Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology

In this paper we present a new approach to tidal theory. Assuming a Maxwell viscoelastic rheology, we compute the instantaneous deformation of celestial bodies using a differential equation for the gravity field coefficients. This method allows large eccentricities and it is not limited to quasi-periodic perturbations. It can take into account an extended class of perturbations, including chaotic motions and transient events. We apply our model to some already detected eccentric hot Jupiters and super-Earths in planar configurations. We show that when the relaxation time of the deformation is larger than the orbital period, spin-orbit equilibria arise naturally at half-integers of the mean motion, even for gaseous planets. In the case of super-Earths, these equilibria can be maintained for very low values of eccentricity. Our method can also be used to study planets with complex internal structures and other rheologies.Comment: 16 pages, 13 figures, 2 table

Improvements on analytic modelling of stellar spots

In this work we present the solution of the stellar spot problem using the Kelvin-Stokes theorem. Our result is applicable for any given location and dimension of the spots on the stellar surface. We present explicitely the result up to the second degree in the limb darkening law. This technique can be used to calculate very efficiently mutual photometric effects produced by eclipsing bodies occulting stellar spots and to construct complex spot shapes.Comment: Resubmitted to MNRAS after accounting for minor comments of second review, 9 pages, 5 figures, software available at http://eduscisoft.com/KSINT

Probing the effect of gravitational microlensing on the measurements of the Rossiter-McLaughlin effect

In general, in the studies of transit light-curves and the Rossiter-McLaughlin (RM), the contribution of the planet's gravitational microlensing is neglected. Theoretical studies, have, however shown that the planet's microlensing can affect the transit light-curve and in some extreme cases cause the transit depth to vanish. In this letter, we present the results of our quantitative analysis of microlening on the RM effect. Results indicate that for massive planets in on long period orbits, the planet's microlensing will have considerable contribution to the star's RV measurements. We present the details of our study, and discuss our analysis and results.Comment: 6 pages, 3 figures, accepted for publication in Astronomy & Astrophysic

SOAP-T: A tool to study the light-curve and radial velocity of a system with a transiting planet and a rotating spotted star

We present an improved version of SOAP (Boisse et al. 2012) named "SOAP-T", which can generate the radial velocity variations and light-curves for systems consisting of a rotating spotted star with a transiting planet. This tool can be used to study the anomalies inside transit light-curves and the Rossiter-McLaughlin effect, to better constrain the orbital configuration and properties of planetary systems and active zones of their host stars. Tests of the code are presented to illustrate its performance and to validate its capability when compared with analytical models and real data. Finally, we apply SOAP-T to the active star, HAT-P-11, observed by the NASA Kepler space telescope and use this system to discuss the capability of this tool in analyzing light-curves for the cases where the transiting planet overlaps with the star's spots.Comment: 9 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

Statistical distributions in the folding of elastic structures

The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that leads to complex fold patterns. By studying the case of a rod confined isotropically into a disk, we show that the emergence of the complexity is associated with a well defined underlying statistical measure that determines the energy distribution of sub-elements,``branches'', of the rod. This result suggests that branches act as the ``microscopic'' degrees of freedom laying the foundations for a statistical mechanical theory of this athermal and amorphous system

Degeneracy in the characterization of non-transiting planets from transit timing variations

The transit timing variation (TTV) method allows the detection of non-transiting planets through their gravitational perturbations. Since TTVs are strongly enhanced in systems close to mean-motion resonances (MMR), even a low mass planet can produce an observable signal. This technique has thus been proposed to detect terrestrial planets. In this letter, we analyse TTV signals for systems in or close to MMR in order to illustrate the difficulties arising in the determination of planetary parameters. TTVs are computed numerically with an n-body integrator for a variety of systems close to MMR. The main features of these TTVs are also derived analytically. Systems deeply inside MMR do not produce particularly strong TTVs, while those close to MMR generate quasiperiodic TTVs characterised by a dominant long period term and a low amplitude remainder. If the remainder is too weak to be detected, then the signal is strongly degenerate and this prevents the determination of the planetary parameters. Even though an Earth mass planet can be detected by the TTV method if it is close to a MMR, it may not be possible to assert that this planet is actually an Earth mass planet. On the other hand, if the system is right in the center of a MMR, the high amplitude oscillation of the TTV signal vanishes and the detection of the perturber becomes as difficult as it is far from MMR.Comment: 5 pages, 3 figures, submitted to MNRA

