The road to Earth twins – Karl Schwarzschild Award Lecture 2010

A rich population of low‐mass planets orbiting solar‐type stars on tight orbits has been detected by Doppler spectroscopy. These planets have masses in the domain of super‐Earths and Neptune‐type objects, and periods less than 100 days. In numerous cases these planets are part of very compact multiplanetary systems. Up to seven planets have been discovered orbiting one single star. These low‐mass planets have been detected by the HARPS spectrograph around 30 % of solar‐type stars. This very high occurrence rate has been recently confirmed by the results of the Kepler planetary transit space mission. The large number of planets of this kind allows us to attempt a first characterization of their statistical properties, which in turn represent constraints to understand the formation process of these systems. The achieved progress in the sensitivity and stability of spectrographs have already led to the discovery of planets with masses as small as 1.5 M_⊕ (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constraints on the location of a putative distant massive body in the Solar System from recent planetary data

We analytically work out the long-term variations caused on the motion of a planet orbiting a star by a very distant, pointlike massive object X. Apart from the semi-major axis a, all the other Keplerian osculating orbital elements experience long-term variations which are complicated functions of the orbital configurations of both the planet itself and of X. We infer constraints on the minimum distance d _X at which X may exist by comparing our prediction of the long-term variation of the longitude of the perihelion \({\varpi}\) to the latest empirical determinations of the corrections \({\Delta\dot\varpi}\) to the standard Newtonian/Einsteinian secular precessions of several solar system planets recently estimated by independent teams of astronomers. We obtain the following approximate lower bounds on d _X for the assumed masses of X quoted in brackets: 150–200 au (Mars), 250–450 au \(({0.7 m_{\oplus}})\), 3500–4500 au (4 m _Jup).     

The 1/1 resonance in extrasolar systems

We present families of symmetric and asymmetric periodic orbits at the 1/1 resonance, for a planetary system consisting of a star and two small bodies, in comparison to the star, moving in the same plane under their mutual gravitational attraction. The stable 1/1 resonant periodic orbits belong to a family which has a planetary branch, with the two planets moving in nearly Keplerian orbits with non zero eccentricities and a satellite branch, where the gravitational interaction between the two planets dominates the attraction from the star and the two planets form a close binary which revolves around the star. The stability regions around periodic orbits along the family are studied. Next, we study the dynamical evolution in time of a planetary system with two planets which is initially trapped in a stable 1/1 resonant periodic motion, when a drag force is included in the system. We prove that if we start with a 1/1 resonant planetary system with large eccentricities, the system migrates, due to the drag force, along the family of periodic orbits and is finally trapped in a satellite orbit. This, in principle, provides a mechanism for the generation of a satellite system: we start with a planetary system and the final stage is a system where the two small bodies form a close binary whose center of mass revolves around the star.     

Dynamical relaxation and massive extrasolar planets

Following the suggestion of Black that some massive extrasolar planets may be associated with the tail of the distribution of stellar companions, we investigate a scenario in which 5 N 100 planetary mass objects are assumed to form rapidly through a fragmentation process occuring in a disc or protostellar envelope on a scale of 100 au. These are assumed to have formed rapidly enough through gravitational instability or fragmentation that their orbits can undergo dynamical relaxation on a time-scale of ∼100 orbits.
Under a wide range of initial conditions and assumptions, the relaxation process ends with either (i) one potential 'hot Jupiter' plus up to two 'external' companions, i.e. planets orbiting near the outer edge of the initial distribution; (ii) one or two 'external' planets or even none at all; (iii) one planet on an orbit with a semi-major axis of 10 to 100 times smaller than the outer boundary radius of the inital distribution together with an 'external' companion. Most of the other objects are ejected and could contribute to a population of free-floating planets. Apart from the potential 'hot Jupiters', all the bound objects are on orbits with high eccentricity, and also with a range of inclination with respect to the stellar equatorial plane. We found that, apart from the close orbiters, the probability of ending up with a planet orbiting at a given distance from the central star increases with the distance. This is because of the tendency of the relaxation process to lead to collisions with the central star. The scenario we envision here does not impose any upper limit on the mass of the planets. We discuss the application of these results to some of the more massive extrasolar planets.     

