We present a method to measure the dynamical mass of extrasolar planets in multiple stellar systems with a single aperture from the ground using high-precision relative astrometry. To reach the precision needed, accurate monitoring of the astrometric stability (pixel scale, orientation, and field distortions of the detector) is necessary. Thus, we always observe an astrometric calibration cluster to compare these astrometric criteria with those of our observations. For our first target observed, the binary HD 19994, we achieved a relative precision of 100...150 µas which is sufficient to detect an astrometric companion around the A component down to about 5 MJup.

One of the most efficient methods used for exoplanet detection is the analysis of the radial velocity measurements of the host star, over a period of time. A newly proposed approach to analyze the radial velocity data is based on artificial neural networks (ANNs). The method is inspired from pattern recognition, a domain where ANNs are widely used. Preliminary results show the degree of similarity of the measured radial velocities to the theoretically computed effect of a multi-planetary system on a star. The present analysis can be the starting point for further classification of planetary systems using radial velocity curves.


We ask if Earth-like planets (terrestrial mass and habitable-zone orbit) can be detected in multi-planet systems, using astrometric and radial velocity observations. We report here the preliminary results of double-blind calculations designed to answer this question.


The Penn State/Toruń Centre for Astronomy Search for Planets Around Evolved Stars is a high-accuracy radial velocity (RV) survey aiming at planet detection around giant stars. It is based on observations obtained with the 9.2 m Hobby-Eberly Telescope. As proper interpretation of high accuracy RV data for red giants requires complete spectral analysis of targets we perform spectral modeling of all stars included in the survey. Typically, rotation velocities and metallicities are determined in addition to stellar luminosities and temperatures, which allows us to estimate stellar ages and masses. Here we present preliminary results of metallicity studies in our sample. We search for a metallicity dependence similar to that for dwarfs by comparing our results for a sample of 22 giants earlier than K5 showing significant RV variations with a control sample of 58 relatively RV-stable stars.

In this paper we present a short review of statistical properties of extrasolar planets, and of the core-accretion model and some of its extensions. We also present results of population synthesis models based on extended core-accretion planet formation models (taking into account disk structure and evolution and migration of the protoplanet, see Alibert et al. 2005a). The population synthesis is carried out by calculating the evolution of many disk-protoplanet systems, assuming initial conditions (in particular disk mass, disk lifetime and metallicity of the system) taken from observations. Taking into account the observational bias introduced by radial velocity surveys, we statistically compare the results of our models and the population of known extrasolar planets. We show that our models are able to quantitatively reproduce the mass and semimajor axes of extrasolar planets around solar type stars. Finally, we discuss the effect of the mass of the central star on the planet formation process and on the final planetary population.

As of today over 40 planetary systems have been discovered in binary star systems. In all cases the configuration appears to be circumstellar, where the planets orbit around one of the stars, the secondary acting as a perturber. The formation of planets in binary star systems is more difficult than around single stars due to the gravitational action of the companion on the dynamics of the protoplanetary disk. In this contribution we first briefly present the relevant observational evidence for planets in binary systems. Then the dynamical influence that a secondary companion has on a circumstellar disk will be analyzed through fully hydrodynamical simulations. We demonstrate that the disk becomes eccentric and shows a coherent precession around the primary star. Finally, fully hydrodynamical simulations of evolving protoplanets embedded in disks in binary star systems are presented. We investigate how the orbital evolution of protoplanetary embryos and their mass growth from cores to massive planets might be affected in this very dynamical environment. We consider, in particular, the planet orbiting the primary in the system γ Cephei.

Planet formation in binary star systems is a complex issue due to the gravitational perturbations of the companion star. One of the crucial steps of the core-accretion model is planetesimal accretion into large protoplanets which finally coalesce into planets. In a planetesimal swarm surrounding the primary star, the average mutual impact velocity determines if larger bodies form or if the population is grinded down to dust, halting the planet formation process. This velocity is strongly influenced by the companion gravitational pull and by gas drag. The combined effect of these two forces may act in favour of or against planet formation, setting a lower or equal probability of the existence of extrasolar planets around single or binary stars.
Planetesimal accretion in binaries has been studied so far with two different approaches. N-body codes based on the assumption that the disk is axisymmetric are very cost-effective since they allow the study of the mutual relative velocity with limited CPU usage. A large amount of planetesimal trajectories can be computed making it possible to outline the regions around the star where planet formation is possible. The main limitation of the N-body codes is the axisymmetric assumption. The companion perturbations affect not only the planetesimal orbits, but also the gaseous disk, by forcing spiral density waves. In addition, the overall shape of the disk changes from circular to elliptic.
Hybrid codes have been recently developed which solve the equations for the disk with a hydrodynamical grid code and use the computed gas density and velocity vector to calculate an accurate value of the gas drag force on the planetesimals. These codes are more complex and may compute the trajectories of only a limited number of planetesimals.

