulations, little is known of the actual mechanism leading to instability. Contrary to a constant diffu…
Recent studies claimed that planets around the same star have similar sizes and masses and regular spacings, and that planet pairs usually show ordered sizes such that the outer planet is usually the larger one. Here I show that these patterns can be largely explained by detection biases. The \emph{Kepler} planet detections are set by the transit signal-to-noise ratio (S/N). For different stellar properties and orbital period values, the same S/N corresponds to different planetary sizes. This variation in the detection threshold naturally leads to apparent correlations in planet sizes and the …
When a star is described as a spectral class G2V, we know that the star is similar to our Sun. We know its approximate mass, temperature, age, and size. When working with an extra-solar planet database, it is very useful to have a taxonomy scale (classification) such as, for example, the Harvard classification for stars. The taxonomy has to be easily interpreted and present the most relevant information about extra-solar planets. I propose the following the extra-solar planet taxonomy scale with four parameters. The first parameter concerns the mass of an extra-solar planet in the form of the …
In order to gain possible hints for planet formation from the current data of known extra-solar planets, the period-ratios and mass-ratios of adjacent planet pairs in multi-planet systems are determined. A moderate period-ratio-mass-ratio correlation is found to have a correlation coefficient r=0.5779 with 99% confidence interval (0.464, 0.672). In contrast, for non-adjacent planet pairs, the correlation coefficient is r=0.2820 with 99% confidence interval (0.133, 0.419). Our results reveal the imprint of planet-planet interactions of the adjacent planet pairs in a certain fraction of the mult…
Employing the data from orbital periods and masses of extra-solar planets in 166 multiple planetary systems, the period-ratio and mass-ratio of adjacent planet pairs are studied. The correlation between the period-ratio and mass-ratio is confirmed and found to have a correlation coefficient of 0.5303 with a 99% confidence interval (0.3807, 0.6528). A comparison with the distribution of synthetic samples from a Monte Carlo simulation reveals the imprint of planet-planet interactions on the formation of adjacent planet pairs in multiple planetary systems.
Several properties of the Solar System, including the wide radial spacing of the giant planets, can be explained if planets radially migrated by exchanging orbital energy and momentum with outer disk planetesimals. Neptune's planetesimal-driven migration, in particular, has a strong advocate in the dynamical structure of the Kuiper belt. A dynamical instability is thought to have occurred during the early stages with Jupiter having close encounters with a Neptune-class planet. As a result of the encounters, Jupiter acquired its current orbital eccentricity and jumped inward by a fraction of an…
We investigate whether any multi-planet systems among Kepler candidates (2011 February release) can harbor additional terrestrial-mass planets or smaller bodies. We apply the "packed planetary systems" hypothesis that suggests all planetary systems are filled to capacity, and use a Hill stability criterion to identify eight 2-planet systems with significant gaps between the innermost and outermost planets. For each of these systems, we perform long-term numerical integrations of 10^7 years to investigate the stability of 4000-8000 test particles injected into the gaps. We map out stability reg…
Searching the literature, we found 25 stars with directly imaged planets and candidates. We gathered photometric and spectral information for all these objects to derive their luminosities in a homogeneous way, taking a bolometric correction into account. Using theoretical evolutionary models, one can then estimate the mass from luminosity, temperature, and age. According to our mass estimates, all of them can have a mass below 25 Jup masses, so that they are considered as planets.
The magnetospheric emissions from extrasolar planets represent a science frontier for the next decade. All of the solar system giant planets and the Earth produce radio emissions as a result of interactions between their magnetic fields and the solar wind. In the case of the Earth, its magnetic field may contribute to its habitability by protecting its atmosphere from solar wind erosion and by preventing energetic particles from reaching its surface. Indirect evidence for at least some extrasolar giant planets also having magnetic fields includes the modulation of emission lines of their host …
The effects of multi-layered clouds in the atmospheres of Earth-like planets orbiting different types of stars are studied. The radiative effects of cloud particles are directly correlated with their wavelength-dependent optical properties. Therefore the incident stellar spectra may play an important role for the climatic effect of clouds. We discuss the influence of clouds with mean properties measured in the Earth's atmosphere on the surface temperatures and Bond albedos of Earth-like planets orbiting different types of main sequence dwarf stars.
The GJ 581 planetary system was already known to harbour three planets, including two super-Earths planets which straddle its habitable zone. We report here the detection of an additional planet -- GJ 581e -- with a minimum mass of 1.9 M_earth. With a period of 3.15 days, it is the innermost planet of the system and has a ~5% transit probability. We also correct our previous confusion of the orbital period of GJ 581d (the outermost planet) with a one-year alias, thanks to an extended time span and many more measurements. The revised period is 66.8 days, and locates the semi-major axis inside t…
Exoplanets Prediction in Multi-Planetary Systems and Determining the Correlation Between the Parameters of Planets and Host Stars Using Artificial Intelligence
In the coming years, high contrast imaging surveys are expected to reveal the characteristics of the population of wide-orbit, massive, exoplanets. To date, a handful of wide planetary mass companions are known, but only one such multi-planet system has been discovered: HR8799. For low mass planetary systems, multi-planet interactions play an important role in setting system architecture. In this paper, we explore the stability of these high mass, multi-planet systems. While empirical relationships exist that predict how system stability scales with planet spacing at low masses, we show that e…
We analyzed the behavior of the rotational velocity in the parent stars of extrasolar planets. Projected rotational velocity v sin i and angular momentum were combined with stellar and planetary parameters, for a unique sample of 147 stars, amounting to 184 extrasolar planets, including 25 multiple systems. Indeed, for the present working sample we considered only stars with planets detected by the radial-velocity procedure. Our analysis shows that the v sin i distribution of stars with planets along the HR Diagram follows the well established scenario for the rotation of intermediate to low m…
An Earth-like extra-solar planet emits light which is many orders of magnitude fainter than that of the parent star. We propose a method of identifying bio-signature spectral lines in light from known extra-solar planets based on Fourier spectroscopy in the infra-red, using an off-center part of a Fourier interferogram only. This results in superior sensitivity to narrower molecular-type spectral bands, which are expected in the planet spectrum but are absent in the parent star. We support this idea by numerical simulations which include photon and thermal noise, and show it to be feasible at …