Dynamical friction for accelerated motion in a gaseous medium

Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. This interaction is usually derived assuming that the perturber has a constant velocity. In realistic situations, motion is accelerated as for instance by dynamical friction itself. Here, we study the effect of acceleration on the dynamical friction force. We characterize the density enhancement associated with a constantly accelerating perturber with rectilinear motion in an infinite homogeneous gaseous medium and show that dynamical friction is not a local force and that its amplitude may depend on the perturber's initial velocity. The force on an accelerating perturber is maximal between Mach 1 and Mach 2, where it is smaller than the corresponding uniform motion friction. In the limit where the perturber's size is much smaller than the distance needed to change the Mach number by unity through acceleration, a subsonic perturber feels a force similar to uniform motion friction only if its past history does not include supersonic episodes. Once an accelerating perturber reaches large supersonic speeds, accelerated motion friction is marginally stronger than uniform motion friction. The force on a decelerating supersonic perturber is weaker than uniform motion friction as the velocity decreases to a few times the sound speed. Dynamical friction on a decelerating subsonic perturber with an initial Mach number larger than 2 is much larger than uniform motion friction and tends to a finite value as the velocity vanishes in contrast to uniform motion friction.     

The heliospheric plasma tail under the influence of charge exchange processes with interstellar H atoms

The relative motion of the solar system with respect to the ambient interstellar medium is known to form a plasma interface region where the subsonic interstellar and solar wind plasma flows adapt to a pressure equilibrium surface, called the heliopause. Inside this discontinuity surface the solar plasma is deflected from the upwind to the downwind side, finally escaping from the solar system along a heliospheric tail. Due to continuous charge exchange interactions with interstellar H atoms entering from the tailward flanks of the heliopause tail plasma, originating from shocked solar wind, changes its thermodynamic character by cooling and deceleration while passing along the tail to larger downstream distances. Here we describe this charge-exchange-induced modification of the tail plasma up to a final assimilation into the interstellar plasma. On the other hand neutral H atoms are produced by means of charge exchange interactions in the heliotail with velocities by which these atoms are shot back into the inner heliosphere. We calculate the velocity distribution of such H atoms entering the inner heliosphere from the downwind direction and study their contribution to the H-pick-up ion production in the downwind region. As we show in this paper, total H-pick-up ion production rates in the downwind region are dominated by ionization of such anti-tailward H atoms within the orbit of the earth. They also dominate the pick-up ion energy spectrum beyond 4keV at distances between 1 and 10AU.     

Planetary microlensing signals from the orbital motion of the source star around the common barycentre

With several detections, the technique of gravitational microlensing has proven useful for studying planets that orbit stars at Galactic distances, and it can even be applied to detect planets in neighbouring galaxies. So far, planet detections by microlensing have been considered to result from a change in the bending of light and the resulting magnification caused by a planet around the foreground lens star. However, in complete analogy to the annual parallax effect caused by the revolution of the Earth around the Sun, the motion of the source star around the common barycentre with an orbiting planet can also lead to observable deviations in microlensing light curves that can provide evidence for the unseen companion. We discuss this effect in some detail and study the prospects of microlensing observations for revealing planets through this alternative detection channel. Given that small distances between lens and source star are favoured, and that the effect becomes nearly independent of the source distance, planets would remain detectable even if their host star is located outside the Milky Way with a sufficiently good photometry (exceeding present-day technology) being possible. From synthetic light curves arising from a Monte Carlo simulation, we find that the chances for such detections are not overwhelming and appear practically limited to the most massive planets (at least with current observational set-ups), but they are large enough for leaving the possibility that one or the other signal has already been observed. However, it may remain undetermined whether the planet actually orbits the source star or rather the lens star, which leaves us with an ambiguity not only with respect to its location, but also to its properties.     

