Analysis of Error Sources in STEP Astrometrytwo

The space telescope Search for Terrestrial Exo-Planets (STEP) employed a method of sub-pixel technology which ensures that the astrometric accuracy of the telescope on the focal plane is at the order of 1 μas. This kind of astrometric precision is promising to detect the earth-like planets beyond the solar system. In this paper, we analyze the influence of some key factors, including the errors in the stellar proper motion, parallax, the optical center of the system, and the velocity and position of the satellite, on the detection of exoplanets. We propose a relative angular distance method to evaluate the non-linear terms in the variation of star-pair's angular distance caused by the possibly existing exoplanet. This method could avoid the direct influence of measuring errors of the position and proper motion of the reference stars. Supposing that there are eight reference stars and a target star with a planet system in the same field of view, we simulate their five-year observational data, and use the least square method to get the parameters of the planet orbit. Our results show that the method is robust to detect terrestrial planets based on the 1 μas precision of STEP.     

On the stability of hypothetical satellites coorbital to Mimas or Enceladus

In the present work, we study the stability of hypothetical satellites that are coorbital with Enceladus and Mimas. We performed numerical simulations of 50 particles around the triangular Lagrangian equilibrium points of Enceladus and Mimas taking into account the perturbation of Mimas, Enceladus, Tethys, Dione, Titan and the oblateness of Saturn. All particles remain on tadpole orbits after 10 000 yr of integration. Since in the past the orbit of Enceladus and Mimas expanded due to the tidal perturbation, we also simulated the system with Enceladus and Mimas at several different values of semimajor axes. The results show that in general the particles remain on tadpole orbits. The exceptions occur when Enceladus is at semimajor axes that correspond to 6:7, 5:6 and 4:5 resonances with Mimas. Therefore, if Enceladus and Mimas had satellites librating around their Lagrangian triangular points in the past, they would have been removed if Enceladus crossed one of these first-order resonances with Mimas.     

On the determination of the long period tidal perturbations in the elements of artificial earth satellites

In the present article we develop the theory of the long period tidal effects in the motion of artificial satellites assuming the variability of elastic parameters of the Earth (Love numbers) across the parallels. The dependence of Love numbers on the longitude produces perturbations of the period of one day or less and hence is neglected in the present theory. In this respect we follow in the footsteps of Kaula (1969). If the deviations ofk ₂ andk ₃ from pure constants are not taken into consideration, then the perturbations caused by the variability ofk ₂ andk ₃ across the parallels will be misinterpreted as the perturbations caused byk ₄...-terms, and the spurious values ofk ₄... will be deduced. It is extremely doubtful, however, that the real effects caused byk ₄,k ₅,..., are significant enough to be detected. The short period effects with the period of the revolution of the satellite, or less, were removed from the differential equations for the variation of elements of the satellite by the averaging over the orbit of the satellite. These differential equations are in the form convenient for numerical integration over a long interval of time and also suitable for developing the tidal effects into trigonometric series with the arguments ω, Ω of the satellite andl, l′, F, D, Γ of the Moon. The numerical integration can be performed using some simple quadrature formula, without resorting to a predictor-corrector system.     

Tidal locking of habitable exoplanets

Potentially habitable planets can orbit close enough to their host star that the differential gravity across their diameters can produce an elongated shape. Frictional forces inside the planet prevent the bulges from aligning perfectly with the host star and result in torques that alter the planet’s rotational angular momentum. Eventually the tidal torques fix the rotation rate at a specific frequency, a process called tidal locking. Tidally locked planets on circular orbits will rotate synchronously, but those on eccentric orbits will either librate or rotate super-synchronously. Although these features of tidal theory are well known, a systematic survey of the rotational evolution of potentially habitable exoplanets using classic equilibrium tide theories has not been undertaken. I calculate how habitable planets evolve under two commonly used models and find, for example, that one model predicts that the Earth’s rotation rate would have synchronized after 4.5 Gyr if its initial rotation period was 3 days, it had no satellites, and it always maintained the modern Earth’s tidal properties. Lower mass stellar hosts will induce stronger tidal effects on potentially habitable planets, and tidal locking is possible for most planets in the habitable zones of GKM dwarf stars. For fast-rotating planets, both models predict eccentricity growth and that circularization can only occur once the rotational frequency is similar to the orbital frequency. The orbits of potentially habitable planets of very late M dwarfs ( Open image in new window ) are very likely to be circularized within 1 Gyr, and hence, those planets will be synchronous rotators. Proxima b is almost assuredly tidally locked, but its orbit may not have circularized yet, so the planet could be rotating super-synchronously today. The evolution of the isolated and potentially habitable Kepler planet candidates is computed and about half could be tidally locked. Finally, projected TESS planets are simulated over a wide range of assumptions, and the vast majority of potentially habitable cases are found to tidally lock within 1 Gyr. These results suggest that the process of tidal locking is a major factor in the evolution of most of the potentially habitable exoplanets to be discovered in the near future.     

