In this paper, we present a formalism designed to model tidal interaction with a viscoelastic body made of Maxwell material. Our approach remains regular for any spin rate and orientation, and for any orbital configuration including high eccentricities and close encounters. The method is to integrate simultaneously the rotation and the position of the planet as well as its deformation. We provide the equations of motion both in the body frame and in the inertial frame. With this study, we generalize preexisting models to the spatial case and to arbitrary multipole orders using a formalism taken from quantum theory. We also provide the vectorial expression of the secular tidal torque expanded in Fourier series. Applying this model to close-in exoplanets, we observe that if the relaxation time is longer than the revolution period, the phase space of the system is characterized by the presence of several spin-orbit resonances, even in the circular case. As the system evolves, the planet spin can visit different spin-orbit configurations. The obliquity is decreasing along most of these resonances, but we observe a case where the planet tilt is instead growing. These conclusions derived from the secular torque are successfully tested with numerical integrations of the instantaneous equations of motion on HD 80606 b. Our formalism is also well adapted to close-in super-Earths in multiplanet systems which are known to have non-zero mutual inclinations.

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin–orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star–planet–satellite systems and triple stellar systems.

We present a novel approach for analysing radial velocity data that combines two features: all the planets are searched at once and the algorithm is fast. This is achieved by utilizing compressed sensing techniques,which aremodified to be compatible with theGaussian process framework. The resulting tool can be used like a Lomb-Scargle periodogram and has the same aspect but with much fewer peaks due to aliasing. The method is applied to five systems with published radial velocity data sets: HD 69830, HD 10180, 55 Cnc, GJ 876 and a simulated very active star. The results are fully compatible with previous analysis, though obtained more straightforwardly. We further show that 55 Cnc e and f could have been respectively detected and suspected in early measurements from the Lick Observatory and Hobby-Eberly Telescope available in 2004, and that frequencies due to dynamical interactions in GJ 876 can be seen. © 2016 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.

Context. Ultra-short period planets undergo strong tidal interactions with their host star which lead to planet deformation and orbital tidal decay. Aims. WASP-103b is the exoplanet with the highest expected deformation signature in its transit light curve and one of the shortest expected spiral-in times. Measuring the tidal deformation of the planet would allow us to estimate the second degree fluid Love number and gain insight into the planet’s internal structure. Moreover, measuring the tidal decay timescale would allow us to estimate the stellar tidal quality factor, which is key to constraining stellar physics. Methods. We obtained 12 transit light curves of WASP-103b with the CHaracterising ExOplanet Satellite (CHEOPS) to estimate the tidal deformation and tidal decay of this extreme system. We modelled the high-precision CHEOPS transit light curves together with systematic instrumental noise using multi-dimensional Gaussian process regression informed by a set of instrumental parameters. To model the tidal deformation, we used a parametrisation model which allowed us to determine the second degree fluid Love number of the planet. We combined our light curves with previously observed transits of WASP-103b with the Hubble Space Telescope (HST) and Spitzer to increase the signal-to-noise of the light curve and better distinguish the minute signal expected from the planetary deformation. Results. We estimate the radial Love number of WASP-103b to be hf = 1.59+0.45 −0.53. This is the first time that the tidal deformation is directly detected (at 3σ) from the transit light curve of an exoplanet. Combining the transit times derived from CHEOPS, HST, and Spitzer light curves with the other transit times available in the literature, we find no significant orbital period variation for WASP-103b. However, the data show a hint of an orbital period increase instead of a decrease, as is expected for tidal decay. This could be either due to a visual companion star if this star is bound, the Applegate effect, or a statistical artefact. Conclusions. The estimated Love number of WASP-103b is similar to Jupiter’s. This will allow us to constrain the internal structure and composition of WASP-103b, which could provide clues on the inflation of hot Jupiters. Future observations with James Webb Space Telescope can better constrain the radial Love number of WASP-103b due to their high signal-to-noise and the smaller signature of limb darkening in the infrared. A longer time baseline is needed to constrain the tidal decay in this system.

State of the art. Data from a recent Portuguese national project that studied the toxic effects of children exposure (under 3 years old) to multiple mycotoxins in infant foods (MYCOMIX) reported the co-occurrence of 21 mycotoxins and metabolites present in breakfast cereals primarily marketed for children. This study showed that 96% of the analyzed breakfast cereal samples were contaminated with mycotoxins1,2. The output of this project also highlighted the knowledge gaps on the contra-balance beneficial health effect of these foods, and the need to determine the risk-benefit balance, since the evaluated food products, namely breakfast cereals, are simultaneously recognized vehicles of food components, like nutrients, vitamins and water soluble and insoluble fibers, which could be assumed as beneficial for children health.