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

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

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

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

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

Air quality in Oporto área: comparative analysis

A partir de 1986-1987, on observe une tendance irrégulière de l'augmentation des concentrations moyennes mensuelles d'acidité forte et fumées noires. Les concentrations correspondant aux jours de la semaine sont supérieures à celles obtenues les week-ends et jours fériés, lesquelles mettent en évidence l'apport de l'activité industrielle et du trafic. Aucune corrélation mathématique significative traduisant l'évolution croissante des concentrations moyennes annuelles n'a été mise en évidence. Dans les stations les plus représentatives, les valeurs guides ont été dépassées, les concentrations étant proches de la limite. Bien que nous n'ayons pas enregistré d'épisodes aigus de pollution, l'évolution vérifiée durant la période prise en compte traduit un aggravement de la qualité de l'air. Cette tendance à la hausse est contraire à celle observée dans d'autres pays, où les niveaux d'acidité forte et fumées noires tendent à baisser grâce aux mesures de protection de l'environnement mises en pratique. Les niveaux de monoxyde de carbone, d'oxydes d'azote et d'ozone, observés en 1992 sont plus bas que dans d'autres régions.It was recorded an irregular trend upward for strong acidity and black smoke average monthly concentrations since 1986-1987. Levels in the working days are higher than those monitored in the week-end and days off, which proves the effect of traffic and industrial activities on air quality. It was not possible to establish any overall correlation fiable to express the increase in annual average concentrations. At the most representative stations, the exceedance of guideline values was recorded and concentrations reached values close to the limit. No acute episodes of air pollution were recorded, although the trend patterns monitored show an aggravation of air quality during this period of time. This trend is contrary to the one derived in foreign networks, where strong acidity and black smoke levels have been decreasing in consequence of environmental protection measures put into practice. Carbon monoxyde, nitrogen oxydes and ozone levels measured in 1992 are lower when compared with those monitored in other regions

Dynamics of two planets in co-orbital motion

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same orbital plane. Initially we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analyzed in more detail using a semi-analytical model. Apart from the well known quasi-satellite (QS) orbits and the classical equilibrium Lagrangian points L4 and L5, we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at $(\sigma,\Delta\omega) = (\pm 60\deg, \mp 120\deg)$, where \sigma is the difference in mean longitudes and \Delta\omega is the difference in longitudes of pericenter. The position of these Anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities, and are found for eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation to one of the planets, and analyzed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.Comment: 9 pages, 11 figure

The modulated spin liquid: a new paradigm for URu2_2Si2_2

We argue that near a Kondo breakdown critical point, a spin liquid with spatial modulations can form. Unlike its uniform counterpart, we find that this occurs via a second order phase transition. The amount of entropy quenched when ordering is of the same magnitude as for an antiferromagnet. Moreover, the two states are competitive, and at low temperatures are separated by a first order phase transition. The modulated spin liquid we find breaks $Z_4$ symmetry, as recently seen in the hidden order phase of URu$_2$Si$_2$. Based on this, we suggest that the modulated spin liquid is a viable candidate for this unique phase of matter.Comment: 4 pages, 2 figure