The Rise of New Planets: Super-Earths and Sub-Neptunes

With the ceaseless progress of detecting technology, over 3500 exo-planets have been discovered. It is interesting but unexpected that the majority of the detected exoplanets are unlike any planets in our solar system. They have a size and mass between the Earth and the Neptune, and thus they are called as Super-Earths or Sub-Neptunes. In this article, I introduce these newly rising planets and review our current knowledge of their physical properties, orbital properties, and origins. Finally, I discuss the promising and exciting prospects.     

Tidally induced surface displacements, external potential variations, and gravity variations on Mars

We have used and extended Roosbeek’s tidal potential for Mars to calculate tidal displacements, gravity variations, and external gravitational potential variations. The tides on Mars are caused by the Sun, and to a lesser degree by the natural satellites Phobos (8%, relative to the Sun) and Deimos (0.08%, relative to the Sun). To determine the reaction of Mars to the tidal forcing, the Love numbers h, l, and k and the gravimetric factor δ were calculated for interior models of Mars with different state, density, and radius of the core and for models which include mantle anelasticity. The latitude dependence and frequency dependence of the Love numbers have been taken explicitly into account. The Love numbers are about three times smaller than those for the Earth and are very sensitive to core changes; e.g., a difference of about 30% is found between a model with a liquid core and an otherwise similar model with a solid core. Tidal displacements on Mars are much smaller than on Earth due to the smaller tidal potential, but also due to the smaller reaction of Mars (smaller Love numbers). For both the tidal diplacement and the tidal external potential perturbations, the tidal signal is at the limit of detection and is too small to permit properties of Mars’s interior to be inferred. On the other hand, the Phobos tidally induced gravity changes, which are subdiurnal with typical periods shorter than 12 h, can be measured very precisely by the very broad band seismometer with thermal control of the seismological experiment SEIS of the upcoming NetLander mission. It is shown that the Phobos-induced gravity tides could be used to study the Martian core.     

Effect of Orbital Distance on the Atmospheric Escape of Exoplanets

Atmospheric escape is an important sector in the evolution of planetary atmosphere, and its energy is mainly originated from the radiation of the host star at the high energy band. The radiation flux drops dramatically with the increase of orbital distance, there is a large difference of planetary atmospheric escape in different orbits, so it is necessary to study the impact of orbital distance on the atmospheric escape of an exoplanet. We consider the radiation transfer and the photochemical reactions of multiple kinds of particles to study the variation of planetary atmospheric escape with the orbital distance by using a 1-D hydrodynamic model. Due to the large differences of the spectra of host stars in different evolution stages, the Astrophysical Plasma Emission Code (APEC) in the X-Ray Spectral Fitting Package (XSPEC) is used to obtain the spectra of solar-type stars with different ages as the input spectra of the model. The results indicate that the escape rates of the exoplanets in different orbits are different significantly, and the escape mechanism is converted from the drastic hydrodynamic escape into the moderate Jeans escape as the orbital distance increases, the smaller the planetary gravitational potential, the younger the star-planet system, the larger the distance of this conversion. The correlation between the escape rate and the radiation flux decreases for the short-period exoplanets in a younger star-planet system. It is shown that the classical energy-limited escape theory is not suitable for this kind of exoplanets. These results have enriched the studies on the atmospheric escape of exoplanets, especially, extended the studies on the escape mechanism and energy conversion under different orbital distances and stellar ages.     

