TOI-159 b: an eccentric hot-Jupiter planet around a young, pulsating $\gamma$ Doradus star

Fast-rotating hot stars are challenging targets for exoplanet searches due to rotational broadening and stellar variability. Moreover, hot stars often exhibit pulsations, an additional source of scatter in both photometric and spectroscopic series. Because of these challenges, such stars remain a relatively unexplored environment for planetary architecture and evolution studies. In this study, we present the confirmation and preliminary atmospheric characterisation of a giant planet orbiting a young ($\approx$ 150 Myr), pulsating $\gamma$ Doradus star. TOI-159 b ($P_{\rm orb} \simeq 3.7$ d, $R_{\rm p} \simeq 1.6~R_{\rm J}$, $M_{\rm p} \simeq 3.5 M_{\rm J}$) is an S-type planet in a close binary system and is the hottest ($T_{\rm eq} \simeq 1900$ K) hot Jupiter with a significant eccentricity ($e = 0.24 \pm 0.04$) ever detected. Our joint modelling of radial velocities (HARPS and CORALIE), transits (\textit{TESS}), and spectro-photometry (IMACS) allows us to detect its Keplerian signal at high significance ($13 \sigma$), place strong constraints on its eccentricity ($6 \sigma$), disentangle the stellar rotational modulation and pulsation periods, and generate a low-resolution transmission spectrum, on which we conduct an exploratory analysis to constrain the presence of a planetary atmosphere using combined star-planet retrievals. Whilst our spectrum appears to display some modulation, the data is too coarse to allow for any conclusive detections at this stage. Higher-resolution observations are needed to confirm or refute these features and, if genuine, determine whether they originate from contamination from the star or a planetary atmosphere.