Structure of Polyelectrolytes with Mixed of Monovalent and Divalent Counterions: Poisson-Boltzmann Analysis and SAXS Measurements

International audienceWe have studied by Small Angle X Ray Scattering (SAXS) the structure of salt free polyelectrolytes solutions containing monovalent and divalent counterions. We have considered mixtures of sulfonated polystyrene with monovalent (Na+) and divalent (Ca2+) counterions and measured the position of the scattering peak, q*, as a function of the monomer concentration cp and the monovalent / divalent content. The aim is to understand the variations observed in q* position when the valence of the counterions is gradually increased. This work is a continuation of a previous study in which first measurements were performed on a rather small number of sodium-PSS / calcium-PSS mixtures. In the present work, we used synchrotron radiation improved the quality of the data and varied the monovalent / divalent ratio with a much finer step. Indeed this gives new interesting results in the ranges of low and large divalent content. We analyzed SAXS results through the isotropic model and scaling approach description introduced by de Gennes et al. and developed by Dobrynin et al.. In this model, one key parameter is the chemical charge and / or the effective charge fraction feff of the polyions. Although the chemical charge fraction f of sodium-PSS and calcium-PSS polyelectrolyte is fixed by the synthesis, the effective charge fraction in mixtures varies with the monovalent / divalent ratio. This quantity has been calculated using the resolution of the Poisson-Boltzmann (PB) equation in the frame of the cell model for various monovalent / divalent contents and different concentrations. Severe deviations can be found in the effective charge values of mixtures at finite concentrations compared to the classical Manning-Oosawa prediction (infinite dilution limiting law). We demonstrate that the evolution of q* is still compatible with the isotropic model and the scaling approach in the low concentration range provided that the divalent content is not too high. In particular, a power law relation q * ~ f eff~ 0.3 can be found which looks very close to the one observed for weakly charged polyelectrolytes ( q*~ f 2 / 7 in good solvent or q*~ f 1/ 3 in theta solvent). Mixtures finally provide a way to adjust the effective charge fraction without changing the chemical nature of the polyions. However this procedure gives improvement of data prediction only in a limited range; it is still not able to fully explain the high concentration range, as well as the high divalent content mixtures. This is certainly due to the fact that the PB equations are not able to take into account the local interactions between monomers and divalent counterions, which goes beyond the mean field approach

‘‘Lozenge’’ contour plots in scattering from polymer networks

We present a consistent explanation for the appearance of “lozenge” shapes in contour plots of the two dimensional scattering intensity from stretched polymer networks. By explicitly averaging over quenched variables in a tube model, we show that lozenge patterns arise as a result of chain material that is not directly deformed by the stretch. We obtain excellent agreement with experimental data

First Order Phase Transition of a Long Polymer Chain

We consider a model consisting of a self-avoiding polygon occupying a variable density of the sites of a square lattice. A fixed energy is associated with each $90^\circ$-bend of the polygon. We use a grand canonical ensemble, introducing parameters $\mu$ and $\beta$ to control average density and average (total) energy of the polygon, and show by Monte Carlo simulation that the model has a first order, nematic phase transition across a curve in the $\beta$-$\mu$ plane.Comment: 11 pages, 7 figure

Transit-timing measurements with the model-independent barycenter method: Application to the LHS 6343 system

We present a model-independent technique for calculating the time of mid-transits. This technique, named "barycenter method", uses the light-curve's symmetry to determine the transit timing by calculating the transit light-curve barycenter. Unlike the other methods of calculating mid-transit timing, this technique does not depend on the parameters of the system and central star. We demonstrate the capabilities of the barycenter method by applying this technique to some known transiting systems including several \emph{Kepler} confirmed planets. Results indicate that for complete and symmetric transit lightcurves, the barycenter method achieves the same precision as other techniques, but with fewer assumptions and much faster. Among the transiting systems studied with the barycenter method, we focus in particular on LHS 6343C, a brown dwarf that transits a member of an M+M binary system, LHS 6343AB. We present the results of our analysis, which can be used to set an upper limit on the period and mass of a possible second small perturber.Comment: 10 pages, 15 figures, accepted for publication in Astronomy and Astrophysic