@article{MTMT:1457218, title = {Co-orbital terrestrial planets in exoplanetary systems: a formation scenario}, url = {https://m2.mtmt.hu/api/publication/1457218}, author = {Beauge, C and Sándor, Zsolt and Érdi, Bálint and Süli, Áron}, doi = {10.1051/0004-6361:20066582}, journal-iso = {ASTRON ASTROPHYS}, journal = {ASTRONOMY & ASTROPHYSICS}, volume = {463}, unique-id = {1457218}, issn = {0004-6361}, abstract = {Aims. We study the formation of a hypothetical terrestrial-type body in the equilateral Lagrange points of a giant extrasolar planet. Starting from a swarm of planetesimals in stable tadpole orbits, we simulate its dynamical and collisional evolution under a wide range of different initial conditions and masses for both the Trojan population and its planetary companion. We also analyze the effects of gas drag from the interaction of the planetesimals with the nebular disk. Methods. The formation process is simulated with an N-body code that considers full gravitational interactions between the planetesimals and the giant planet. Gas interaction is modeled with Stokes and Epstein drags, where the drag coefficients are chosen following the results of full hydrodynamic simulations performed with the 2D public hydro-code FARGO. Results. In both gas-free and gas-rich scenarios, we have been able to obtain a single final terrestrial-type body in a stable tadpole orbit around one of the triangular Lagrange points of the system. However, due to gravitational instabilities within the swarm, the accretional process is not very efficient and the mass of the final planet never seems to exceed similar to 0.6 Earth masses, even when the total mass of the swarm is five times this value. Finally, we also included an orbital decay of the giant planet due to a type II migration. Although the accretional process shows evidence of a lower efficiency, a small terrestrial planet is still able to form, and follows the giant planet towards the habitable zone of the hosting star.}, keywords = {STABILITY; MIGRATION; MOTION; ACCRETION; PLANETESIMALS; DISKS; DYNAMICAL EVOLUTION; PRIMORDIAL SOLAR NEBULA; methods : N-body simulations; planets and satellites : formation; JUPITERS TROJAN ASTEROIDS; 1/1 RESONANCE; celestial mechanics}, year = {2007}, eissn = {1432-0746}, pages = {359-367}, orcid-numbers = {Sándor, Zsolt/0000-0003-1216-913X; Süli, Áron/0000-0003-0049-0233} } @article{MTMT:1457216, title = {Secondary resonances of co-orbital motions}, url = {https://m2.mtmt.hu/api/publication/1457216}, author = {Érdi, Bálint and Nagy, Imre and Sándor, Zsolt and Süli, Áron and Fröhlich, Georgina}, doi = {10.1111/j.1365-2966.2007.12228.x}, journal-iso = {MON NOT R ASTRON SOC}, journal = {MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY}, volume = {381}, unique-id = {1457216}, issn = {0035-8711}, abstract = {The size distribution of the stability region around the Lagrangian point L-4 is investigated in the elliptic restricted three-body problem as the function of the mass parameter and the orbital eccentricity of the primaries. It is shown that there are minimum zones in the size distribution of the stability regions, and these zones are connected with the secondary resonances between the frequencies of librational motions around L-4. The results can be applied to hypothetical Trojan planets for predicting values of the mass parameter and the eccentricity for which such objects can be expected or their existence is less probable.}, keywords = {EVOLUTION; STABILITY; planetary systems; 3 BODIES; TRIANGULAR POINTS; EXTRASOLAR PLANETARY SYSTEMS; JUPITERS TROJAN ASTEROIDS; methods : numerical; EXOPLANETARY SYSTEMS; SOLAR-SYSTEM; ELLIPTIC RESTRICTED PROBLEM; HABITABLE ZONES; methods: numerical; celestial mechanics}, year = {2007}, eissn = {1365-2966}, pages = {33-40}, orcid-numbers = {Nagy, Imre/0000-0002-1420-4296; Sándor, Zsolt/0000-0003-1216-913X; Süli, Áron/0000-0003-0049-0233; Fröhlich, Georgina/0000-0001-6428-6536} } @article{MTMT:1457212, title = {Survey of the stability region of hypothetical habitable Trojan planets}, url = {https://m2.mtmt.hu/api/publication/1457212}, author = {Schwarz, Richárd and Dvorak, R and Süli, Áron and Érdi, Bálint}, doi = {10.1051/0004-6361:20077994}, journal-iso = {ASTRON ASTROPHYS}, journal = {ASTRONOMY & ASTROPHYSICS}, volume = {474}, unique-id = {1457212}, issn = {0004-6361}, abstract = {Aims. In this work we study the dynamical possibility in extrasolar planetary systems that a terrestrial planet can exist in 1:1 mean motion resonance with a Jovian-like planet. We compiled a catalogue of hypothetical habitable Trojan planets, to be able to make a stability forecast for further extrasolar planetary systems discovered in the future. When speaking of habitability we also took the influence of the spectral type of the central star into account. Methods. We integrated some 106 orbits of fictitious Trojans around the Lagrangian points for up to 107 orbital periods of the primary bodies and checked the stability of the orbital elements and their chaoticity with the aid of the Lyapunov characteristic indicator and maximum eccentricity. The computations were carried out using the dynamical model of the elliptic, restricted three-body problem that consists of a central star, a gas giant moving in the habitable zone, and a hypothetical (massless) terrestrial planet. Results. Our investigations have shown that 7 exoplanetary systems can harbour habitable Trojan planets with stable orbits (HD93083, HD17051, HD28185, HD27442, HD188015, HD99109, and HD221287, which is a recently discovered system). The comparison of the investigated systems with our catalogue showed matching results, so that we can use the catalogue in practice.}, keywords = {DYNAMICS; CAPTURE; EXPONENTS; STARS; 1/1 RESONANCE; ZONES; CO-ORBITAL MOTION; astrobiology; stars : planetary systems; ASTEROIDS; EXOPLANETARY SYSTEMS; SOLAR-SYSTEM; celestial mechanics}, year = {2007}, eissn = {1432-0746}, pages = {1023-1029}, orcid-numbers = {Süli, Áron/0000-0003-0049-0233} } @article{MTMT:1457220, title = {Trojan planets in HD 108874?}, url = {https://m2.mtmt.hu/api/publication/1457220}, author = {Schwarz, Richárd and Dvorak, R and Lohinger, EP and Süli, Áron and Érdi, Bálint}, doi = {10.1051/0004-6361:20066284}, journal-iso = {ASTRON ASTROPHYS}, journal = {ASTRONOMY & ASTROPHYSICS}, volume = {462}, unique-id = {1457220}, issn = {0004-6361}, abstract = {Aims: It turned out recently that, in addition to a large planet with a semimajor axis a similar to 1 AU and a low eccentricity (e similar to 0.07), the extrasolar planetary system HD 108874 harbors another massive planet with 2.43 AU < a < 2.93 AU. The inner planet is orbiting the G5 host star in the habitable zone (= HZ); so that we could established stable regions for Earth-like Trojan planets. Methods. We integrated some 105 orbits of fictitious Trojans around the Lagrangian points for up to 107 years and checked the stability of the orbital elements and their chaoticity with the aid of the Fast Lyapunov Indicator. Results. It turns out that this multiplanetary system is the first one where-with the uncertainties in eccentricity and semimajor axes of the outer planet-the existence of Trojan terrestrial planets in stable orbits in the HZ is possible for some combinations of the orbital parameters.}, keywords = {SYSTEMS; DYNAMICS; STABILITY; CHAOS; MOTION; STARS; 1/1 RESONANCE; stars : planetary systems; ORBITS; HABITABLE ZONES; celestial mechanics}, year = {2007}, eissn = {1432-0746}, pages = {1165-1170}, orcid-numbers = {Süli, Áron/0000-0003-0049-0233} } @article{MTMT:2794766, title = {Optimized Nekhoroshev stability estimates for the Trojan asteroids with a symplectic mapping model of co-orbital motion}, url = {https://m2.mtmt.hu/api/publication/2794766}, author = {Efthymiopoulos, C and Sándor, Zsolt}, doi = {10.1111/j.1365-2966.2005.09572.x}, journal-iso = {MON NOT R ASTRON SOC}, journal = {MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY}, volume = {364}, unique-id = {2794766}, issn = {0035-8711}, abstract = {This paper reports analytic estimates of the domain of Nekhoroshev stability for the orbits of Jupiter's Trojan asteroids calculated in the space of proper elements (Dp, ep), for a stability time exceeding the age of the Solar system (tstability= 1010 yr). The model used is a family of Hadjidemetriou mappings, for different values of the proper eccentricity ep, that represent the