arXiv subjects

Krzysztof Gozdziewski

Publications and source records attributed to Krzysztof Gozdziewski.

36 records · Page 2Linked to original sources

arXiv2009

Relative equilibria in the unrestricted problem of a sphere and symmetric rigid body

We consider the unrestricted problem of two mutually attracting rigid bodies, an uniform sphere (or a point mass) and an axially symmetric body. We present a global, geometric approach for finding all relative equilibria (stationary solutions) in this model, which was already studied by Kinoshita (1970). We extend and generalize his results, showing that the equilibria solutions may be found by solving at most two non-linear, algebraic equations, assuming that the potential function of the symmetric rigid body is known explicitly. We demonstrate that there are three classes of the relative equilibria, which we call "cylindrical", "inclined co-planar", and "conic" precessions, respectively. Moreover, we also show that in the case of conic precession, although the relative orbit is circular, the point-mass and the mass center of the body move in different parallel planes. This solution has been yet not known in the literature.

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arXiv2009

First Results from the CHEPS: Exoplanets and the Discovery of an Eccentric Brown Dwarf in the Desert

We report the discovery of a brown dwarf on an eccentric orbit and with a semimajor axis that places it in the brown dwarf desert region around the star HD191760. The star has a spectral type of G3IV/V and a metallicity ([Fe/H]) of 0.29 dex. HD191760 adds to the small number of metal-rich stars with brown dwarf companions. The brown dwarf (HD191760b) is found to have an orbital period of 505.57+/-0.40 days and semimajor axis of 1.35+/-0.01 AU, placing it firmly in the brown dwarf desert. The eccentricity of HD191760b is found to be 0.63+/-0.01, meaning it reaches as close as 0.5 AU from the host star. Dynamical simulations indicate that no inner planets could reside at separations beyond ~0.17 AU due to the disastrous gravity imposed by HD191760b. In addition to these first results we also refine the orbits found for the exoplanets around the stars HD48265, HD143361 and HD154672. All 1-planet solutions are in agreement with those previously published by the Magellan Planet Search.

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arXiv2009

Is the HR 8799 extrasolar system destined for planetary scattering?

The recent discovery of a three-planet extrasolar system of HR 8799 by Marois et al. is a breakthrough in the field of the direct imaging. This great achievement raises questions on the formation and dynamical stability of the HR 8799 system, because Keplerian fits to astrometric data are strongly unstable during ~0.2Myr. We search for stable, self-consistent N-body orbits with the so called GAMP method that incorporates stability constraints into the optimization algorithm. Our searches reveal only small regions of stable motions in the phase space of three-planet, coplanar configurations. Most likely, if the planetary masses are in 10-Jupiter-mass range, they may be stable only if the planets are involved in two- or three-body mean motion resonances (MMRs). We found that 80% systems found by GAMP that survived 30Myr backwards integrations, eventually become unstable after 100Myr. It could mean that the HR 8799 system undergo a phase of planet-planet scattering. We test a hypothesis that the less certain detection of the innermost object is due to a blending effect. In such a case, two-planet best-fit systems are mostly stable, on quasi-circular orbits and close to the 5:2 MMR, resembling the Jupiter-Saturn pair.

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arXiv2009

Equilibria in the secular, non-coplanar two-planet problem

We investigate the secular dynamics of a planetary system composed of the parent star and two massive planets in mutually inclined orbits. The dynamics are investigated in wide ranges of semi-major axes ratios (0.1-0.667), and planetary masses ratios (0.25-2) as well as in the whole permitted ranges of the energy and total angular momentum. The secular model is constructed by semi-analytic averaging of the three-body system. We focus on equilibria of the secular Hamiltonian (periodic solutions of the full system), and we analyze their stability. We attempt to classify families of these solutions in terms of the angular momentum integral. We identified new equilibria, yet unknown in the literature. Our results are general and may be applied to a wide class of three-body systems, including configurations with a star and brown dwarfs and sub-stellar objects. We also describe some technical aspects of the semi-numerical averaging. The HD 12661 planetary system is investigated as an example configuration.

