Nodal precession of WASP-33b for 11 yr by Doppler tomographic and transit photometric observations

WASP-33b, a hot Jupiter around a hot star, is a rare system in which nodal precession has been discovered. We updated the model for the nodal precession of WASP-33b by adding new observational points. Consequently, we found a motion of the nodal precession spanning 11 yr. We present homogenous Doppler tomographic analyses of eight data sets, including two new data sets from TS23 and HIDES, obtained between 2008 and 2019, to illustrate the variations in the projected spin-orbit obliquity of WASP-33b and its impact parameter. We also present its impact parameters based on photometric transit observations captured by MuSCAT in 2017 and MuSCAT2 in 2018. We derived its real spin-orbit obliquity ψ, stellar spin inclination i_s, and stellar gravitational quadrupole moment J₂ from the time variation models of the two orbital parameters. We obtained $\psi = 108.19^{+0.95}_{-0.97}$ deg, $i_\mathit{ s} = 58.3^{+4.6}_{-4.2}$ deg, and $J_2=(1.36^{+0.15}_{-0.12}) \times 10^{-4}$. Our J₂ value was slightly smaller than the theoretically predicted value, which may indicate that its actual stellar internal structure is different from the theoretical one. We derived the nodal precession speed $\dot{\theta }=0.507^{+0.025}_{-0.022}$ deg yr^-1, and its period $P_{\mathrm{pre}}=709^{+33}_{-34}$ yr, and found that WASP-33b transits in front of WASP-33 for only ~ 20 per cent of the entire nodal precession period.