Simulations of the Dynamics of the Debris Disks in the Systems Kepler-16, Kepler-34, and Kepler-35

We investigate the long-term dynamics of planetesimals in debris disks in models with the parameters of the binary star systems Kepler-16, Kepler-34, and Kepler-35 with planets. Our calculations show that the formation of a stable ring coorbital with the planet is possible for Kepler-16 and Kepler-35. In Kepler-34 significant orbital eccentricities of the binary system and the planet can prevent the formation of such a structure. The detection of circumbinary ring-like structures in observations of binary star systems can be evidence for the existence of planets retaining coorbital rings of dust and planetesimals.     

On the chaotic orbital dynamics of the planet in the system 16 Cyg

The chaotic orbital dynamics of the planet in the wide visual binary star system 16 Cyg is considered. The only planet in this system has a significant orbital eccentricity, e = 0.69. Previously, Holman et al. suggested the possibility of chaos in the orbital dynamics of the planet due to the proximity of 16 Cyg to the separatrix of the Lidov–Kozai resonance. We have calculated the Lyapunov characteristic exponents on the set of possible orbital parameters for the planet. In all cases, the dynamics of 16 Cyg is regular with a Lyapunov time of more than 30 000 yr. The dynamics is considered in detail for several possible models of the planetary orbit; the dependences of Lyapunov exponents on the time of their calculation and the time dependences of osculating orbital elements have been constructed. Phase space sections for the system dynamics near the Lidov–Kozai resonance have been constructed for all models. A chaotic behavior in the orbital motion of the planet in 16 Cyg is shown to be unlikely, because 16 Cyg in phase space is far from the separatrix of the Lidov–Kozai resonance at admissible orbital parameters, with the chaotic layer near the separatrix being very narrow.     

Planetary dynamics in the system α Centauri: The stability diagrams

The stability of the motion of a hypothetical planet in the binary system ?? Cen A?CB has been investigated. The analysis has been performed within the framework of a planar (restricted and full) three-body problem for the case of prograde orbits. Based on a representative set of initial data, we have obtained the Lyapunov spectra of the motion of a triple system with a single planet. Chaotic domains have been identified in the pericenter distance-eccentricity plane of initial conditions for the planet through a statistical analysis of the data obtained. We have studied the correspondence of these chaotic domains to the domains of initial conditions that lead to the planet??s encounter with one of the binary??s stars or to the escape of the planet from the system. We show that the stability criterion based on the maximum Lyapunov exponent gives a more clear-cut boundary of the instability domains than does the encounterescape criterion at the same integration time. The typical Lyapunov time of chaotic motion is ??500 yr for unstable outer orbits and ??60 yr for unstable inner ones. The domain of chaos expands significantly as the initial orbital eccentricity of the planet increases. The chaos-order boundary has a fractal structure due to the presence of orbital resonances.     

系外行星系统掩星周期变化研究进展

在掩星法发现的系外行星系统中,如果存在其他未知的伴星绕同一颗恒星运动,掩星行星由于受到伴星引力的影响,运动轨道将发生变化,轨道周期不再是常数,而是变化的。利用这种变化探测掩星系统中的其他行星,已成为一种新的方法。主要介绍了未知行星与掩星行星之间的引力作用引起的掩星周期变化效应,以及掩星周期变化法探测系外行星的理论和研究进展状况,最后简要讨论了几种影响掩星周期变化的其他因素:共轨行星、卫星、潮汐效应、相对论效应及恒星的引力四极矩等。     

A dynamical analysis of the 14 Herculis planetary system

Precision radial velocity measurements of the Sun-like dwarf 14 Herculis published by Naef et al., Butler et al. and Wittenmyer, Endl & Cochran reveal a Jovian planet in a 1760-d orbit and a trend indicating the second distant object. On the grounds of dynamical considerations, we test a hypothesis that the trend can be explained by the presence of an additional giant planet. We derive dynamical limits to the orbital parameters of the putative outer Jovian companion in an orbit within ∼13 au. In this case, the mutual interactions between the Jovian planets are important for the long-term stability of the system. The best self-consistent and stable Newtonian fit to an edge-on configuration of Jovian planets has the outer planet in 9-au orbit with a moderate eccentricity of ∼0.2 and confined to a zone spanned by the low-order mean motion resonances 5:1 and 6:1. This solution lies in a shallow minimum of (χ²_ν)^1/2 and persists over a wide range of the system inclination. Other stable configurations within 1σ confidence interval of the best fit are possible for the semimajor axis of the outer planet in the range of (6,13) au and the eccentricity in the range of (0, 0.3). The orbital inclination cannot yet be determined but when it decreases, both planetary masses approach ∼10 m _J and for i ∼ 30° the hierarchy of the masses is reversed.     