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arXiv2009

On the habitability of the OGLE-2006-BLG-109L planetary system

We investigate the dynamics of putative Earth-mass planets in the habitable zone (HZ) of the extrasolar planetary system OGLE-2006-BLG-109L, a close analog of the Solar system. Our work is inspired by work of Malhotra and Minton (2008). Using the linear Laplace-Lagrange theory, they identified a strong secular resonance that may excite large eccentricity of orbits in the HZ. However, due to uncertain or unconstrained orbital parameters, the sub-system of Jupiters may be found in dynamically active region of the phase space spanned by low-order mean-motion resonances. To generalize this secular model, we construct a semi-analytical averaging method in terms of the restricted problem. The secular orbits of large planets are approximated by numerically averaged osculating elements. They are used to calculate the mean orbits of terrestrial planets by means of a high-order analytic secular theory developed in our previous works. We found regions in the parameter space of the problem in which stable, quasi-circular orbits in the HZ are permitted. The excitation of eccentricity in the HZ strongly depends on the apsidal angle of jovian orbits. For some combinations of that angle, eccentricities and semi-major axes consistent with the observations, a terrestrial planet may survive in low eccentric orbits. We also study the effect of post-Newtonian gravity correction on the innermost secular resonance.

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arXiv2008

Relativistic Lidov-Kozai resonance in binaries

We consider the secular dynamics of a binary and a planet in terms of non-restricted, hierarchical three-body problem, including the general relativity corrections to the Newtonian gravity. We determine regions in the parameter space where the relativistic corrections may be important for the long-term dynamics. We try to constrain the inclinations of putative Jovian planets in recently announced binary systems of HD 4113 and HD 156846.

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arXiv2008

Secular dynamics of coplanar, non-resonant planetary system under the general relativity and quadrupole moment perturbations

We construct a secular theory of a coplanar system of N-planets not involved in strong mean motion resonances, and which are far from collision zones. Besides the point-to-point Newtonian mutual interactions, we consider the general relativity corrections to the gravitational potential of the star and the innermost planet, and also a modification of this potential by the quadrupole moment and tidal distortion of the star. We focus on hierarchical planetary systems. A survey regarding model parameters (the masses, semi-major axes, spin rate of the star) reveals a rich and non-trivial dynamics of the secular system. Our study is focused on its equilibria. Such solutions predicted by the classic secular theory, which correspond to aligned (mode I) or anti-aligned (mode II) apsides, may be strongly affected by the gravitational corrections. The so called true secular resonance, which is a new feature of the classic two-planet problem discovered by Michtchenko & Malhotra (2004), may appear in other, different regions of the phase space of the generalized model. We found bifurcations of mode II which emerge new, yet unknown in the literature, secularly unstable equilibria and a complex structure of the phase space. These equilibria may imply secularly unstable orbital configurations even for nitially moderate eccentricities. The point mass gravity corrections can affect the long term-stability in the secular time scale, which may directly depend on the age of the host star through its spin rate. We also analyze the secular dynamics of the upsilon Andromede system in the realm of the generalized model. Also in this case of the three-planet system, new secular equilibria may appear.

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arXiv2008

A secular theory of coplanar, non-resonant planetary system

We present the secular theory of coplanar $N$-planet system, in the absence of mean motion resonances between the planets. This theory relies on the averaging of a perturbation to the two-body problem over the mean longitudes. We expand the perturbing Hamiltonian in Taylor series with respect to the ratios of semi-major axes which are considered as small parameters, without direct restrictions on the eccentricities. Next, we average out the resulting series term by term. This is possible thanks to a particular but in fact quite elementary choice of the integration variables. It makes it possible to avoid Fourier expansions of the perturbing Hamiltonian. We derive high order expansions of the averaged secular Hamiltonian (here, up to the order of 24) with respect to the semi-major axes ratio. The resulting secular theory is a generalization of the octupole theory. The analytical results are compared with the results of numerical (i.e., practically exact) averaging. We estimate the convergence radius of the derived expansions, and we propose a further improvement of the algorithm. As a particular application of the method, we consider the secular dynamics of three-planet coplanar system. We focus on stationary solutions in the HD 37124 planetary system.

