Extrasolar Planets in Mean-Motion Resonance: Apses Alignment and Asymmetric Stationary Solutions

In recent years several pairs of extrasolar planets have been discovered in the vicinity of mean-motion commensurabilities. In some cases, such as the Gliese 876 system, the planets seem to be trapped in a stationary solution, the system exhibiting a simultaneous libration of the resonant angle theta_1 = 2 lambda_2 - lambda_1 - varpi_1 and of the relative position of the pericenters. In this paper we analyze the existence and location of these stable solutions, for the 2/1 and 3/1 resonances, as function of the masses and orbital elements of both planets. This is undertaken via an analytical model for the resonant Hamiltonian function. The results are compared with those of numerical simulations of the exact equations. In the 2/1 commensurability, we show the existence of three principal families of stationary solutions: (i) aligned orbits, in which theta_1 and varpi_1 - varpi_2 both librate around zero, (ii) anti-aligned orbits, in which theta_1=0 and the difference in pericenter is 180 degrees, and (iii) asymmetric stationary solutions, where both the resonant angle and varpi_1 - varpi_2 are constants with values different of 0 or 180 degrees. Each family exists in a different domain of values of the mass ratio and eccentricities of both planets. Similar results are also found in the 3/1 resonance. We discuss the application of these results to the extrasolar planetary systems and develop a chart of possible planetary orbits with apsidal corotation. We estimate, also, the maximum planetary masses in order that the stationary solutions are dynamically stable.Comment: 25 pages, 10 figures. Submitted to Ap

Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition

The Kardar-Parisi-Zhang (KPZ) class is a paradigmatic example of universality in nonequilibrium phenomena, but clear experimental evidences of asymptotic 2D-KPZ statistics are still very rare, and far less understanding stems from its short-time behavior. We tackle such issues by analyzing surface fluctuations of CdTe films deposited on polymeric substrates, based on a huge spatio-temporal surface sampling acquired through atomic force microscopy. A \textit{pseudo}-steady state (where average surface roughness and spatial correlations stay constant in time) is observed at initial times, persisting up to deposition of $\sim 10^{4}$ monolayers. This state results from a fine balance between roughening and smoothening, as supported by a phenomenological growth model. KPZ statistics arises at long times, thoroughly verified by universal exponents, spatial covariance and several distributions. Recent theoretical generalizations of the Family-Vicsek scaling and the emergence of log-normal distributions during interface growth are experimentally confirmed. These results confirm that high vacuum vapor deposition of CdTe constitutes a genuine 2D-KPZ system, and expand our knowledge about possible substrate-induced short-time behaviors.Comment: 13 pages, 8 figures, 2 table

On planetary mass determination in the case of super-Earths orbiting active stars. The case of the CoRoT-7 system

This investigation uses the excellent HARPS radial velocity measurements of CoRoT-7 to re-determine the planet masses and to explore techniques able to determine mass and elements of planets discovered around active stars when the relative variation of the radial velocity due to the star activity cannot be considered as just noise and can exceed the variation due to the planets. The main technique used here is a self-consistent version of the high-pass filter used by Queloz et al. (2009) in the first mass determination of CoRoT-7b and CoRoT-7c. The results are compared to those given by two alternative techniques: (1) The approach proposed by Hatzes et al. (2010) using only those nights in which 2 or 3 observations were done; (2) A pure Fourier analysis. In all cases, the eccentricities are taken equal to zero as indicated by the study of the tidal evolution of the system; the periods are also kept fixed at the values given by Queloz et al. Only the observations done in the time interval BJD 2,454,847 - 873 are used because they include many nights with multiple observations; otherwise it is not possible to separate the effects of the rotation fourth harmonic (5.91d = Prot/4) from the alias of the orbital period of CoRoT-7b (0.853585 d). The results of the various approaches are combined to give for the planet masses the values 8.0 \pm 1.2 MEarth for CoRoT-7b and 13.6 \pm 1.4 MEarth for CoRoT 7c. An estimation of the variation of the radial velocity of the star due to its activity is also given.The results obtained with 3 different approaches agree to give masses larger than those in previous determinations. From the existing internal structure models they indicate that CoRoT-7b is a much denser super-Earth. The bulk density is 11 \pm 3.5 g.cm-3 . CoRoT-7b may be rocky with a large iron core.Comment: 12 pages, 11 figure

