In this review we have studied possible formation scenarios of the observed mean-motion resonances in extrasolar planetary systems. As the majority of resonant systems are locked in a 2:1 resonance we concentrate in particular on these systems.
We have shown that planet-disk interaction between young embedded protoplanets and the protoplanetary disk may usually lead to a differential migration where the outer planet approaches the inner one. To analyze the outcome of the convergent migration we first perform full hydrodynamical simulations with two embedded planets and then compare these to forced three-body simulations where additional forces mimicking the planet-disk interaction have been added. We find that resonant capture into the 2:1 resonance indeed occurs frequently and that continued driving of the disk will move the system deep into the resonance with significant growth of the eccentricity of the two planets. Additionally, the final configuration of the orbits is symmetric where the periapses are aligned with only small libration. We refer to this state as apsidal co-rotation.
The well observed system GJ 876 is, in fact, in this symmetric configuration with only small libration of the two resonant angles. The relatively small planetary eccentricities in this system can only be explained if one assumes that after resonant capture occurred the length of migration was limited by disk dispersal. Alternatively, it may be possible that an additional damping mechanism has operated on the eccentricities during their migration process.
In the other two systems analyzed (HD 128311 and HD 73526) the eccentricities in the current observed state vary much more strongly and vanish peri odically for one planet. We demonstrate that the dynamical structure of these two systems may be the results of the mixed evolutionary scenario, melting together inward migration and a sudden perturbation.
In summary, the complex dynamical behavior of the observed resonant planetary systems can be understood in the framework of their formation process. Interaction with the protoplanetary disk and possibly more sudden planet-planet scattering events are important ingredients in shaping planetary systems.
Part of this work has been supported by the Hungarian Scientific Research Fund (OTKA) under the grants D048424, T043739 and by the German Science Foundation (DFG) under grant 436 UNG 17/1/07.
1 Peale, S. J.: 1976, Orbital resonances in the solar system, ARAA, 14, 215-246.
2 Goldreich, P.: 1965, An explanation of the frequent occurrence of commensurable mean motions in the solar system, MN-RAS, 130, 159.
3 Greenberg, R. J., Counselman, III, C. C., and Shapiro, 1.1.: 1972, Orbit-orbit resonance capture in the solar system, Science, 178, 747-749.
4 Greenberg, R.: 1973, Evolution of satellite resonances by tidal dissipation, AJ, 78, 338.
5 Malhotra, R.: 1993, The origin of Pluto's peculiar orbit, Nature, 365, 819.
6 Malhotra, R.: 1995, The origin of Pluto's orbit: implications for the solar system beyond Neptune, AJ, 110, 420.
7 Roy, A. E. and Ovenden, M. W.: 1954, On the occurrence of commensurable mean motions in the solar system, MNRAS, 114, 232.
8 von Weizsäcker, C. F.: 1948, Zur Kosmogo-nie, Zeitschrift fur Astrophysik, 24,181.
9 Patterson, C. W.: 1987, Resonance capture and the evolution of the planets, Icarus, 70, 319-333.
10 Beauge, C., Aarseth, S. J., and Ferraz-Mello, S.: 1994, Resonance capture and the formation of the outer planets, MNRAS, 270, 21.
11 Cameron, A. G. W.: 1978, Physics of the primitive solar accretion disk, Moons and Planets, 18, 5-40.
12 Mizuno, H.: 1980, Formation of the giant planets, Progress of Theoretical Physics, 64 544-557.
13 Murray, C. D. and Dermott, S. F.: 1999, Solar system dynamics, in Solar system dynamics by Murray, C. D.
14 Nelson, R. P. and Papaloizou, J. C. B.: 2002, Possible commensurabilities among pairs of extrasolar planets, MNRAS, 333, L26-L30.
15 Butler, R. P., Wright, J. T., Marcy, G. W., Fischer, D. A., Vogt, S. S., Tinney, C. G., Jones, H. R. A., Carter, B. D., Johnson,
J. A., McCarthy, C., and Penny, A. J.: 2006, Catalog of nearby exoplanets, ApJ, 646, 505-522.
16 Marcy, G. W., Butler, R. P., Fischer, D., Vogt, S. S., Lissauer, J. J., and Rivera, E. J.: 2001, A pair of resonant planets orbiting GJ 876, ApJ, 556, 296-301.