The sulfur species in hot rocky exoplanet atmospheres

The first JWST observations of hot Jupiters showed an unexpected detection of SO ${}_2$ in their hydrogen-rich atmospheres. We investigate how much sulfur can be expected in the atmospheres of rocky exoplanets and which sulfur molecules can be expected to be most abundant and detectable by transmission spectroscopy. We run thermochemical equilibrium models at the crust–atmosphere interface, considering surface temperatures 500–5000 K, surface pressures 1–100 bar, and various sets of element abundances based on common rock compositions. Between 1000 and 2000 K, we find gaseous sulfur concentrations of up to 25% above the rock in our models. SO ${}_2$, SO, H ${}_2$S, and S ${}_2$ are by far the most abundant sulfur molecules. SO ${}_2$ shows potentially detectable features in transmission spectra at about 4 $\mu$m, between 7 and 8 $\mu$m, and beyond 15 $\mu$m. In contrast, the sometimes abundant H ${}_2$S molecule is difficult to detect in these spectra, which are mostly dominated by H ${}_2$O and CO ${}_2$. Although the molecule PS only occurs with concentrations ppm, it can cause a strong absorption feature between 0.3 and 0.65 $\mu$m in some of our models for high surface pressures. The detection of sulfur molecules would enable a better characterization of the planetary surface.     

Weak lensing signal in unified dark matter models

This paper is an extension of the work done by Pierens & Nelson in which they investigated the behaviour of a two-planet system embedded in a protoplanetary disc. They put a Jupiter mass gas giant on the internal orbit and a lower mass planet on the external one. We consider here a similar problem taking into account a gas giant with mass in the range 0.5 to  1 M _J  and a Super-Earth (i.e. a planet with mass  ≤10 M _⊕  ) as the outermost planet. By changing disc parameters and planet masses, we have succeeded in getting the convergent migration of the planets which allows for the possibility of their resonant locking. However, in the case in which the gas giant has the mass of Jupiter, before any mean-motion first-order commensurability could be achieved, the Super-Earth is caught in a trap when it is very close to the edge of the gap opened by the giant planet. This confirms the result obtained by Pierens & Nelson in their simulations. Additionally, we have found that, in a very thin disc, an apsidal resonance is observed in the system if the Super-Earth is captured in the trap. Moreover, the eccentricity of the small planet remains low, while the eccentricity of the gas giant increases slightly due to the imbalance between Lindblad and corotational resonances. We have also extended the work of Pierens & Nelson by studying analogous systems in which the gas giant is allowed to take sub-Jupiter masses. In this case, after conducting an extensive survey over all possible parameters, we have succeeded in getting the 1:2 mean-motion resonant configuration only in a disc with low aspect ratio and low surface density. However, the resonance is maintained just for a few thousand orbits. Thus, we conclude that for typical protoplanetary discs the mean-motion commensurabilities are rare if the Super-Earth is located on the external orbit relative to the gas giant.     

Can Cassini detect a subsurface ocean in Titan from gravity measurements?

Recent models of Titan's interior predict that the satellite contains an ocean of water and ammonia under an icy layer. Direct evidence for the presence of an ocean can be provided on the Cassini mission only by radio science determination of Titan Love number k₂. Simulations that use the five flybys T11, T22 T33, T45, and T68 (the latter two belonging to the extended mission) lead to the result that in the elastic case, where the Love number is real, k₂ will be determined with a one-sigma accuracy of 0.1. In the viscoelastic case, where k₂ is complex, the real and imaginary parts of k₂ will be determined with one sigma accuracies of 0.138 and 0.115, respectively. Ocean and oceanless models that include a viscoelastic rheology are built. In the viscoelastic case, there is a 93% probability to correctly predict the presence or absence of an ocean; this probability improves to 97% in the elastic case.     

