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

Abstract

By using the most recently published Doppler tomography measurements and accurate theoretical modeling 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 $i_{\mathrm{p}}$ to the plane of the sky and of the sky-projected spin-orbit misalignment $\lambda$ at two epochs about six years apart allowed for the determination of the longitude of the ascending node $\Omega$ and of the orbital inclination $I$ to the apparent equatorial plane at the same epochs. As a consequence, average rates of change ${\dot{\Omega }}_{\exp },{\dot{I}}_{\exp }$ of this two orbital elements, accurate to a $\approx 10^{-2}\mathrm{deg}{\mathrm{yr}}^{-1}$ level, were calculated as well. By comparing them to general theoretical expressions ${\dot{\Omega }}_{J_2},{\dot{I}}_{J_2}$ for their precessions induced by an oblate star whose symmetry axis is arbitrarily oriented, we were able to determine the angle $i^{\star }$ between the line of sight the star's spin $S^{\star }$ and its first even zonal harmonic $J_2^{\star }$ obtaining $i^{\star }=142_{-11}^{+10}\mathrm{deg},J_2^{\star }=(2.1_{-0.5}^{+0.8})\times 10^{-4}.$ As a by-product, the angle between $S^{\star }$ and the orbital angular momentum $L$ is as large as about $\psi \approx 100$ deg $({\psi }^{2008}=99_{-4}^{+5}\mathrm{deg},{\psi }^{2014}=103_{-4}^{+5}\mathrm{deg})$, and changes at a rate $\dot{\psi }=0.7_{-1.6}^{+1.5}\mathrm{deg}{\mathrm{yr}}^{-1}$. The predicted general relativistic Lense-Thirring precessions, or the order of $\approx 10^{-3}\mathrm{deg}{\mathrm{yr}}^{-1}$, are, at present, about one order of magnitude below the measurability threshold.

LaTex2e, 1 figure, 1 table, 8 pages. Finale version accepted for publication in Monthly Notices of the Royal Astronomical Society (MNRAS)

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