On the dynamics of Extrasolar Planetary Systems under dissipation. Migration of planets

We study the dynamics of planetary systems with two planets moving in the same plane, when frictional forces act on the two planets, in addition to the gravitational forces. The model of the general three-body problem is used. Different laws of friction are considered. The topology of the phase space is essential in understanding the evolution of the system. The topology is determined by the families of stable and unstable periodic orbits, both symmetric and non symmetric. It is along the stable families, or close to them, that the planets migrate when dissipative forces act. At the critical points where the stability along the family changes, there is a bifurcation of a new family of stable periodic orbits and the migration process changes route and follows the new stable family up to large eccentricities or to a chaotic region. We consider both resonant and non resonant planetary systems. The 2/1, 3/1 and 3/2 resonances are studied. The migration to larger or smaller eccentricities depends on the particular law of friction. Also, in some cases the semimajor axes increase and in other cases they are stabilized. For particular laws of friction and for special values of the parameters of the frictional forces, it is possible to have partially stationary solutions, where the eccentricities and the semimajor axes are fixed.Comment: Accepted in Celestial Mechanics and Dynamical Astronom

The 1:1 resonance in Extrasolar Systems: Migration from planetary to satellite orbits

We present families of symmetric and asymmetric periodic orbits at the 1/1 resonance, for a planetary system consisting of a star and two small bodies, in comparison to the star, moving in the same plane under their mutual gravitational attraction. The stable 1/1 resonant periodic orbits belong to a family which has a planetary branch, with the two planets moving in nearly Keplerian orbits with non zero eccentricities and a satellite branch, where the gravitational interaction between the two planets dominates the attraction from the star and the two planets form a close binary which revolves around the star. The stability regions around periodic orbits along the family are studied. Next, we study the dynamical evolution in time of a planetary system with two planets which is initially trapped in a stable 1/1 resonant periodic motion, when a drag force is included in the system. We prove that if we start with a 1/1 resonant planetary system with large eccentricities, the system migrates, due to the drag force, {\it along the family of periodic orbits} and is finally trapped in a satellite orbit. This, in principle, provides a mechanism for the generation of a satellite system: we start with a planetary system and the final stage is a system where the two small bodies form a close binary whose center of mass revolves around the star.Comment: to appear in Cel.Mech.Dyn.Ast

Congenital Unilateral Corneal Anaesthesia with Microphthalmos: A Case Report

Congenital corneal anaesthesia (CCA) is an uncommon condition difficult to diagnose. We report the case of a 20-month-old boy who presented with unilateral congenital corneal anaesthesia. The child was referred with a persistent corneal epithelial defect, unresponsive to symptomatic local treatment for over 10 months. Intensive topical treatment and strict corneal protection led to quick corneal healing. Congenital corneal anaesthesia occurs either alone or in association with neurological diseases or systemic congenital abnormalities. It is important to search for corneal anaesthesia in children with chronic ulcerations of the cornea and self-inflicted injuries. Early diagnosis and treatment are important due to the risk of poor visual prognosis. Management of CCA should aim for the prevention of epithelial defects and is a life-long process

The Emission of Electromagnetic Radiation from Charges Accelerated by Gravitational Waves and its Astrophysical Implications

We provide calculations and theoretical arguments supporting the emission of electromagnetic radiation from charged particles accelerated by gravitational waves (GWs). These waves have significant indirect evidence to support their existence, yet they interact weakly with ordinary matter. We show that the induced oscillations of charged particles interacting with a GW, which lead to the emission of electromagnetic radiation, will also result in wave attenuation. These ideas are supported by a small body of literature, as well as additional arguments for particle acceleration based on GW memory effects. We derive order of magnitude power calculations for various initial charge distributions accelerated by GWs. The resulting power emission is extremely small for all but very strong GWs interacting with large quantities of charge. If the results here are confirmed and supplemented, significant consequences such as attenuation of early universe GWs could result. Additionally, this effect could extend GW detection techniques into the electromagnetic regime. These explorations are worthy of study to determine the presence of such radiation, as it is extremely important to refine our theoretical framework in an era of active GW astrophysics.Comment: Appears in Gravitational Wave Astrophysics, Editor C.F. Sopuerta, Astrophysics and Space Science Proceedings, Volume 40. ISBN 978-3-319-10487-4. Springer International Publishing Switzerland, 2015, p. 30

Resonances of low orders in the planetary system of HD37124

The full set of published radial velocity data (52 measurements from Keck + 58 ones from ELODIE + 17 ones from CORALIE) for the star HD37124 is analysed. Two families of dynamically stable high-eccentricity orbital solutions for the planetary system are found. In the first one, the outer planets c and d are trapped in the 2/1 mean-motion resonance. The second family of solutions corresponds to the 5/2 mean-motion resonance between these planets. In both families, the planets are locked in (or close to) an apsidal corotation resonance. In the case of the 2/1 MMR, it is an asymmetric apsidal corotation (with the difference between the longitudes of periastra $\Delta\omega\sim 60^\circ$), whereas in the case of the 5/2 MMR it is a symmetric antialigned one ($\Delta\omega = 180^\circ$). It remains also possible that the two outer planets are not trapped in an orbital resonance. Then their orbital eccentricities should be relatively small (less than, say, 0.15) and the ratio of their orbital periods is unlikely to exceed $2.3-2.5$.Comment: 28 pages, 10 figures, 3 tables; Accepted to Celestial Mechanics and Dynamical Astronom