Dynamic portrait of the planetary 2/1 mean-motion resonance - I. Systems with a more massive outer planet

We analyse the global structure of the phase space of the planar planetary 2/1 mean-motion resonance in cases where the outer planet is more massive than its inner companion. Inside the resonant domain, we show the existence of two families of periodic orbits, one associated to the librational motion of resonant angle (sigma-family) and the other related to the circulatory motion of the difference in longitudes of pericentre (Delta pi-family). The well-known apsidal corotation resonances (ACR) appear as intersections between both families. A complex web of secondary resonances is also detected for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. The construction of dynamical maps for various values of the total angular momentum shows the evolution of the families of stable motion with the eccentricities, identifying possible configurations suitable for exoplanetary systems. For low-moderate eccentricities, several different stable modes exist outside the ACR. For larger eccentricities, however, all stable solutions are associated to oscillations around the stationary solutions. Finally, we present a possible link between these stable families and the process of resonance capture, identifying the most probable routes from the secular region to the resonant domain, and discussing how the final resonant configuration may be affected by the extension of the chaotic layer around the resonance region.

SIMULATIONS OF WINDS OF WEAK-LINED T TAURI STARS. II. THE EFFECTS OF A TILTED MAGNETOSPHERE AND PLANETARY INTERACTIONS

Based on our previous work, we investigate here the effects on the wind and magnetospheric structures of weak-lined T Tauri stars due to a misalignment between the axis of rotation of the star and its magnetic dipole moment vector. In such a configuration, the system loses the axisymmetry presented in the aligned case, requiring a fully three-dimensional (3D) approach. We perform 3D numerical magnetohydrodynamic simulations of stellar winds and study the effects caused by different model parameters, namely the misalignment angle theta(t), the stellar period of rotation, the plasma-beta, and the heating index.. Our simulations take into account the interplay between the wind and the stellar magnetic field during the time evolution. The system reaches a periodic behavior with the same rotational period of the star. We show that the magnetic field lines present an oscillatory pattern. Furthermore, we obtain that by increasing theta(t), the wind velocity increases, especially in the case of strong magnetic field and relatively rapid stellar rotation. Our 3D, time-dependent wind models allow us to study the interaction of a magnetized wind with a magnetized extrasolar planet. Such interaction gives rise to reconnection, generating electrons that propagate along the planet`s magnetic field lines and produce electron cyclotron radiation at radio wavelengths. The power released in the interaction depends on the planet`s magnetic field intensity, its orbital radius, and on the stellar wind local characteristics. We find that a close-in Jupiter-like planet orbiting at 0.05 AU presents a radio power that is similar to 5 orders of magnitude larger than the one observed in Jupiter, which suggests that the stellar wind from a young star has the potential to generate strong planetary radio emission that could be detected in the near future with LOFAR. This radio power varies according to the phase of rotation of the star. For three selected simulations, we find a variation of the radio power of a factor 1.3-3.7, depending on theta(t). Moreover, we extend the investigation done in Vidotto et al. and analyze whether winds from misaligned stellar magnetospheres could cause a significant effect on planetary migration. Compared to the aligned case, we show that the timescale tau(w) for an appreciable radial motion of the planet is shorter for larger misalignment angles. While for the aligned case tau(w) similar or equal to 100 Myr, for a stellar magnetosphere tilted by theta(t) = 30 degrees, tau(w) ranges from similar to 40 to 70 Myr for a planet located at a radius of 0.05 AU. Further reduction on tau(w) might occur for even larger misalignment angles and/or different wind parameters.

Revisiting 2D numerical models for the 19th century outbursts of eta Carinae

We present here new results of two-dimensional hydrodynamical simulations of the eruptive events of the 1840s (the great) and the 1890s (the minor) eruptions suffered by the massive star eta Carinae (Car). The two bipolar nebulae commonly known as the Homunculus and the little Homunculus (LH) were formed from the interaction of these eruptive events with the underlying stellar wind. We assume here an interacting, non-spherical multiple-phase wind scenario to explain the shape and the kinematics of both Homunculi, but adopt a more realistic parametrization of the phases of the wind. During the 1890s eruptive event, the outflow speed decreased for a short period of time. This fact suggests that the LH is formed when the eruption ends, from the impact of the post-outburst eta Car wind (that follows the 1890s event) with the eruptive flow (rather than by the collision of the eruptive flow with the pre-outburst wind, as claimed in previous models; Gonzalez et al.). Our simulations reproduce quite well the shape and the observed expansion speed of the large Homunculus. The LH (which is embedded within the large Homunculus) becomes Rayleigh-Taylor unstable and develop filamentary structures that resemble the spatial features observed in the polar caps. In addition, we find that the interior cavity between the two Homunculi is partially filled by material that is expelled during the decades following the great eruption. This result may be connected with the observed double-shell structure in the polar lobes of the eta Car nebula. Finally, as in previous work, we find the formation of tenuous, equatorial, high-speed features that seem to be related to the observed equatorial skirt of eta Car.

Effects of the planetary migration on some primordial satellites of the outer planets

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estudo da dinâmica de captura em discos proto-planetários

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

ORBITAL PERTURBATIONS OF THE GALILEAN SATELLITES DURING PLANETARY ENCOUNTERS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

From stellar nebula to planets: The refractory components

Context. To date, calculations of planet formation have mainly focused on dynamics, and only a few have considered the chemical composition of refractory elements and compounds in the planetary bodies. While many studies have been concentrating on the chemical composition of volatile compounds (such as H2O, CO, CO2) incorporated in planets, only a few have considered the refractory materials as well, although they are of great importance for the formation of rocky planets. Aims. We computed the abundance of refractory elements in planetary bodies formed in stellar systems with a solar chemical composition by combining models of chemical composition and planet formation. We also considered the formation of refractory organic compounds, which have been ignored in previous studies on this topic. Methods. We used the commercial software package HSC Chemistry to compute the condensation sequence and chemical composition of refractory minerals incorporated into planets. The problem of refractory organic material is approached with two distinct model calculations: the first considers that the fraction of atoms used in the formation of organic compounds is removed from the system (i.e., organic compounds are formed in the gas phase and are non-reactive); and the second assumes that organic compounds are formed by the reaction between different compounds that had previously condensed from the gas phase. Results. Results show that refractory material represents more than 50 wt % of the mass of solids accreted by the simulated planets with up to 30 wt % of the total mass composed of refractory organic compounds. Carbide and silicate abundances are consistent with C/O and Mg/Si elemental ratios of 0.5 and 1.02 for the Sun. Less than 1 wt % of carbides are present in the planets, and pyroxene and olivine are formed in similar quantities. The model predicts planets that are similar in composition to those of the solar system. Starting from a common initial nebula composition, it also shows that a wide variety of chemically different planets can form, which means that the differences in planetary compositions are due to differences in the planetary formation process. Conclusions. We show that a model in which refractory organic material is absent from the system is more compatible with observations. The use of a planet formation model is essential to form a wide diversity of planets in a consistent way.