TESS Giants Transiting Giants II: The hottest Jupiters orbiting evolved stars

Giant planets on short-period orbits are predicted to be inflated and eventually engulfed by their host stars. However, the detailed timescales and stages of these processes are not well known. Here we present the discovery of three hot Jupiters (P $<$ 10 d) orbiting evolved, intermediate-mass stars ($M_\star$ $\approx$ 1.5 M$_\odot$, 2 R$_\odot$ $<$ $R_\star <$ 5 R$_\odot$). By combining \tess photometry with ground-based photometry and radial velocity measurements, we report masses and radii for these three planets between 0.4 and 1.8 M$_\mathrm{J}$ and 0.8 and 1.8 R$_\mathrm{J}$. \planet has the shortest period (P=\period) of any planet discovered around a red giant star to date. Both \planettwo and \planetthree appear to be inflated, but \planet does not show any sign of inflation. The large radii and relatively low masses of \planettwo and \planetthree place them among the lowest density hot Jupiters currently known, while \planet is conversely one of the highest. All three planets have orbital eccentricities below 0.2. The large spread in radii for these systems implies that planet inflation has a complex dependence on planet mass, radius, incident flux, and orbital properties. We predict that \planet has the shortest orbital decay timescale of any planet currently known, but do not detect any orbital decay in this system. Transmission spectroscopy of \planettwo would provide a favorable opportunity for the detection of water, carbon dioxide and carbon monoxide features in the atmosphere of a planet orbiting an evolved star, and could yield new information about planet formation and atmospheric evolution.