A New Way that Planets Can Affect the Sun

We derive a perturbation inside a rotating star that occurs when the star is accelerated by orbiting bodies. If a fluid element has rotational and orbital components of angular momentum with respect to the inertially fixed point of a planetary system that are of opposite sign, then the element may have potential energy that could be released by a suitable flow. We demonstrate the energy with a very simple model in which two fluid elements of equal mass exchange positions, calling to mind a turbulent field or natural convection. The exchange releases potential energy that, with a minor exception, is available only in the hemisphere facing the barycenter of the planetary system. We calculate its strength and spatial distribution for the strongest case (“vertical”) and for weaker horizontal cases whose motions are all perpendicular to gravity. The vertical cases can raise the kinetic energy of a few well positioned convecting elements in the Sun’s envelope by a factor ≤7. This is the first physical mechanism by which planets can have a nontrivial effect on internal solar motions. Occasional small mass exchanges near the solar center and in a recently proposed mixed shell centered at 0.16R _s would carry fresh fuel to deeper levels. This would cause stars like the Sun with appropriate planetary systems to burn somewhat more brightly and have shorter lifetimes than identical stars without planets. The helioseismic sound speed and the long record of sunspot activity offer several bits of evidence that the effect may have been active in the Sun’s core, its envelope, and in some vertically stable layers. Additional proof will require direct evidence from helioseismology or from transient waves on the solar surface.     

Development of a comet as it pursues its orbit

The properties of cometary dust-swarms in almost parabolic long-period orbits are examined. In general their self-gravitation is stronger than the solar disruptive influence for all except the relatively small part of the orbit within planetary distances during which the sun dominates by so great a factor that the individual particles of the swarm pursue independent orbits apart from the possibility of collisions between them. At aphelion the internal relative speeds of particles are only a few centimetres per second, but at and near perihelion they may rise to the order of a kilometre per second. For purely dynamical reasons the extent of the swarm in directions perpendicular to the orbital motion will strongly diminish as perihelion is approached and correspondingly increase thereafter, while the dimension along the orbit will change in direct proportion to the orbital velocity. Every particle must cross through the median orbital plane near perihelion, and collisions between a proportion of the particles will occur at speeds capable of fragmenting them into myriads of smaller dustparticles, also heating them at and near the colliding elements of their surfaces. Increase of reflected sunlight will result and also release of material in gaseous form by solar plus collisional heating. Sufficiently finely divided dust particles will be driven out of the comet by radiation-pressure to form a dust-tail, while suitable gaseous compounds if present will be driven out to give a gas-tail. For Sungrazing comets, complete gasification must occur at and near perihelion, and very considerable extension along the orbit. Such comets would recondense to small solid particles on receding again from the Sun. The effect of passage of the solar system through interstellar gas-clouds is shown to be capable of substantially affecting the angular momentum of a comet about the Sun, thus accounting for the existence of comets with high values of perihelion-distance. This same process would enable cometary particles to adsorb interstellar gases at their surfaces and regenerate their gas-content. The mass-loss by a comet at each return strongly indicates, that comets cannot have originated at the same time as the planets, a result further supported by the rapid expulsion of entire comets through purely dynamical action of the planets. That the quiescent structure of comets consists of a vast widely spaced swarm of minute dust-particles receives circumstantial support from the highly varied and peculiar properties long since recorded for numerous comets. These properties exhibit such erratic diversity as to make clear that only a theory involving considerable range of essential parameters can be capable of accounting for them adequately.     

HD 12661行星系统构形的形成与稳定性

最近的多普勒观测表明恒星HD 12661周围存在两颗中等偏心率轨道上运行的行星,内行星的最小质量为2．3木星质量,轨道周期为263．6天;外行星的最小质量为1．57木星质量,轨道周期为1444．5天．该系统的稳定性要求两颗行星处在平运动轨道共振．用数值方法研究了该系统形成初期在恒星气体盘作用下的轨道迁移与稳定性,计算了行星在迁移中被平运动共振俘获的概率．发现这两颗行星目前很可能正处在11:2平运动共振边缘,且运动是混沌的,从而澄清了关于系统目前构形的不同说法,并且很可能在系统形成后行星迁移到目前构形时,气体盘几乎消失了．     

Extraterrestrial microspherules and iron needles in the interstellar medium

Microspherules in Paleozoic-Mesozoic bedded chert, presumed to be of extraterrestrial origin and comprised of clusters of iron needles,may represent an early stage in the aggregation of the inner planets. A fraction of the constituent iron needles will be expected to be carried along with expanding gas to the periphery of the solar nebula where the outer planets and comets condensed. A substantial fraction of iron needles would escape into interstellar space and add to the population of interstellar grains. Iron needles could contribute substantially to interstellar polarization and to the infrared opacity of the interstellar medium.     