天体运动的轨道偏心率研究概述---从恒星系统到行星系统

偏心率是描述天体运动轨道的重要参数之一, 能够为揭示天体的动力学演化提供重要线索, 进而帮助理解天体形成与演化的过程及背后的物理机制. 随着天文观测技术的不断发展, 人们对于天体运动轨道的研究已经走出太阳系, 包含的系统也从大质量端的恒星系统延伸到了低质量端的行星系统. 聚焦天体轨道偏心率研究, 回顾了目前在恒星系统(包括主序恒星、褐矮星以及致密星)和行星系统(包括太阳系外巨行星以及``超级地球''、``亚海王星''等小质量系外行星)方面取得的进展, 总结了不同尺度结构下偏心率研究的一些共同之处和待解决的问题. 并结合当下和未来的相关天文观测设备和项目, 对未来天体轨道偏心率方面的研究工作进行了展望.     

Simultaneous determination of global topography, tidal Love number and libration amplitude of Mercury by laser altimetry

Solar tidal forces generate elevation changes of Mercury's surface of the order 1 m within one Hermean year, and solar torques on the non-symmetric permanent mass distribution of the planet cause an uneven rotation of Mercury's surface with a libration amplitude of the order of 40 arcsec. Knowledge of the precise reaction of the planet to tidal forcing, expressed by the Love numbers h₂ and k₂, as well as accurate knowledge of the amplitude of forced libration Φ_lib, puts constraints on the internal structure, for example the state and the size of the core. The MESSENGER and BepiColombo missions to Mercury carry laser altimeters, whose primary goal is to accurately map the topography. Here we investigate if the Love number h₂ and the amplitude of forced libration can be determined together with the static topography of the planet from a global altimetry record. We do this by creating synthetic altimeter data for the nominal orbit of BepiColombo over the nominal mission duration of approximately four Mercury years and inverting them for the static and time-dependent parts of the topography. We assume purely Gaussian noise. We find that it is possible to extract both parameters h₂ and Φ_lib with an accuracy of approximately 10%, while the static topography coefficients of a spherical harmonic expansion can be determined simultaneously with an accuracy at the centimetre level. Extraction of the static topography to higher harmonic degrees improves the precision of the measurement of h₂ and Φ_lib. The simulation results demonstrate that it seems feasible to test current models on Mercury's interior with sufficient precision using BepiColombo Laser Altimeter data.     

The Polarization Characteristics of Mercury-like Exoplanets

This paper aimed at studying the polarization characteristics of Mercury-like exoplanets via the polarimetric phase curve of the unresolvable Mercury. We utilized the Bayesian non-linear ?tting method to get the photo- metric phase curve and the polarimetric phase curve of Mercury. From these two kinds of curves, we obtained further the polarimetric phase curve of the unresolvable Mercury. The results derived from this curve are as follows: ?rst, in the visible light waveband the order of magnitude of the polarization degree is 10−12; second, the maximum degree of polarization parallel to the scattering plane is comparable to that vertical to the scattering plane, but their corre- sponding phase angles have changed evidently in comparison with the case of the resolvable Mercury; third, when the phase angle is greater than 158°, the polarization degree of the unresolvable Mercury is almost reduced to zero.     

Photometric Follow-up Transit (Primary Eclipse) Observations of WASP-43 b and TrES-3b and A Study on Their Transit Timing Variations

Two photometric follow-up transit (primary eclipse) observations on WASP-43 b and four observations on TrES-3 b are performed using the Xuyi Near-Earth Object Survey Telescope. After differential photometry and light curve analysis, the physical parameters of the two systems are obtained and are in good match with the literature. Combining with transit data from a lot of literature, the residuals (O ? C) of transit observations of both systems are fitted with the linear and quadratic functions. With the linear fitting, the periods and transit timing variations (TTVs) of the planets are obtained, and no obvious periodic TTV signal is found in both systems after an analysis. The maximum mass of a perturbing planet located at the 1:2 mean motion resonance (MMR) for WASP-43 b and TrES-3 b is estimated to be 1.826 and 1.504 Earth mass, respectively. By quadratic fitting, it is confirmed that WASP-43 b may have a long-term TTV which means an orbital decay. The decay rate is shown to be P? = (?0.005248 ± 0.001714) s·yr^?1, and compared with the previous results. Based on this, the lower limit of the stellar tidal quality parameter of WASP-43 is calculated to be ${Q^{\prime }}_{*}\ge 1.5\times {10}^5$, and the remaining lifetimes of the planets are presented for the different ${Q^{\prime }}_{*}$ values of the two systems, correspondingly.     

