An independent determination of Fomalhaut bs orbit and the dynamical effects on the outer dust belt

The nearby star Fomalhaut harbours a cold, moderately eccentric dust belt with a sharp inner edge near 133 au. A low-mass, common proper motion companion (Fom b), was discovered near the inner edge and was identified as a planet candidate that could account for the belt morphology. However, the most recent orbit determination based on four epochs of astrometry over eight years reveals a highly eccentric orbit that appears to cross the belt in the sky plane projection. We perform here a full orbital determination based on the available astrometric data to independently validate the orbit estimates previously presented. Adopting our values for the orbital elements and their associated uncertainties, we then study the dynamical interaction between the planet and the dust ring, to check whether the proposed disk sculpting scenario by Fom b is plausible. We used a dedicated MCMC code to derive the statistical distributions of the orbital elements of Fom b. Then we used symplectic N-body integration to investigate the dynamics of the dust belt, as perturbed by a single planet. Different attempts were made assuming different masses for Fom b. We also performed a semi-analytical study to explain our results. Our results are in good agreement with others regarding the orbit of Fom b. We find that the orbit is highly eccentric, is close to apsidally aligned with the belt, and has a moderate mutual inclination relative to the belt plane of. If coplanar, this orbit crosses the disk. Our dynamical study then reveals that the observed planet could sculpt a transient belt configuration with a similar eccentricity to what is observed, but it would not be simultaneously apsidally aligned with the planet. This transient configuration only occurs a short time after the planet is placed on such an orbit (assuming an initially circular disk), a time that is inversely proportional to the planets mass, and that is in any case much less than the 440 Myr age of the star. We constrain how long the observed dust belt could have survived with Fom b on its current orbit, as a function of its possible mass. This analysis leads us to conclude that Fom b is likely to have low mass, that it is unlikely to be responsible for the sculpting of the belt, and that it supports the hypothesis of a more massive, less eccentric planet companion Fom c.

Masses and age of the Chemically Peculiar double-lined binary $chi$~Lupi

We aim at measuring the stellar parameters of the two Chemically Peculiar components of the B9.5Vp HgMn + A2 Vm double-lined spectroscopic binary HD141556, whose period is 15.25 days. We combined historical radial velocity measurements with new spatially resolved astrometric observations from PIONIER/VLTI to reconstruct the three-dimensional orbit of the binary, and thus obtained the individual masses. We fit the available photometric points together with the flux ratios provided by interferometry to constrain the individual sizes, which we compared to predictions from evolutionary models.The individual masses of the components are $Ma = 2.84 pm 0.12 Msun$ and $Mb = 1.94 pm 0.09 Msun$. The dynamical distance is compatible with the Hipparcos parallax. We find linear stellar radii of $Ra=2.85 pm 0.15 Rsun$ and $Rb=1.75 pm 0.18 Rsun$. This result validates a posteriori the flux ratio used in previous detailed abundance studies. We determine a sub-solar initial metallicity $Z=0.012pm0.003$ and an age of $(2.8pm0.3)times10^8 $years. Our results imply that the primary rotates more slowly than its synchronous velocity, while the secondary is probably synchronous. We show that strong tidal coupling during the pre-main sequence evolution followed by a full decoupling at zero-age main sequence provides a plausible explanation for these very low rotation rates.

On the observability of resonant structures in planetesimal disks due to planetary migration

We present a thorough study of the impact of a migrating planet on a planetesimal disk, by exploring a broad range of masses and eccentricities for the planet. We discuss the sensitivity of the structures generated in debris disks to the basic planet parameters. We perform many N-body numerical simulations, using the symplectic integrator SWIFT, taking into account the gravitational influence of the star and the planet on massless test particles. A constant migration rate is assumed for the planet. The effect of planetary migration on the trapping of particles in mean motion resonances is found to be very sensitive to the initial eccentricity of the planet and of the planetesimals. A planetary eccentricity as low as 0.05 is enough to smear out all the resonant structures, except for the most massive planets. The planetesimals also initially have to be on orbits with a mean eccentricity of less than than 0.1 in order to keep the resonant clumps visible. This numerical work extends previous analytical studies and provides a collection of disk images that may help in interpreting the observations of structures in debris disks. Overall, it shows that stringent conditions must be fulfilled to obtain observable resonant structures in debris disks. Theoretical models of the origin of planetary migration will therefore have to explain how planetary systems remain in a suitable configuration to reproduce the observed structures.