A Perturbative Treatment of The Co-Orbital Motion

We develop a formalism of the non-singular evaluation of the disturbing function and its derivatives with respect to the canonical variables. We apply this formalism to the case of the perturbed motion of a massless body orbiting the central body (Sun) with a period equal to that of the perturbing (planetary) body. This situation is known as the co-orbital motion, or equivalently, as the 1/1 mean motion commensurability. Jupiter's Trojan asteroids, Earth's co-orbital asteroids (e.g., (3753) Cruithne, (3362) Khufu), Mars' co-orbital asteroids (e.g., (5261) Eureka), and some Jupiter-family comets are examples of the co-orbital bodies in our solar system. Other examples are known in the satellite systems of the giant planets. Unlike the classical expansions of the disturbing function, our formalism is valid for any values of eccentricities and inclinations of the perturbed and perturbing body. The perturbation theory is used to compute the main features of the co-orbital dynamics in three approximations of the general three-body model: the planar-circular, planar-elliptic, and spatial-circular models. We develop a new perturbation scheme, which allows us to treat cases where the classical perturbation treatment fails. We show how the families of the tadpole, horseshoe, retrograde satellite and compound orbits vary with the eccentricity and inclination of the small body, and compute them also for the eccentricity of the perturbing body corresponding to a largely eccentric exoplanet's orbit.This revised version was published online in October 2005 with corrections to the Cover Date.     

Regularity of Extrasolar Planetary Systems and the Role of the Star Metallicity in the Formation of Planets (Review)

The discovery in 1995 of the first extrasolar giant planet 51 Peg b initiated the physics of extrasolar planetary systems. By May 2004, the total number of the detected planets orbiting other stars was 122, including 24 hot jupiters, which have a semimajor axis of the orbit of less than 0.15 AU. Due to the high activity of researchers who work with the radial-velocity method, the probable candidates, say, in the 75-parsec radius, are quickly exhausted. The OGLE-type objects, even if their number increases, may only slightly contribute to the physics of extrasolar planets (or exoplanets), because even to determine the type of the companion (a giant planet, brown dwarf, or star of small mass) is extremely problematic for such weak objects. A search for Earth-like planets is still far beyond the technical capabilities: the Keplerian velocity of the Sun induced by the Earth is only 0.09 m/s, which requires to improve the results obtained by a factor of 20–30. Particularly important results were obtained in the observations of transits of the object HD 209458b, which became the only object of this type namely due to transits. The hope of finding another short-period object with similar transits is becoming less and less. The important role of the star metallicity in the formation of planetary systems predicted during the first years after the discovery of exoplanets has gained recognition and been developed successfully. Metallicity has become an indicator of the possible presence of planetary systems and, probably, even determines the type of planets. This review also considers the statistical data on the orbital and mass characteristics of exoplanets.     

The approach to collapse of molecular clouds

The dense molecular cloud cores that form stars, like other self-gravitating objects, undergo bulk oscillations. Just at the point of gravitational instability, their fundamental oscillation mode has zero frequency. We study, using perturbation theory, the evolution of a spherical cloud that possesses such a frozen mode. We find that the cloud undergoes a prolonged epoch of subsonic, accelerating contraction. This slow contraction occurs whether the cloud is initially inflated or compressed by the oscillation. The subsonic motion described here could underlie the spectral infall signature observed in many starless dense cores.     

Generation of a secular system in the analytical theory for the motion of the moon

In order to generate an analytical theory of the motion of the Moon by considering planetary perturbations, a procedure of general planetary theory (GPT) is used. In this case, the Moon is considered as an addition planet to the eight principal planets. Therefore, according to the GPT procedure, the theory of the Moon’s orbital motion can be presented in the form of series with respect to the evolution of eccentric and oblique variables with quasi-periodic coefficients, which are the functions of mean longitudes for principal planets and the Moon. The relationship between evolution variables and the time is determined by a trigonometric solution for the independent secular system that describes the secular motion of a perigee and the Moon node by considering secular planetary inequalities. Principal planetary coordinates required for generating the theory of the motion of the Moon includes only Keplerian terms, the intermediate orbit, and the linear theory with respect to eccentricities and inclinations in the first order relative to the masses. All analytical calculations are performed by means of the specialized echeloned Poisson Series Processor EPSP.     