Dynamics of Enceladus and Dione inside the 2:1 Mean-Motion Resonance under Tidal Dissipation

In a previous work (Callegari and Yokoyama 2007, Celest. Mech. Dyn. Astr. vol. 98), the main features of the motion of the pair Enceladus-Dione were analyzed in the frozen regime, i.e., without considering the tidal evolution. Here, the results of a great deal of numerical simulations of a pair of satellites similar to Enceladus and Dione crossing the 2:1 mean-motion resonance are shown. The resonance crossing is modeled with a linear tidal theory, considering a two-degrees-of-freedom model written in the framework of the general three-body planar problem. The main regimes of motion of the system during the passage through resonance are studied in detail. We discuss our results comparing them with classical scenarios of tidal evolution of the system. We show new scenarios of evolution of the Enceladus-Dione system through resonance not shown in previous approaches of the problem.Comment: 36 pages, 12 figures. Accepted in Celestial Mechanics and Dynamical Astronom

A new analysis of the GJ581 extrasolar planetary system

We have done a new analysis of the available observations for the GJ581 exoplanetary system. Today this system is controversial due to choices that can be done in the orbital determination. The main ones are the ocurrence of aliases and the additional bodies - the planets f and g - announced in Vogt et al. 2010. Any dynamical study of exoplanets requires the good knowledge of the orbital elements and the investigations involving the planet g are particularly interesting, since this body would lie in the Habitable Zone (HZ) of the star GJ581. This region,for this system, is very attractive of the dynamical point of view due to several resonances of two and three bodies present there. In this work, we investigate the conditions under which the planet g may exist. We stress the fact that the planet g is intimately related with the orbital elements of the planet d; more precisely, we conclude that it is not possible to disconnect its existence from the determination of the eccentricity of the planet d. Concerning the planet f, we have found one solution with period $\approx 450$ days, but we are judicious about any affirmation concernig this body because its signal is in the threshold of detection and the high period is in a spectral region where the ocorruence of aliases is very common. Besides, we outline some dynamical features of the habitable zone with the dynamical map and point out the role played by some resonances laying there.Comment: 12 pages, 9 figure

Evolution of Migrating Planet Pairs in Resonance

In this paper we present numerical simulations of the evolution of planets or massive satellites captured in the 2/1 and 3/1 resonances, under the action of an anti-dissipative tidal force. The evolution of resonant trapped bodies show a richness of solutions: librations around stationary symmetric solutions with aligned periapses (w1-w2=0) or anti-aligned periapses (w1-w2=180 deg), and librations around stationary solutions in which the periapses configuration is fixed, but with w1-w2 taking values in a wide range of angles. Many of these solutions exist for large values of the eccentricities and, during the semimajor axis drift, the solutions show turnabouts from one configuration to another. These results are valid for other non-conservative forces leading to adiabatic covergent migration and capture into one of these resonances

The role of the observed tropical convection in the generation of frost events in the southern cone of South America

Based on previous results obtained from observations and linear wave theory analysis, the hypothesis that large-scale patterns can generate extreme cold events in southeast South America through the propagation of remotely excited Rossby waves was already suggested. This work will confirm these findings and extend their analysis through a series of numerical experiments using a primitive equation model where waves are excited by a thermal forcing situated in positions chosen according to observed convection anomalies over the equatorial region. The basic state used for these experiments is a composite of austral winters with maximum and minimum frequency of occurrence of generalized frosts that can affect a large area known as the Wet Pampas located in the central and eastern part of Argentina. The results suggest that stationary Rossby waves may be one important mechanism linking anomalous tropical convection with the extreme cold events in the Wet Pampas. The combination of tropical convection and a specific basic state can generate the right environment to guide the Rossby waves trigged by the tropical forcing towards South America. Depending on the phase of the waves entering the South American continent, they can favour the advection of anomalous wind at low levels from the south carrying cold and dry air over the whole southern extreme of the continent, producing a generalized frost in the Wet Pampa region. On the other hand, when a basic state based on the composites of minimum frosts is used, an anomalous anticyclone over the southern part of the continent generates a circulation with a south-southeast wind which brings maritime air and therefore humidity over the Wet Pampas region, creating negative temperature anomalies only over the northeastern part of the region. Under these conditions even if frosts occur they would not be generalized, as observed for the other basic state with maximum frequency of occurrence of generalized frosts