17 Laughlin, G., Butler, R. P., Fischer, D. A., Marcy, G. W., Vogt, S. S., and Wolf, A. S.: 2005, The GJ 876 planetary system: a progress report, ApJ, 622,1182-1190.
18 Mayor, M., Udry, S., Naef, D., Pepe, F., Queloz, D., Santos, N. C., and Burnet, M.: 2004, The CORALIE survey for southern extrasolar planets. XII. Orbital solutions for 16 extrasolar planets discovered with CORALIE, A&A, 415,391-402.
19 McArthur, B. E., Endl, M., Cochran, W. D., Benedict, G. F., Fischer, D. A., Marcy,
G. W., Butler, R. P., Naef, D., Mayor, M., Queloz, D., Udry, S., and Harrison, T. E.: 2004, Detection of a Neptune-mass planet in the p1 Cancri system using the Hobby-Eberly telescope, ApJ, 614, L81-L84.
20 Vogt, S. S., Butler, R. P., Marcy, G. W., Fischer, D. A., Henry, G. W., Laughlin, G., Wright, J. T., and Johnson, J. A.: 2005, Five new multicomponent planetary systems, ApJ, 632, 638-658.
21 Correia, A. C. M., Udry, S., Mayor, M., Laskar, J., Naef, D., Pepe, F., Queloz, D., and Santos, N. C.: 2005, The CORALIE survey for southern extrasolar planets. XIII. A pair of planets around HD 202206 or a circumbinary planet?, A&A, 440, 751758.
22 Tinney, C. G., Butler, R. P., Marcy, G. W., Jones, H. R. A., Laughlin, G., Carter, B. D., Bailey, J. A., and O'Toole, S.: 2006, The 2:1 resonant exoplanetary system orbiting HD 73526, ApJ, 647, 594-599.
23 Laughlin, G. and Chambers, J. E.: 2001, Short-term dynamical interactions among extrasolar planets, ApJ, 551, L109-L113.
24 Lee, M. H. and Peale, S. J.: 2002, Dynamics and origin of the 2:1 orbital resonances of the GJ 876 planets, ApJ, 567, 596-609.
25 Ferraz-Mello, S., Michtchenko, T. A., and Beauge, C.: 2005, The orbits of the extrasolar planets HD 82943c and b, ApJ, 621, 473-481.
26 Lee, M. H., Butler, R. P., Fischer, D. A., Marcy, G. W., and Vogt, S. S.: 2006, On the 2:1 orbital resonance in the HD 82943 planetary system, ApJ, 641, 1178-1187.
27 Sandor, Z. and Kley, W.: 2006, On the evolution of the resonant planetary system HD 128311, A&A, 451, L31-L34.
28 Naef, D., Mayor, M., Beuzit, J. L., Perrier, C., Queloz, D., Sivan, J. P., and Udry, S.:
2004, The ELODIE survey for northern extrasolar planets. III. Three planetary candidates detected with ELODIE, A&A, 414, 351-359.
29 Psychoyos, D. and Hadjidemetriou, J. D.:
2005, Dynamics of extrasolar systems at the 5/2 resonance: application to 47 UMa, Dynamics of Populations of Planetary Systems, IAU Colloq. 197, 55-62.
30 Goldreich, P. and Tremaine, S.: 1980, Disk-satellite interactions, ApJ, 241, 425-441.
31 Lin, D. N. C. and Papaloizou, J.: 1986, On the tidal interaction between protoplanets and the protoplanetary disk. III - Orbital migration of protoplanets, ApJ, 309, 846857.
32 Ward, W., R.: 1997, Protoplanet migration by nebula tides, Icarus, 126 261-281.
33 Murray, N., Hansen, B., Holman, M., and Tremaine, S.: 1998, Migrating planets, Science, 279, 69.
34 Ogilvie, G. I. and Lubow, S. H.: 2002, On the wake generated by a planet in a disc, MNRAS, 330, 950-954.
35 Kley, W.: 1999, Mass flow and accretion through gaps in accretion discs, MNRAS, 303, 696-710.
36 de Val-Borro, M., Edgar, R. G., Arty-mowicz, P., Ciecielag, P., Cresswell, P., D'Angelo, G., Delgado-Donate, E. J., Dirk-sen, G., Fromang, S., Gawryszczak, A., Klahr, H., Kley, W., Lyra, W., Masset, F., MeHema, G., Nelson, R. P., Paardekooper, S.-J., Peplinski, A., Pierens, A., Plewa, T., Rice, K., Schäfer, C., and Speith, R.: 2006, A comparative study of disc-planet interaction, MNRAS, 370, 529-558.