Orbital migrations in planetesimal discs: N-body simulations and the resonant dynamical friction

We have performed N -body numerical simulations of the exchange of angular momentum between a massive planet and a 3D Keplerian disc of planetesimals. Our interest is directed at the study of the classical analytical expressions of the lineal theory of density waves, as representative of the dynamical friction in discs 'dominated by the planet' and the orbital migration of the planets with regard to this effect. By means of a numerical integration of the equations of motion, we have carried out a set of numerical experiments with a large number of particles  ( N ≥10 000)  , and planets with the mass of Jupiter, Saturn and one core mass of the giant planets in the Solar system  ( M _c=10 M_⊕)  . The torque, measured in a phase in which a 'steady forcing' is clearly measurable, yields inward migration in a minimum-mass solar disc  (Σ∼10 g cm^-2  ), with a characteristic drift time of ∼ a few 10⁶ yr. The planets predate the disc, but the orbital decay rate is not sufficient to allow accretion in a time-scale relevant to the formation of giant planets. We found reductions of the measured torque on the planet, with respect to the linear theory, by a factor of 0.38 for M _c, 0.04 for Saturn and 0.01 for Jupiter, due to the increase in the perturbation on the disc. The behaviour of planets whose mass is larger than M _c is similar to the one of type II migrators in gaseous discs. Our results suggest that, in a minimum mass, solar planetesimals disc, type I migrations occur for masses smaller than M _c, whereas for this mass value it could be a transition zone between the two types of migration.     

Dynamics Of 2/1 Resonant Extrasolar Systems Application to HD82943 and GLIESE876

A complete study is made of the resonant motion of two planets revolving around a star, in the model of the general planar three body problem. The resonant motion corresponds to periodic motion of the two planets, in a rotating frame, and the position and stability properties of the periodic orbits determine the topology of the phase space and consequently play an important role in the evolution of the system. Several families of symmetric periodic orbits are computed numerically, for the 2/1 resonance, and for the masses of some observed extrasolar planetary systems. In this way we obtain a global view of all the possible stable configurations of a system of two planets. These define the regions of the phase space where a resonant extrasolar system could be trapped, if it had followed in the past a migration process.The factors that affect the stability of a resonant system are studied. For the same resonance and the same planetary masses, a large value of the eccentricities may stabilize the system, even in the case where the two planetary orbits intersect. The phase of the two planets (position at perihelion or aphelion when the star and the two planets are aligned) plays an important role, and the change of the phase, other things being the same, may destabilize the system. Also, the ratio of the planetary masses, for the same total mass of the two planets, plays an important role and the system, at some resonances and some phases, is destabilized when this ratio changes.The above results are applied to the observed extrasolar planetary systems HD 82943, Gliese 876 and also to some preliminary results of HD 160691. It is shown that the observed configurations are close to stable periodic motion.     

第三体摄动分析解的一种表达式

在太阳系中,大行星、小行星和卫星（包括自然卫星和人造卫星）等对应的运动问题,都可以处理成受摄二体问题,而摄动源又多为第三体,作为第三体的摄动天体,有的比运动天体离中心天体近,有的则相反,前者称为内摄内体,全者则称为外摄天体,对一个具体的运动天体,可以同时出现这两个摄动天体,但是,只要运动天体与摄动天体的轨道都建立在以中心天体（质心）为坐标原点的同一坐标系内,那么在一定条件下（即除运动天体与摄动天体     

Exobiology, the study of the origin, evolution and distribution of life within the context of cosmic evolution: a review

The primary goal of exobiological research is to reach a better understanding of the processes leading to the origin, evolution and distribution of life on Earth or elsewhere in the universe. In this endeavour, scientists from a wide variety of disciplines are involved, such as astronomy, planetary research, organic chemistry, palaeontology and the various subdisciplines of biology including microbial ecology and molecular biology. Space technology plays an important part by offering the opportunity for exploring our solar system, for collecting extraterrestrial samples, and for utilizing the peculiar environment of space as a tool. Exobiological activities include comparison of the overall pattern of chemical evolution of potential precursors of life, in the interstellar medium, and on the planets and small bodies of our solar system; tracing the history of life on Earth back to its roots; deciphering the environments of the planets in our solar system and of their satellites, throughout their history, with regard to their habitability; searching for other planetary systems in our Galaxy and for signals of extraterrestrial civilizations; testing the impact of space environment on survivability of resistant life forms. This evolutionary approach towards understanding the phenomenon of life in the context of cosmic evolution may eventually contribute to a better understanding of the processes regulating the interactions of life with its environment on Earth.