Accurate characterization of the stellar and orbital parameters of the exoplanetary systemWASP-33 b from orbital dynamics

Abstract

By using the most recently published Doppler tomography measurements and accurate theoretical modelling of the oblateness-driven orbital precessions, we tightly constrain some of the physical and orbital parameters of the planetary system hosted by the fast rotating star WASP-33. In particular, the measurements of the orbital inclination ip to the plane of the sky and of the sky-projected spin-orbit misalignment λ at two epochs about six years apart allowed for the determination of the longitude of the ascending node Ω and of the orbital inclination I to the apparent equatorial plane at the same epochs. As a consequence, average rates of change Ωexp, Iexp of this two orbital elements, accurate to a ≈10-2 deg yr-1 level, were calculated as well. By comparing them to general theoretical expressions ΩJ2, I˙J2 for their precessions induced by an oblate star whose symmetry axis is arbitrarily oriented, we were able to determine the angle i* between the line of sight the star's spin S* and its first even zonal harmonic J * 2 obtaining i* = 142+10 -11deg, J* 2 = (2.1+0.8-0.5) × 10-4. As a by-product, the angle between S* and the orbital angular momentum L is as large as about Ψ ≈ 100 ° (Ψ2008 = 99+5-4 deg,Ψ2014 = 103+5-4 deg), and changes at a rate Ψ = 0.7+1.5-1.6 deg yr-1. The predicted general relativistic Lense-Thirring precessions, of the order of ~10-3deg yr-1, are, at present, about one order of magnitude below the measurability threshold.