37 Kley, W.: 1989, Radiation hydrodynamics of the boundary layer in accretion disks. I - Numerical methods, A&A, 208, 98-110.
38 Kley, W.: 1998, On the treatment of the Coriolis force in computational astrophysics, A&A, 338, L37-L41.
39 Crida, A., Morbidelli, A., and Masset, F.: 2006, On the width and shape of gaps in protoplanetary disks, Icarus, 181, 587-604.
40 Nelson, R. P., Papaloizou, J. C. B., Masset, F., and Kley, W.: 2000, The migration and growth of protoplanets in protostellar discs, MNRAS, 318,18-36.
41 Bryden, G., Rözyczka, M., Lin, D. N. C., and Bodenheimer, P.: 2000, On the interaction between protoplanets and protostellar disks, ApJ, 540,1091-1101.
42 Kley, W.: 2000, On the migration of a system of protoplanets, MNRAS, 313, L47-L51.
43 Snellgrove, M. D., Papaloizou, J. C. B., and Nelson, R. P.: 2001, On disc driven inward migration of resonantly coupled planets with application to the system around GJ876, A&A, 374,1092-1099.
44 Kley, W., Peitz, J., and Bryden, G.: 2004, Evolution of planetary systems in resonance, A&A, 414, 735-747.
45 Beauge, C., Michtchenko, T. A. and Ferraz-Mello, S.: 2006, Planetary migration and extrasolar planets in the 2/1 mean-motion resonance, MNRAS, 365,1160-1170.
46 Tanaka, H. and Ward, W. R.: 2004, Three-dimensional interaction between a planet and an isothermal gaseous disk. II. Eccentricity waves and bending waves, ApJ, 602, 388-395.
47 Beauge, C., Ferraz-Mello, S., and Michtchenko, T. A.: 2003, Extrasolar planets in mean-motion resonance: apses alignment and asymmetric stationary solutions, ApJ, 593,1124-1133.
48 Henrard, J. and Lemaitre, A.: 1983, A second fundamental model for resonance, Cel. Mech., 30,197-218.
49 Rivera, E. J., Lissauer, J. J., Butler, R. P., Marcy, G. W., Vogt, S. S., Fischer, D. A., Brown, T. M., Laughlin, G., and Henry, G. W.: 2005, A - 7.5M® planet orbiting the nearby star, GJ 876, ApJ, 634, 625-640.
50 Kley, W., Lee, M. H., Murray, N., and Peale, S. J.: 2005, Modeling the resonant planetary system GJ 876, A&A, 437, 727742.
51 Sandor, Z., Kley, W., and Klagyivik, P.: 2007, On the formation of resonant planetary system HD 73526, A&A, 2007arXiv0706.2128S in press.
52 Sándor, Z., Érdi, B., Széll, A., and Funk, B.: 2004, The relative Lyapunov indicator: an efficient method of chaos detection, CMDA, 90,127-138.
53 Calvet, N., D'Alessio, P., Watson, D. M., Franco-Hernández, R., Furlan, E., Green, J., Sutter, P. M., Forrest, W. J., Hartmann, L., Uchida, K. I., Keller, L. D., Sargent, B., Najita, J., Herter, T. L., Barry, D. J., and Hall, P.: 2005, Disks in transition in the Taurus population: Spitzer IRS spectra of GM Aurigae and DM Tauri, ApJ, 630, L185-L188.
54 D'Alessio, P., Hartmann, L., Calvet, N., Franco-Hernández, R., Forrest, W. J., Sargent, B., Furlan, E., Uchida, K., Green,
J. D., Watson, D. M., Chen, C. H., Kemper, F., Sloan, G. C., and Najita, J.: 2005, The truncated disk of CoKu Tau/4, ApJ, 621, 461-472.
55 Ford, E. B., Lystad, V., and Rasio, F. A.: 2005, Planet-planet scattering in the upsilon Andromedae system, Nature, 434, 873-876.
Was this article helpful?