Planetans—oceanic planets

The development of principles, systems, and instruments enable the detection of exoplanets with 6–8 Earth masses or less. The launches of specialized satellites, such as CoRoT (2006) and Kepler (2009), into orbits around the Earth have enabled the discovery of new exoplanetary systems. These missions are searching for relatively low-mass planets by observing their transits over the disks of their parent stars. At the same time, supporting studies of exoplanets using ground-based facilities (that measure Keplerian components of radial velocities) are in progress. The properties of at least two objects discovered by different methods, Kepler-22 and GJ 1214b, suggested that there was another class of celestial bodies among the known types of extrasolar planets: planetans, or oceanic planets. The structure of Kepler-22 and GJ 1214b suggest that they can be these oceanic planets. In this paper, we consider to what extent this statement is valid. The consideration of exoplanet Gl 581g as an oceanic planet is more feasible. Some specific features of the physical nature of these unusual planets are presented.     

Kepler-9b、c的近2:1平运动共振分析

对多行星系统中行星周期比的统计发现,行星周期比在简单整数比2:1、3:2的右侧边缘处有明显聚集,而在其紧邻的左边有明显空缺.针对这一现象有各种不同的动力学解释. Kepler-9系统中已发现的3个行星中,行星b、c周期比约为2.03,是接近2:1共振的一个典型例子.利用关于偏心率的二阶哈密顿方程,针对只考虑长期作用和加入共振摄动两种情况,通过研究当前状态下系统在能量等高线图与相空间截面图中的位置,讨论了两行星可能的近共振状态.     

Stability of fictitious Trojan planets in extrasolar systems

Our work deals with the dynamical possibility that in extrasolar planetary systems a terrestrial planet may have stable orbits in a 1:1 mean motion resonance with a Jovian like planet. We studied the motion of fictitious Trojans around the Lagrangian points L₄/L₅ and checked the stability and/or chaoticity of their motion with the aid of the Lyapunov Indicators and the maximum eccentricity. The computations were carried out using the dynamical model of the elliptic restricted three‐body problem that consists of a central star, a gas giant moving in the habitable zone, and a massless terrestrial planet. We found 3 new systems where the gas giant lies in the habitable zone, namely HD99109, HD101930, and HD33564. Additionally we investigated all known extrasolar planetary systems where the giant planet lies partly or fully in the habitable zone. The results show that the orbits around the Lagrangian points L₄/L₅ of all investigated systems are stable for long times (10⁷ revolutions). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

GJ 581 update: Additional evidence for a Super‐Earth in the habitable zone

We present an analysis of the significantly expanded HARPS 2011 radial velocity data set for GJ 581 that was presented by Forveille et al. (2011). Our analysis reaches substantially different conclusions regarding the evidence for a Super‐Earth‐mass planet in the star's Habitable Zone. We were able to reproduce their reported χ²_ν and RMS values only after removing some outliers from their models and refitting the trimmed down RV set. A suite of 4000 N‐body simulations of their Keplerian model all resulted in unstable systems and revealed that their reported 3.6σ detection of e = 0.32 for the eccentricity of GJ 581e is manifestly incompatible with the system's dynamical stability. Furthermore, their Keplerian model, when integrated only over the time baseline of the observations, significantly increases the χ²_ν and demonstrates the need for including non‐Keplerian orbital precession when modeling this system. We find that a four‐planet model with all of the planets on circular or nearly circular orbits provides both an excellent self‐consistent fit to their RV data and also results in a very stable configuration. The periodogram of the residuals to a 4‐planet all‐circular‐orbit model reveals significant peaks that suggest one or more additional planets in this system. We conclude that the present 240‐point HARPS data set, when analyzed in its entirety, and modeled with fully self‐consistent stable orbits, by and of itself does offer significant support for a fifth signal in the data with a period near 32 days. This signal has a false alarm probability of <4% and is consistent with a planet of minimum mass 2.2 M_⊕, orbiting squarely in the star's habitable zone at 0.13 AU, where liquid water on planetary surfaces is a distinct possibility (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Could CoRoT-7b and Kepler-10b be remnants of evaporated gas or ice giants?