Interior structure models of solid exoplanets using material laws in the infinite pressure limit

The detection of low-mass extrasolar planets has initiated growing interest in massive rocky bodies (super-Earths) for which no Solar System analogue does exist. Here, we present a new model approach to investigate their interior structure and thermal state. We improve and extend previous interior models mainly in two areas: the first improvement is due to the consequent application of equations of state (EoS) that are compliant with the thermodynamics of the high-pressure limit and facilitate reinvestigating mass-radius relations for terrestrial-type exoplanets. To quantify the uncertainty due to extrapolation, we compare a generalized Rydberg and a Keane EoS, which are both consistent with the high-pressure limit. Furthermore, we consider a reciprocal K′ EoS that fits the seismologically obtained Preliminary Reference Earth Model (PREM), thereby accounting for the mineralogical composition of the Earth. As a result, the predicted planetary radii of terrestrial-type exoplanets of up to 10 Earth masses would differ by less than 2% between all three EoS, well within current observational limits. The second extension arises from the adoption of a mixing length formulation instead of the commonly used, more simplified parameterized approach to model convective heat transport in planetary mantles. In comparison to parameterized convection models, our results indicate generally hotter interiors with increasing planetary mass and a cumulative tendency to extended regimes of sluggish convection in the lowermost mantle. The latter is attributed to less efficient convective heat transport with increasing mantle pressures. An improved knowledge of the present thermal state is prerequisite to gain a better understanding of the pathways of internal evolution of terrestrial-type exoplanets.     

Construction of Martian Interior Model

We present the results of extensive numerical modeling of the Martian interior. Yoder et al. in 2003 reported a mean moment of inertia of Mars that was somewhat smaller than the previously used value and the Love number k₂ obtained from observations of solar tides on Mars. These values of k₂ and the mean moment of inertia impose a strong new constraint on the model of the planet. The models of the Martian interior are elastic, while k₂ contains both elastic and inelastic components. We thoroughly examined the problem of partitioning the Love number k₂ into elastic and inelastic components. The information necessary to construct models of the planet (observation data, choice of a chemical model, and the cosmogonic aspect of the problem) are discussed in the introduction. The model of the planet comprises four submodels—a model of the outer porous layer, a model of the consolidated crust, a model of the silicate mantle, and a core model. We estimated the possible content of hydrogen in the core of Mars. The following parameters were varied while constructing the models: the ferric number of the mantle (Fe#) and the sulfur and hydrogen content in the core. We used experimental data concerning the pressure and temperature dependence of elastic properties of minerals and the information about the behavior of Fe(γ-Fe ), FeS, FeH, and their mixtures at high P and T. The model density, pressure, temperature, and compressional and shear velocities are given as functions of the planetary radius. The trial model M13 has the following parameters: Fe#=0.20; 14 wt % of sulfur in the core; 50 mol % of hydrogen in the core; the core mass is 20.9 wt %; the core radius is 1699 km; the pressure at the mantle-core boundary is 20.4 GPa; the crust thickness is 50 km; Fe is 25.6 wt %; the Fe/Si weight ratio is 1.58, and there is no perovskite layer. The model gives a radius of the Martian core within 1600–1820 km while ≥30 mol % of hydrogen is incorporated into the core. When the inelasticity of the Martian interior is taken into account, the Love number k₂ increases by several thousandths; therefore, the model radius of the planetary core increases as well. The prognostic value of the Chandler period of Mars is 199.5 days, including one day due to inelasticity. Finally, we calculated parameters of the equilibrium figure of Mars for the M13 model: J ₂ ⁰ = 1.82 × 10^?3, J ₄ ⁰ = ?7.79 × 10^?6, e _c-m ^D = 1/242.3 (the dynamical flattening of the core-mantle boundary).     