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arXiv2008

The Successful Prediction of the Extrasolar Planet HD 74156 d

Most of the first-discovered extrasolar multi-planet systems were found to lie close to dynamically unstable configurations. However a few observed multi-planet systems (e.g. HD 74156) did not show this trait. Those systems could share this property if they contain an additional planet in between those that are known. Previous investigations identified the properties of hypothetical planets that would place these systems near instability. The hypothetical planet in HD 74156 was expected to have a mass about equal to that of Saturn, a semi-major axis between 0.9 and 1.4 AU, and an eccentricity less than 0.2. HD 74156 d, a planet with a mass of 1.3 Saturn masses at 1.04 AU with an eccentricity of 0.25, was recently announced. We have reanalyzed all published data on this system in order to place tighter constraints on the properties of the new planet. We find two possible orbits for this planet, one close to that already identified and another (with a slightly better fit to the data) at ~0.89 AU. We also review the current status of other planet predictions, discuss the observed single planet systems, and suggest other systems which may contain planets in between those that are already known. The confirmation of the existence of HD 74156 d suggests that planet formation is an efficient process, and planetary systems should typically contain many planets.

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arXiv2007

The long-term stability of extrasolar system HD 37124. Numerical study of resonance effects

We describe numerical tools for the stability analysis of extrasolar planetary systems. In particular, we consider the relative Poincare variables and symplectic integration of the equations of motion. We apply the tangent map to derive a numerically efficient algorithm of the fast indicator MEGNO (a measure of the maximal Lyapunov exponent) that helps to distinguish chaotic and regular configurations. The results concerning the three-planet extrasolar system HD 37124 are presented and discussed. The best fit solutions found in earlier works are studied more closely. The system involves Jovian planets with similar masses. The orbits have moderate eccentricities, nevertheless the best fit solutions are found in dynamically active region of the phase space. The long term stability of the system is determined by a net of low-order two-body and three-body mean motion resonances. In particular, the three-body resonances may induce strong chaos that leads to self-destruction of the system after Myrs of apparently stable and bounded evolution. In such a case, numerically efficient dynamical maps are useful to resolve the fine structure of the phase space and to identify the sources of unstable behavior.

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arXiv2006

On the extrasolar multi-planet system around HD160691

We re-analyze the precision radial velocity (RV) observations of HD160691 (mu Ara) by the Anglo-Australian Planet Search Team. The star is supposed to host two Jovian companions (HD160691b, HD160691c) in long-period orbits about 630 days and about 2500 days, respectively) and a hot-Neptune (HD160691d) in about 9 days orbit. We perform a global search for the best fits in the orbital parameters space with a hybrid code employing the genetic algorithm and simplex method. The stability of Keplerian fits is verified with the N-body model of the RV signal that takes into account the dynamical constraints (so called GAMP method). Our analysis reveals a signature of the fourth, yet unconfirmed, Jupiter-like planet HD160691e in about 307 days orbit. Overall, the global architecture of four-planet configuration recalls the Solar system. All companions of mu Ara move in quasi-circular orbits. The orbits of two inner Jovian planets are close to the 2:1 mean motion resonance. The alternative three-planet system involves two Jovian planets in eccentric orbits (e about 0.3), close to the 4:1 MMR, but it yields a significantly worse fit to the data. We also verify a hypothesis of the 1:1 MMR in the subsystem of two inner Jovian planets in the four-planet model.

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arXiv2006

Trojan pairs in the HD 128311 and HD 82943 planetary systems?