Hot super-Earths are exoplanets with masses ≤10 M⊕ and orbital periods ≤20 days. Around 8 hot super-Earths have been discovered in the neighborhood of the Solar System. In this lecture, we review the mechanisms for the formation of hot super-Earths, and dynamical effects that play important roles in sculpting the architecture of multiple planetary systems. Two example systems (HD 40307 and GJ 436) are presented to show the formation and evolution of hot super-Earths or Neptunes.

The resolution criterion for self-gravity in AMR codes derived by Truelove et al.  (1997) based on the Jeans length is a very robust one and thus quite popular. We believe that for some configurations, such as self-gravitating discs, there are reasons to supplement it in order to properly resolve gravitational instabilities and clump formation processes at reasonable computational costs.

We present a new multi-fluid, grid-based magnetohydrodynamics (MHD) code PIERNIK, which is based on the Relaxing Total Variation Diminishing (RTVD) scheme. The original scheme has been extended by an addition of dynamically independent, but interacting fluids: dust and a diffusive cosmic ray (CR) gas, described within the fluid approximation, with an option to add other fluids in an easy way. The code has been equipped with shearing-box boundary conditions, a selfgravity module, an Ohmic resistivity module, as well as other facilities which are useful in astrophysical fluid-dynamical simulations. The code is parallelized by means of an MPI library. In this paper we briefly introduce the basic elements of the RTVD MHD algorithm, following Trac & Pen (2003) and Pen et al.  (2003), and then focus on a conservative implementation of the shearing-box model, constructed with the aid of Masset's (2000) method. We present the results of a test example of the formation of a gravitationally bound object (a planet) in a self-gravitating and differentially rotating fluid.

We present a new multi-fluid, grid-based magnetohydrodynamics (MHD) code PIERNIK, which is based on the Relaxing Total Variation Diminishing (RTVD) scheme (Jin & Xin 1995). The original scheme (see Trac & Pen 2003 and Pen et al.  2003) has been extended by an addition of dynamically independent, but interacting fluids: dust and a diffusive cosmic ray (CR) gas, described within the fluid approximation, with an option to add other fluids in an easy way. The code has been equipped with shearing-box boundary conditions, a selfgravity module, an Ohmic resistivity module, as well as other facilities which are useful in astrophysical fluid-dynamical simulations. The code is parallelized by means of an MPI library. In this paper we introduce a multifluid extension of the RTVD scheme and present a test case of dust migration in a two-fluid disk composed of gas and dust. We demonstrate that due to the difference in azimuthal velocities of gas and dust and the drag force acting on both components, dust drifts towards maxima of the gas pressure distribution.

The first study of migration-induced resonances in a pair of Earth-like planets has been performed by Papaloizou & Szuszkiewicz (2005). They concluded that in the case of disparate masses embedded in a disc with the surface density expected for a minimum mass solar nebula at 5.2 au, the most likely resonances are ratios of large integers, such as 8:7. For equal masses, planets tend to enter into the 2:1 or 3:2 resonance. In Papaloizou & Szuszkiewicz (2005) the two low-mass planets have masses equal to 4 Earth masses, chosen to mimic the very well known example of two pulsar planets which are close to the 3:2 resonance. That study has stimulated quite a few interesting questions. One of them is considered here, namely how the behaviour of the planets close to the mean-motion resonance depends on the actual values of the masses of the planets. We have chosen a 3:2 commensurability and investigated the outcome of an orbital migration in the vicinity of this resonance in the case of a pair of equal mass super-Earths, whose mass is either 5 or 8 Earth masses.

We have investigated the evolution of a pair of interacting planets embedded in a gaseous disc, considering the possibility of the resonant capture of a Super-Earth by a Jupiter mass gas giant. First, we have examined the situation where the Super-Earth is on the internal orbit and the gas giant on the external one. It has been found that the terrestrial planet is scattered from the disc or the gas giant captures the Super-Earth into an interior 3:2 or 4:3 mean-motion resonance. The stability of the latter configurations depends on the initial planet positions and on eccentricity evolution. The behaviour of the system is different if the Super-Earth is the external planet. We have found that instead of being captured in the mean-motion resonance, the terrestrial planet is trapped at the outer edge of the gap opened by the gas giant. This effect prevents the occurrence of the first order mean-motion commensurability. These results are particularly interesting in light of recent exoplanet discoveries and provide predictions of what will become observationally testable in the near future.