We present thermal mass loss calculations over evolutionary time scales for the investigation if the smallest transiting rocky exoplanets CoRoT-7b (∼1.68R_Earth) and Kepler-10b (∼1.416R_Earth) could be remnants of an initially more massive hydrogen-rich gas giant or a hot Neptune-class exoplanet. We apply a thermal mass loss formula which yields results that are comparable to hydrodynamic loss models. Our approach considers the effect of the Roche lobe, realistic heating efficiencies and a radius scaling law derived from observations of hot Jupiters. We study the influence of the mean planetary density on the thermal mass loss by placing hypothetical exoplanets with the characteristics of Jupiter, Saturn, Neptune, and Uranus to the orbital location of CoRoT-7b at 0.017 AU and Kepler-10b at 0.01684 AU and assuming that these planets orbit a K- or G-type host star. Our findings indicate that hydrogen-rich gas giants within the mass domain of Saturn or Jupiter cannot thermally lose such an amount of mass that CoRoT-7b and Kepler-10b would result in a rocky residue. Moreover, our calculations show that the present time mass of both rocky exoplanets can be neither a result of evaporation of a hydrogen envelope of a “Hot Neptune” nor a “Hot Uranus”-class object. Depending on the initial density and mass, these planets most likely were always rocky planets which could lose a thin hydrogen envelope, but not cores of thermally evaporated initially much more massive and larger objects.     

Gravitational focusing and shielding of meteoroid streams

The gravitational attraction of planets can cause significant perturbation of the trajectories of meteoroids. The resulting deflection can result in significant enhancement of the flux of meteoric particles in the neighbourhood of the planet. We give an analytical method for calculating the relative flux of stream meteoroids in the vicinity of a planet. We include the effect of shielding of certain regions that are not accessible to the meteoroids that have impacted the planet. We compare our results with those of Divine et al. and although we confirm the accuracy of their trajectory equations, the fluxes predicted by their calculations are not consistent with integrated fluxes over a planet predicted by the classic work of Öpik. Our method yields predictions for the integrated flux enhancement factor that are identical to Öpik's. We present the results of these calculations and find that in all cases, tail-like regions of enhanced meteoroid flux appear downstream of the planet, with very large enhancements possible in the case of the giant planets for all probable stream velocities.     

Stability of S-type Orbits in Binaries

This numerical investigation is concerned with the stability of planets moving around one component of a double star system. Since the discovery of four extra solar planets moving in such orbits, there is a growing interest of stability studies thereto. We determined the stable regions in the elliptic restricted three body problem, for the whole range of mass-ratios from 0.1 to 0.9, by means of the Fast Lyapunov Indicators. The computations have been carried out for eccentricities of the binary and of the planet in the range 0–0.5. Therefore, we present for the first time the variation of the stable regions when the initial eccentricity of the planet is increased. We have found a correlation between the reduction of the stable zones if the eccentricity of the planet or of the binary is increased — of course the latter one is more effective.This revised version was published online in October 2005 with corrections to the Cover Date.     

On possible circumbinary configurations of the planetary systems of α Centauri and EZ Aquarii

Possible configurations of the planetary systems of the binary stars α Cen A–BandEZAqr A–C are analyzed. The P-type orbits—circumbinary ones, i.e., the orbits around both stars of the binary, are studied. The choice of these systems is dictated by the fact that α Cen is closest to us in the Galaxy, while EZ Aqr is the closest system whose circumbinary planets, as it turns out, may reside in the “habitability zone.” The analysis has been performed within the framework of the planar restricted three-body problem. The stability diagrams of circumbinary motion have been constructed: on representative sets of initial data (in the pericentric distance–eccentricity plane), we have computed the Lyapunov spectra of planetary motion and identified the domains of regular and chaotic motion through their statistical analysis. Based on present views of the dynamics and architecture of circumbinary planetary systems, we have determined the most probable planetary orbits to be at the centers of the main resonance cells, at the boundary of the dynamical chaos domain around the parent binary star, which allows the semimajor axes of the orbits to be predicted. In the case of EZ Aqr, the orbit of the circumbinary planet is near the habitability zone and, given that the boundary of this zone is uncertain, may belong to it.     

