2016MNRAS.455..207I

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 {dot}Ω_exp, {dot}I_exp of this two orbital elements, accurate to a ~10-2deg/yr level, were calculated as well. By comparing them to general theoretical expressions {dot}Ω_J_2, {dot}I_J_2 for their precessions induced by an oblate star whose symmetry axis is arbitrarily oriented, we were able to determine the angle i{sstarf} 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^* = \left(2.1^+0.8_-0.5\right)×10^-4. As a by-product, the angle between S^* and the orbital angular momentum L is as large as about ψ ~ 100 ° \left(ψ^2008 = 99^+5_-4 deg, ψ^2014 = 10^3^^+5_-4 deg\right), and changes at a rate {dot}ψ= 0.7^+1.5_-1.6 deg yr^-1. The predicted general relativistic Lense-Thirring precessions, of the order of ~10-3deg/yr, are, at present, about one order of magnitude below the measurability threshold.