Two nearby stars, HD 128311 and HD 82943, are believed to host pairs of Jupiter-like planets involved in a strong first order 2:1 mean motion resonance (MMR). In this work we reanalyze available radial velocity (RV) measurements and demonstrate that it is also possible to explain the observed RV variations of the parents stars as being induced by a pair of Trojan planets (i.e., in a 1:1 MMR). We show that these Trojan configurations reside in extended zones of stability in which such systems may easily survive in spite of large masses of the planets, large eccentricities and nonzero mutual inclinations of their orbits. We also show that HD 82943 could harbor a previously unknown third planet about of 0.5 Jupiter masses in 2.1 AU orbit.

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arXiv2005

Orbital configurations and dynamical stability of multi-planet systems around Sun-like stars HD 202206, 14 Her, HD 37124 and HD 108874

We perform a dynamical analysis of the recently published radial velocity (RV) measurements of a few solar type stars which host multiple Jupiter-like planets. In particular, we re-analyze the data for HD 202206, 14 Her, HD 37124 and HD 108874. We derive dynamically stable configurations which reproduce the observed RV signals using our method called GAMP (an acronym of the Genetic Algorithm with MEGNO Penalty). The GAMP relies on the N-body dynamics and makes use of genetic algorithms merged with a stability criterion. For this purpose, we use the maximal Lyapunov exponent computed with the dynamical fast indicator MEGNO. Through a dynamical analysis of the phase-space in a neighborhood of the obtained best-fit solutions, we derive meaningful limits on the parameters of the planets. We demonstrate that GAMP is especially well suited for the analysis of the RV data which only partially cover the longest orbital period and/or correspond to multi-planet configurations involved in low-order mean motion resonances (MMRs). In particular, our analysis reveals a presence of a second Jupiter-like planet in the 14 Her system (14 Her c) involved in a 3:1 or 6:1 MMR with the known companion b. We also show that the dynamics of the HD 202206 system may be qualitatively different when coplanar and mutually-inclined orbits of the companions are considered. We demonstrate that the two outer planets in the HD 37124 system may reside in a close neighborhood of the 5:2 MMR. Finally, we found a clear indication that the HD 108874 system may be very close to, or locked in an exact 4:1 MMR.

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arXiv2005

About putative Neptune-like extrasolar planetary candidates

We re-analyze the precision radial velocity (RV) data of HD188015, HD114729, HD190360, HD147513 and HD208487. All these stars are supposed to host Jovian companions in long-period orbits. We test a hypothesis that the residuals of the 1-planet model of the RV or an irregular scatter of the measurements about the synthetic RV curve may be explained by the existence of additional planets in short-period orbits. We perform a global search for the best fits in the orbital parameters space with genetic algorithms and simplex method. This makes it possible to verify and extend the results obtained with an application of commonly used FFT-based periodogram analysis for identifying the leading periods. Our analysis confirms the presence of a periodic component in the RV data of HD190360 which may correspond to a hot-Neptune planet. We found four new cases when the 2-planet model yields significantly better fits to the RV data than the best 1-planet solutions. If the periodic variability of the residuals of single-planet fits has indeed a planetary origin then hot-Neptune planets may exist in these extrasolar systems. We estimate their orbital periods in the range of 7-20d and minimal masses about of 20 masses od the Earth.