Her X-1 35天开关周期是由于中子星的自由进动产生的吗?(英文)

一些作者提出Her X-1的35天开关周期是由中子星的自由进动引起的。对这个模型我们进行了理论计算,并将理论结果和观测资料进行了比较,我们发现: (1)Hcr X-1的35天周期的光变曲线的理论值与观测(Jones ＆ Forman,1976)不符。 (2)在这个模型中脉冲宽度和强度随35天周期有很大的变化(见图4和图5),也与观测不符(如Gruber等人1980年的观测)。 (3)Parmar等人(1985)报道他们没有发现预期的Her X-1的X射线辐射35天周期的变化,这也同中子星自由进动的模型不一致。 Pravdo等(1977)建议观测到的X射线脉冲是由产生于中子星表面附近的、对称的辐射束经汤姆逊散射而形成。我们用强磁场中的汤姆逊散射理论所作的分析表明,该模型可以较好地与观测相符。     

A gas-poor planetesimal capture model for the formation of giant planet satellite systems

Assuming that an unknown mechanism (e.g., gas turbulence) removes most of the subnebula gas disk in a timescale shorter than that for satellite formation, we develop a model for the formation of regular (and possibly at least some of the irregular) satellites around giant planets in a gas-poor environment. In this model, which follows along the lines of the work of Safronov et al. [1986. Satellites. Univ. of Arizona Press, Tucson, pp. 89-116], heliocentric planetesimals collide within the planet's Hill sphere and generate a circumplanetary disk of prograde and retrograde satellitesimals extending as far out as ∼RH/2. At first, the net angular momentum of this proto-satellite swarm is small, and collisions among satellitesimals leads to loss of mass from the outer disk, and delivers mass to the inner disk (where regular satellites form) in a timescale ?¹⁰⁵ years. This mass loss may be offset by continued collisional capture of sufficiently small <1 km interlopers resulting from the disruption of planetesimals in the feeding zone of the giant planet. As the planet's feeding zone is cleared in a timescale ?¹⁰⁵ years, enough angular momentum may be delivered to the proto-satellite swarm to account for the angular momentum of the regular satellites of Jupiter and Saturn. This feeding timescale is also roughly consistent with the independent constraint that the Galilean satellites formed in a timescale of ¹⁰⁵-¹⁰⁶ years, which may be long enough to accommodate Callisto's partially differentiated state [Anderson et al., 1998. Science 280, 1573; Anderson et al., 2001. Icarus 153, 157-161]. In turn, this formation timescale can be used to provide plausible constraints on the surface density of solids in the satellitesimal disk (excluding satellite embryos for satellitesimals of size ∼1 km), which yields a total disk mass smaller than the mass of the regular satellites, and means that the satellites must form in several ∼10 collisional cycles. However, much more work will need to be conducted concerning the collisional evolution both of the circumplanetary satellitesimals and of the heliocentric planetesimals following giant planet formation before one can assess the significance of this agreement. Furthermore, for enough mass to be delivered to form the regular satellites in the required timescale one may need to rely on (unproven) mechanisms to replenish the feeding zone of the giant planet. We compare this model to the solids-enhanced minimum mass (SEMM) model of Mosqueira and Estrada [2003a. Icarus 163, 198-231; 2003b. Icarus 163, 232-255], and discuss its main consequences for Cassini observations of the saturnian satellite system.     

Improvement of the position of planet X based on the motion of nearly parabolic comets

Based on the motion of nearly parabolic comets, we have improved the position of planet X in its orbit obtained by Batygin and Brown (2016). By assuming that some of the comets discovered to date could have close encounters with this planet, we have determined the comets with a small minimum orbit intersection distance with the planet. Five comets having hyperbolic orbits before their entry into the inner Solar system have been separated out from the general list. By assuming that at least one of them had a close encounter with the planet, we have determined the planet’s possible position. The planet’s probable ephemeris positions at the present epoch have been obtained by assuming the planet to have prograde and retrograde motions. In the case of a prograde motion, the planet is currently at a distance Δ whose value belongs to the interval Δ ∈ (1110, 1120) AU and has a right ascension α and declination δ within the intervals α ∈ (83?, 90?) and δ ∈ (8?, 10?); the true anomaly υ belongs to the interval υ ∈ (176?, 184?). In the case of a retrograde motion: α ∈ (48?, 58?), δ ∈ (?12?, ?6?), Δ ∈ (790, 910) AU, and υ ∈ (212?, 223?). It should be noted that in the case of a retrograde motion of the planet, its ephemeris position obtained from the motion of comets agrees with the planet’s position obtained byHolman and Payne (2016) from highly accurate Cassini observations and is consistent with the results of Fienga et al. (2016).     

