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

Ward Identities and chiral anomalies for coupled fermionic chains

Coupled fermionic chains are usually described by an effective model written in terms of bonding and anti-bonding spinless fields with linear dispersion in the vicinities of the respective Fermi points. We derive for the first time exact Ward Identities (WI) for this model, proving the existence of chiral anomalies which verify the Adler-Bardeen non-renormalization property. Such WI are expected to play a crucial role in the understanding of the thermodynamic properties of the system. Our results are non-perturbative and are obtained analyzing Grassmann functional integrals by means of Constructive Quantum Field Theory methods.Comment: TeX file, 26 pages, 7 figures. Published version, new section added to answer referee remarks and derive the Ward Identites, no modifications in the main resul

Larval condition and growth of Sardinella brasiliensis (Steindachner, 1879): preliminary results from laboratory studies

Brazilian sardine, the most important resource along the southeastern Brazilian coast, presented great variations and declines in its stocks. The main factors contributing to this are: oceanographic structure changes; recruitment failures; excessive catches of juveniles and increase in fishery effort. In spite of this, no alterations in the density-dependent parameters were detected. Consequently, methods analysing the condition of the larvae coupled with methods determining growth using sagittae otolith increment width were applied to evaluate growth under experimental conditions. The results of the readings on the sagittae were compared with the age of the laboratory-reared sardine larvae and confirmed that increments are formed on a daily basis. Under poor feeding conditions, sardine larvae showed a low growth expressed by dry weight, RNA/DNA ratio and tryptic enzyme activity and by the narrow and low contrast increments in the otoliths. The results of the biochemical indices showed an unexpected decline in the feeding group coupled with a decrease in width of increment numbers 8 and 10. Other factors than food availability were affecting the condition of the larvae and might be indicative of physiological processes and ontogenetic changes occurring in sardine larvae

Surface nano-patterning through styrene adsorption on Si(100)

We present an ab initio study of the structural and electronic properties of styrene molecules adsorbed on the dimerized Si(100) surface at different coverages, ranging from the single-molecule to the full monolayer. The adsorption mechanism primarily involves the vinyl group via a [2+2] cycloaddition process that leads to the formation of covalent Si-C bonds and a local surface derelaxation, while it leaves the phenyl group almost unperturbed. The investigation of the functionalized surface as a function of the coverage (e.g. 0.5 -- 1 ML) and of the substrate reconstruction reveals two major effects. The first results from Si dimer-vinyl interaction and concerns the controlled variation of the energy bandgap of the interface. The second is associated to phenyl-phenyl interactions, which gives rise to a regular pattern of electronic wires at surface, stemming from the pi-pi coupling. These findings suggest a rationale for tailoring the surface nano-patterning of the surface, in a controlled way.Comment: 19 pages (preprint), 4 figures, supplementary materia

The structure of chromospheres around late-type giants and supergiants

Observations alpha Tau (K5III) and beta Gru (M2II) made at high resolution are used to confirm line identifications of features blended at low resolution. The high resolution spectra allow selected pairs of lines to be used to find the electron density and the opacity. Methods for determining these factors and the usual emission measure are presented. The electron density and opacity can be used together with the emission measure to place constraints on the structure of the atmosphere. The line formation processes are briefly discussed. Photo-excitation by strong lines appears to be important in these late type atmospheres

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

Dissipation in planar resonant planetary systems

Close-in planetary systems detected by the Kepler mission present an excess of periods ratio that are just slightly larger than some low order resonant values. This feature occurs naturally when resonant couples undergo dissipation that damps the eccentricities. However, the resonant angles appear to librate at the end of the migration process, which is often believed to be an evidence that the systems remain in resonance. Here we provide an analytical model for the dissipation in resonant planetary systems valid for low eccentricities. We confirm that dissipation accounts for an excess of pairs that lie just aside from the nominal periods ratios, as observed by the Kepler mission. In addition, by a global analysis of the phase space of the problem, we demonstrate that these final pairs are non-resonant. Indeed, the separatrices that exist in the resonant systems disappear with the dissipation, and remains only a circulation of the orbits around a single elliptical fixed point. Furthermore, the apparent libration of the resonant angles can be explained using the classical secular averaging method. We show that this artifact is only due to the severe damping of the amplitudes of the eigenmodes in the secular motion.Comment: 18 pages, 20 figures, accepted to A&