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arXiv2004

Orbital solutions to the HD160691 (mu Arae) Doppler signal

We perform a dynamical analysis of the recently updated set of the radial velocity (RV) measurements of the HD160691 (mu Arae). The kinematic, 2-Keplerian model of the measurements leads to the best-fit solution in which the eccentricity of the outer planet is about 0.7 and its semi-major axis is about 4AU. The parameters of the inner planet are well determined. The eccentricity is about 0.3 and the semi-major axis is about 1.65AU. The best 2-Keplerian model leads to a catastrophically unstable configuration, self disrupting in less than 20,000yr. To derive dynamically stable configurations which are simultaneously consistent with the RV data, we use the so called GAMP (Genetic Algorithm with MEGNO Penalty). Using this method, we derive meaningful limits on the parameters of the outer planet which provide a stable behavior of the system. The best-fit solutions are located in a shallow valley of Chi^2, in the (a_c,e_c)-plane, extending over 2AU (for the formal 1sigma confidence interval of the best fit). We find two equally good best-fit solutions leading to the qualitatively different orbital configurations. One of them corresponds to the center of the 5:1 mean motion resonance (MMR) and the second one describes a configuration between the 6:1 and 17:2MMRs. The mu Arae system can be found in the zone confined to other low-order MMRs of the type p:1 with p>5. Our results support the classification of the mu Arae as a hierarchical planetary system, dynamically similar to other known multi-planet systems around HD12661 and HD169830. The results of the GAMP on the extended data set are fully consistent with our previous conclusions concerning a much shorter observational window.

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arXiv2004

Long term stability and dynamical environment of the PSR 1257+12 planetary system

We study the long-term dynamics of the PSR 1257+12 planetary system. Using the recently determined accurate initial condition by Konacki & Wolszczan (2003) who derived the orbital inclinations and the absolute masses of the planets B and C, we investigate the system stability by long-term, 1Gyr direct integrations. No secular changes of the semi-major axes eccentricities and inclinations appear during such an interval. This stable behavior is confirmed with the fast indicator MEGNO. The analysis of the orbital stability in the neighborhood of the nominal initial condition reveals that the PSR 1257+12 system is localized in a wide stable region of the phase space but close to a few weak 2 and 3-body mean motion resonances. The long term stability is additionally confirmed by a negligible exchange of the Angular Momentum Deficit between the innermost planet A and the pair of the outer planets B and C. An important feature of the system that helps sustain the stability is the secular apsidal resonance (SAR) between the planets B and C with the center of libration about 180deg. We find useful limits on the elements of the innermost planet A which are otherwise unconstrained by the observations. We also perform a preliminary study of the short-term dynamics of massless particles in the system.

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arXiv2003

The exosystems about HD169830 and HD12661: are they dynamical twins?

The new 2-planetary system around HD169830 has been announced during the XIX-th IAP Colloquium "Extrasolar Planets: Today & Tomorrow" (Paris, June 30 - July 4, 2003) by the Geneva Extrasolar Planet Search team. We study the orbital dynamics of this system in the framework of the $N$-body problem. The analysis of its orbital stability is performed using the long-term integrations and the fast indicators, the Mean Exponential Growth factor of Nearby Orbits and the Frequency Map Analysis. The HD169830 appears to be located in a wide stable region of the phase space. The ratio of the mean motions of the planets HD169830b and c is between low-order mean motion resonances, 9:1 and 10:1. The long-term integration of the coplanar configurations, conducted over 1Gyr, reveals that the eccentricities of the companions vary with a large amplitude about 0.4-0.5 but there is no sign of instability. The orbital parameters of the planets resemble those of another 2-planetary system, around HD12661. Both of them can be classified as hierarchical planetary systems. We investigate whether these two exosystems are dynamically similar. Such similarities may be important for finding out if the formation and subsequent orbital evolution of exoplanetary systems obey common rules.

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arXiv2003

The Janus head of the HD 12661 planetary system

In this work we perform a global analysis of the radial velocity curve of the HD 12661 system. Orbital fits that are obtained by the genetic and gradient algorithms of minimization reveal the proximity of the system to the 6:1 mean motion resonance. The orbits are locked in the secular resonance with apsidal axes librating about 180 deg with the full amplitude $\simeq (90,180) deg$. Our solution incorporates the mutual interaction between the companions. The stability analysis with the MEGNO fast indicator shows that the system is located in an extended stable zone of quasi-periodic motions. These results are different from those obtained on the basis of the orbital fit published by Fischer et al. (2003)

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