Disk-planets interactions and the diversity of period ratios in Kepler's multi-planetary systems

The Kepler mission is dramatically increasing the number of planets known in multi-planetary systems. Many adjacent planets have orbital period ratios near resonant values, with a tendency to be larger than required for exact first-order mean-motion resonances. This intriguing feature has been shown to be a natural outcome of orbital circularization of resonant planetary pairs due to star-planet tidal interactions. However, this feature holds in multi-planetary systems with periods longer than ten days, for which tidal circularization is unlikely to provide efficient divergent evolution of the planets orbits. Gravitational interactions between planets and their parent protoplanetary disk may instead provide efficient divergent evolution. For a planet pair embedded in a disk, we show that interactions between a planet and the wake of its companion can reverse convergent migration, and significantly increase the period ratio from a near-resonant value. Divergent evolution due to wake-planet interactions is particularly efficient when at least one of the planets opens a partial gap around its orbit. This mechanism could help account for the diversity of period ratios in Kepler's multiple systems comprising super-Earth to sub-jovian planets with periods greater than about ten days. Diversity is also expected for planet pairs massive enough to merge their gap. The efficiency of wake-planet interactions is then much reduced, but convergent migration may stall with a variety of period ratios depending on the density structure in the common gap. This is illustrated for the Kepler-46 system, for which we reproduce the period ratio of Kepler-46b and c.Comment: 15 pages, 11 figures, accepted for publication in Ap

Mean-Motion Resonances of High Order in Extrasolar Planetary Systems

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 procedure allows us to form high order MMRs and predict new planets using a genetic N-body code.Comment: To appear in Proceedings: Extrasolar Planets in Multi-body Systems: Theory and Observations; Editors K. Gozdziewski, A. Niedzielski and J. Schneider; 5 pages, 2 figures

Dynamical architectures of planetary systems induced by orbital migration

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.Comment: 10 pages with 5 figures, pdflatex, to appear in the proceedings of the conference "Extra-solar Planets in Multi-body Systems: Theory and Observations"; eds. K. Gozdziewski, A. Niedzielski and J. Schneider, EAS Publication Serie

Hydrodynamic Simulations of the Bardeen-Petterson Effect

We present SPH simulations of accretion discs in orbit about rotating compact objects such as black holes and neutron stars, and study the structure of warped discs produced by the Bardeen-Petterson effect. We calculate the transition radius out to which the disc specific angular momentum vector is aligned with that of the black hole. We focus on the parameter regime where the warp dynamics are controlled by bending wave propagation, but also consider models in which warps are subject to diffusion rather than wave transport, and are able to consider the fully nonlinear regime. Because of hydrodynamic or pressure effects, for the parameter range investigated, the transition radius is always found to be much smaller than that obtained by Bardeen & Petterson (1975). For discs with midplane Mach numbers of about 10, the transition occurs between 10 - 16 gravitational radii, whereas for a Mach number of about 30 it occurs at around 30 gravitational radii. A thicker disc with a Mach number of 5 is found to produce no discernible warped structure. The rate of black hole - disc alignment is found to be consistent with the ideas of Ress (1978), with the alignment torque behaving as if it arises from the accreted material transferring its misaligned component of angular momentum at the larger transition radius of Bardeen & Petterson (1975). The inclusion of Einstein precession in the calculations modified both the warped disc structure and, consistent with linear analysis, produced an increased alignment rate by up to a factor of 4 because of the effect that a non Keplerian potential has on the propagation of warps.Comment: 18 pages, 14 figures. Accepted for publication in M.N.R.A.S. A version with posctcript figures included can be obtained from http://www.maths.qmw.ac.uk/~rp

Bending Instabilities in Magnetized Accretion Discs

We study the global bending modes of a thin annular disc subject to both an internally generated magnetic field and a magnetic field due to a dipole embedded in the central star with axis aligned with the disc rotation axis. When there is a significant inner region of the disc corotating with the star, we find spectra of unstable bending modes. These may lead to elevation of the disc above the original symmetry plane facilitating accretion along the magnetospheric field lines. The resulting non-axisymmetric disc configuration may result in the creation of hot spots on the stellar surface and the periodic photometric variations observed in many classical T Tauri stars (CTTS). Time-dependent behaviour may occur including the shadowing of the central source in magnetic accretors even when the dipole and rotation axes are aligned.Comment: Accepted by MNRAS. 18 pages, 11 figures. LaTeX2e in the MN style. PostScript and HTML files are also available from http://www-star.qmw.ac.uk/~va/ or by e-mail: [email protected]

The TRAPPIST-1 system: Orbital evolution, tidal dissipation, formation and habitability

We study the dynamical evolution of the TRAPPIST-1 system under the influence of orbital circularization through tidal interaction with the central star. We find that systems with parameters close to the observed one evolve into a state where consecutive planets are linked by first order resonances and consecutive triples, apart from planets c, d and e, by connected three body Laplace resonances. The system expands with period ratios increasing and mean eccentricities decreasing with time. This evolution is largely driven by tides acting on the innermost planets which then influence the outer ones. In order that deviations from commensurability become significant only on $Gy$ time scales or longer, we require that the tidal parameter associated with the planets has to be such that $Q' > \sim 10^{2-3}.$ At the same time, if we start with two subsystems, with the inner three planets comprising the inner one, $Q'$ associated with the planets has to be on the order (and not significantly exceeding) $10^{2-3}$ for the two subsystems to interact and end up in the observed configuration. This scenario is also supported by modelling of the evolution through disk migration which indicates that the whole system cannot have migrated inwards together. Also in order to avoid large departures from commensurabilities, the system cannot have stalled at a disk inner edge for significant time periods. We discuss the habitability consequences of the tidal dissipation implied by our modelling, concluding that planets d, e and f are potentially in habitable zones.Comment: 27 pages, 15 figures, accepted for publication in MNRA