A new analysis of the GJ581 extrasolar planetary system

We have done a new analysis of the available observations of the GJ581 exoplanetary system. Today this system is controversial due to choices that can be done in the orbital determination. The main ones are the occurrence of aliases and the additional bodies??the planets f and g??announced in Vogt et?al. (Astrophys J 723:954?C965, 2010). Any dynamical study of exoplanets requires the good knowledge of the orbital elements and the investigations involving the planet g are particularly interesting, since this body would lie in the habitable zone (HZ) of the star GJ581. This region, for this system, is very attractive of the dynamical point of view due to several resonances of two and three bodies present there. In this work, we investigate the conditions under which the planet g may exist. We stress the fact that the planet g is intimately related with the orbital elements of the planet d; more precisely, we conclude that it is not possible to disconnect its existence from the determination of the eccentricity of the planet d. Concerning the planet f, we have found one solution with period ??450?days, but we are judicious about any affirmation concerning this body because its signal is in the threshold of detection and the high period is in a spectral region where the occurrence of aliases is very common. Besides, we outline some dynamical features of the HZ with the dynamical map and point out the role played by some resonances laying there.     

Resonant orbits in the vicinity of asteroid 216 Kleopatra

This investigation examines the resonant orbits in the vicinity of asteroid 216 Kleopatra using a precise gravitational model, with emphasis on their crucial role in determining the global orbital behaviors. Three-dimensional Monte Carlo simulations of test particle trajectories are launched to find the condition and probability distribution of resonance. It is revealed the resonant orbits are rich and concentrated in the near-field regime, which provides a short-term mechanism to clear the vicinal ejecta away from the asteroid. The unstable boundary predicted in our calculations is consistent with the observed mutual orbits of satellites S/2008 (216) 1 and S/2008 (216) 2. The probability distribution of resonance is considered as an indicator of the stability of vicinal orbits, and the results are identical to the previous analysis by Scheeres et al. (Icarus 121:67, 1996) for the stability of retrograde orbits around asteroid 4769 Castalia.     

小行星主带上单个行星的质量上限

介绍了N体模拟的Hermite算法,并利用该算法研究了不同质量行星在小行星主带上轨道的演化情况．采用的演化模型是太阳系N体模型(N=7),即把水星、金星、地球的质量加到太阳上,忽略冥王星,同时在小行星主带附近增加一个假想行星,系统演化时间为1亿年．数值模拟显示能够稳定存在于小行星主带上的单个天体的质量上限其量级为10~(25)kg．模拟同时还显示在某些情况下,假想行星与木星之间的低阶共振可以增强系统的稳定性．     

Search for circum‐planetary material and orbital period variations of short‐period Kepler exoplanet candidates

A unique short‐period (P = 0.65356(1) d) Mercury‐size Kepler exoplanet candidate KIC012557548b has been discovered recently by Rappaport et al. (2012). This object is a transiting disintegrating exoplanet with a circum‐planetary material–comet‐like tail. Close‐in exoplanets, like KIC012557548b, are subjected to the greatest planet‐star interactions. This interaction may have various forms. In certain cases it may cause formation of the comet‐like tail. Strong interaction with the host star, and/or presence of an additional planet may lead to variations in the orbital period of the planet. Our main aim is to search for comet‐like tails similar to KIC012557548b and for long‐term orbital period variations. We are curious about frequency of comet‐like tail formation among short‐period Kepler exoplanet candidates. We concentrate on a sample of 20 close‐in candidates with a period similar to KIC012557548b from the Kepler mission. We first improved the preliminary orbital periods and obtained the transit light curves. Subsequently we searched for the signatures of a circum‐planetary material in these light curves. For this purpose the final transit light curve of each planet was fitted with a theoretical light curve, and the residuals were examined for abnormalities. We then searched for possible long‐term changes of the orbital periods using the method of phase dispersion minimization. In 8 cases out of 20 we found some interesting peculiarities, but none of the exoplanet candidates showed signs of a comet‐like tail. It seems that the frequency of comet‐like tail formation among short‐period Kepler exoplanet candidates is very low. We searched for comet‐like tails based on the period criterion. Based on our results we can conclude that the short‐period criterion is not enough to cause comet‐like tail formation. This result is in agreement with the theory of the thermal wind and planet evaporation (Perez‐Becker & Chiang 2013). We also found 3 cases of candidates which showed some changes of the orbital period. Based on our results we can see that orbital period changes are not caused by comet‐like tail disintegration processes, but rather by possible massive outer companions. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)