Jupiter and Super-Earth embedded in a gaseous disc

In this paper we investigate the evolution of a pair of interacting planets – a Jupiter-mass planet and a Super-Earth with a mass of  5.5 M _⊕  – orbiting a Solar-type star and embedded in a gaseous protoplanetary disc. We focus on the effects of type I and II orbital migrations, caused by the planet–disc interaction, leading to the capture of the Super-Earth in first-order mean-motion resonances by the Jupiter. The stability of the resulting resonant system in which the Super-Earth is on the internal orbit relative to the Jupiter is studied numerically by means of full 2D hydrodynamical simulations. Our main aim is to determine the Super-Earth behaviour in the presence of the gas giant in the system. It is found that the Jupiter captures the Super-Earth into the interior 3:2 or 4:3 mean-motion resonance, and that the stability of such configurations depends on the initial positions of the planets and on the evolution of the eccentricity. If the initial separation of the orbits of the planets is larger than or close to that required for the exact resonance, the final outcome is the migration of the pair of planets at a rate similar to that of the gas giant, at least for the time of our simulations. Otherwise, we observe a scattering of the Super-Earth from the disc. The evolution of planets immersed in a gaseous disc is compared with their behaviour in the case of the classical three-body problem when the disc is absent.     

基于无量纲的轨道参数开展卫星性质统计研究

目前已发现了285颗围绕太阳系八大行星公转的卫星, 它们的轨道和物理性质呈现了丰富多样性. 目前为止, 几乎所有的卫星研究工作都基于单个卫星系统或者卫星群, 似乎缺少统一的研究. 提出了一个新的与行星性质无关、只与恒星半径有关的轨道参数n, 定义为以太阳半径为单位的轨道半长轴的自然对数. 不同行星的卫星的n值都存在双极分布, 绝大部分卫星在$n\gtrsim2$区间, 其次在$n\lesssim-1$区间, 位于中间区域的行星则很少. 从卫星物理参数和轨道参数与n的关系中发现, 分属六大行星的卫星有明显的共同特征. 首先, 轨道偏心率和轨道倾角偏大的卫星的n值都在3.5左右, 它们都是巨行星的不规则卫星. 其次, n值在-1和1之间的卫星绝大部分体积大、质量大、反照率高、自转速度慢. 从文献中找到11颗系外卫星候选体, 获得了它们轨道n值和卫星质量, 发现后者也是在-1< n< 1区间最大,其他区间偏小.这些统一的 规律暗示,太阳系内不同行星的卫星形成机制以及太阳系外卫星的形成机制可能一样或类似.     

A Modified Gooding Method to Calculate Inclination Functions

In this paper, the expression of V k_lm(I) in the Gooding method is rewritten to be the form convenient for calculation, and a standard recursive lm procedure is used to calculate Ak_lm(I). We have rewritten the Gooding's program under the assumption that l and k have the same odd-even parity, this makes the program be shorten for one half, the computational effciency and readability of the program be raised, the computing time be shortened for 41%, and the computational accuracy and stability are also slightly improved.     

Ringlet–satellite interactions

We study the interaction of a satellite and a nearby ringlet on eccentric and inclined orbits. Secular torques originate from mean motion resonances and the secular interaction potential which represents the m  = 1 global modes of the ring. The torques act on the relative eccentricity and inclination. The resonances damp the relative eccentricity. The inclination instability owing to the resonances is turned off by a finite differential eccentricity of the order of 0.27 for nearly coplanar systems. The secular potential torque damps the eccentricity and inclination and does not affect the relative semi-major axis; also, it suppresses the inclination instability that persists at small differential eccentricities. The damping of the relative eccentricity and inclination forces an initially circular and planar small mass ringlet to reach the eccentricity and inclination of the satellite. When the planet is oblate, the interaction of the satellite damps the proper precession of a small mass ringlet so that it precesses at the satellite's rate independently of their relative distance. The oblateness of the primary modifies the long-term eccentricity and inclination magnitudes and introduces a constant shift in the apsidal and nodal lines of the ringlet with respect to those of the satellite. These results are applied to Saturn's F-ring, which orbits between the moons Prometheus and Pandora.