Poincaré sections of co-orbital motion in the Hamiltonian of the planar and circular restricted three-body problem. These explicit mappings are shown to reproduce accurately the dynamics that is implicitly induced by the corresponding Hamiltonian model. Optimal Nekhoroshev estimates are obtained by constructing the Birkhoff normal form for symplectic mappings. Our optimization is based on an `iterated remainder' criterion. The asymptotic behaviour of the Birkhoff series is determined by a precise analysis of the accumulation of small divisors in the series terms at consecutive orders of normalization. About 35 per cent of asteroids from a recent catalogue (AstDys), with proper inclination Ip<= 5°, are shown to be Nekhoroshev-stable over the age of the Solar system. By calculating a resonant Birkhoff normal form, this percentage increases to 48 per cent.}, keywords = {ASTEROIDS; celestial mechanics; Solar system: General; MINOR PLANETS}, year = {2005}, eissn = {1365-2966}, pages = {253-271}, orcid-numbers = {Sándor, Zsolt/0000-0003-1216-913X} } @article{MTMT:2215810, title = {Stability of co-orbital motion in exoplanetary systems}, url = {https://m2.mtmt.hu/api/publication/2215810}, author = {Érdi, Bálint and Sándor, Zsolt}, doi = {10.1007/s10569-004-3114-5}, journal-iso = {CELEST MECH DYN ASTR}, journal = {CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY}, volume = {92}, unique-id = {2215810}, issn = {0923-2958}, abstract = {The stability of co-orbital motions is investigated in such exoplanetary systems, where the only known giant planet either moves fully in the habitable zone, or leaves it for some part of its orbit. If the regions around the triangular Lagrangian points are stable, they are possible places for smaller Trojan-like planets. We have determined the nonlinear stability regions around the Lagrangian point L 4 of nine exoplanetary systems in the model of the elliptic restricted three-body problem by using the method of the relative Lyapunov indicators. According to our results, all systems could possess small Trojan-like planets. Several features of the stability regions are also discussed. Finally, the size of the stability region around L 4 in the elliptic restricted three-body problem is determined as a function of the mass parameter and eccentricity. © Springer 2005.}, keywords = {CO-ORBITAL MOTION; EXOPLANETS; Nonlinear stability}, year = {2005}, eissn = {1572-9478}, pages = {113-121}, orcid-numbers = {Sándor, Zsolt/0000-0003-1216-913X} } @article{MTMT:2215809, title = {Trojans in habitable zones}, url = {https://m2.mtmt.hu/api/publication/2215809}, author = {Schwarz, R and Pilat-Lohinger, E and Dvorak, R and Érdi, Bálint and Sándor, Zsolt}, doi = {10.1089/ast.2005.5.579}, journal-iso = {ASTROBIOLOGY}, journal = {ASTROBIOLOGY}, volume = {5}, unique-id = {2215809}, issn = {1531-1074}, abstract = {With the aid of numerical experiments we examined the dynamical stability of fictitious terrestrial planets in 1:1 mean motion resonance with Jovian-like planets of extrasolar planetary systems. In our stability study of the so-called "Trojan" planets in the habitable zone, we used the restricted three-body problem with different mass ratios of the primary bodies. The application of the three-body problem showed that even massive Trojan planets can be stable in the 1:1 mean motion resonance. From the 117 extrasolar planetary systems only 11 systems were found with one giant planet in the habitable zone. Out of this sample set we chose four planetary systems - HD17051, HD27442, HD28185, and HD108874 - for further investigation. To study the orbital behavior of the stable zone in the different systems, we used direct numerical computations (Lie Integration Method) that allowed us to determine the escape times and the maximum eccentricity of the fictitious "Trojan planets." © Mary Ann Liebert, Inc.}, keywords = {ARTICLE; PLANTS; Models, Biological; computer simulation; PLANT; biological model; Environment; PLANETS; Habitable zone; astronomy; Extraterrestrial Environment; Microclimate; EXOPLANETS; Trojan planet; Dynamical astronomy}, year = {2005}, eissn = {1557-8070}, pages = {579-586}, orcid-numbers = {Sándor, Zsolt/0000-0003-1216-913X} }