Many multi-planet systems have been discovered in recent years. Some of them are in mean-motion resonances (MMR). Planet formation theory was successful in explaining the formation of 2:1, 3:1 and other low resonances as a result of convergent migration. However, higher order resonances require high initial orbital eccentricities in order to be formed by this process and these are in general unexpected in a dissipative disk. We present a way of generating large initial eccentricities using additional planets. This precedure allows us to form high order MMRs and predict new planets using a genetic N-body code.

The aim of this talk is to present the most recent advances in establishing plausible planetary system architectures determined by the gravitational tidal interactions between the planets and the disc in which they are embedded during the early epoch of planetary system formation. We concentrate on a very well defined and intensively studied process of the disc-planet interaction leading to the planet migration. We focus on the dynamics of the systems in which low-mass planets are present. Particular attention is devoted to investigation of the role of resonant configurations. Our studies, apart from being complementary to the fast progress occurring just now in observing the whole variety of planetary systems and uncovering their structure and origin, can also constitute a valuable contribution in support of the missions planned to enhance the number of detected multiple systems.

This chapter is a review of the dynamics of two-planet systems. It includes the study of averaged models of both secular and resonant planetary configurations. The introduction describes our understanding of long-term planetary behavior and stability. The next section introduces the presently known sample of 31 extra-solar systems and the classification of these systems with respect to their dynamical behavior. Their secular dynamics are described in Section 3, where we also introduce the main techniques commonly used for exploring dynamical features. We conclude this section by describing the effects of the proximity of a secular system to mean-motion resonances. Finally, phenomena related to mean-motion resonances are presented in Section 4.

The dynamical interactions that occur in newly formed planetary systems may reflect the conditions occurring in the protoplanetary disk out of which they formed. With this in mind, we explore the attainment and maintenance of orbital resonances by migrating planets in the terrestrial mass range. Migration time scales varying between ~106 yr and ~103 yr are considered. In the former case, for which the migration time is comparable to the lifetime of the protoplanetary gas disk, a 2:1 resonance may be formed. In the latter, relatively rapid migration regime commensurabilities of high degree such as 8:7 or 11:10 may be formed. However, in any one large-scale migration several different commensurabilities may be formed sequentially, each being associated with significant orbital evolution. We also use a simple analytic theory to develop conditions for first order commensurabilities to be formed. These depend on the degree of the commensurability, the imposed migration and circularization rates, and the planet mass ratios. These conditions are found to be consistent with the results of our simulations.

We consider two different general problems: a three body problem with one solid body, and a two body problem with two interacting solids. This can be a Sun-planet-satellite problem and a binary system of non spherical bodies respectively. We demonstrate that after adequate averaging, these problems can be reduced to non-trivial integrable problems for which we provide the complete solutions. These results should be useful for the understanding of the evolution of planetary and satellites' spin axes over long time-scales, and thus for the search of dynamical constraints on the evolution of the Solar System.

The outermost bodies of planetary systems embedded in a planetesimal disk migrate much faster than the other planets. The outward migration of such bodies is self-sustained by supplying fresh planetesimals up to the edge of the disk. We study the dynamics of gravitational interactions between an outer planet and massive planetesimals during this process. The investigation is based on using our N-body symplectic integrator. It is shown that the efficiency of the resonant capture of planetesimals during outward planetary migration depends on many parameters of the model. As a result of planetary migration, planetesimals can be transferred to a region located far from the planet without any resonant trapping. The reversion of the planetary migration is an important element of the process studied. We show that the migration of an Earth-mass planet in the trans-Neptunian planetesimal disk well reproduces the main orbital features of the “cold” Kuiper belt population.

Given the tendency of planets to form in multiples, and the observational evidence in support of the existence of potential planet-hosting stars in binaries or clusters, it is expected that extrasolar terrestrial planets are more likely to be found in multiple body systems. This paper discusses the prospects of the detection of terrestrial/habitable planets in multibody systems by presenting the results of a study of the long-term stability of these objects in systems with multiple giant planets (particularly those in eccentric and/or in mean-motion resonant orbits), systems with close-in Jupiter-like bodies, and systems of binary stars. The results of simulations show that while short-period terrestrial-class objects that are captured in near mean-motion resonances with migrating giant planets are potentially detectable via transit photometry or the measurement of the variations of the transit-timing due to their close-in Jovian-mass planetary companions, the prospect of the detection of habitable planets with the radial velocity technique is higher in systems with multiple giant planets outside the habitable zone and binary systems with moderately separated stellar companions.