The TESS-Keck Survey. XII. A Dense 1.8 R$_\oplus$ Ultra-Short-Period Planet Possibly Clinging to a High-Mean-Molecular-Weight Atmosphere After the First Gyr

The extreme environments of ultra-short-period planets (USPs) make excellent laboratories to study how exoplanets obtain, lose, retain, and/or regain gaseous atmospheres. We present the confirmation and characterization of the USP TOI-1347 b, a $1.8 \pm 0.1$ R$_\oplus$ planet on a 0.85 day orbit that was detected with photometry from the TESS mission. We measured radial velocities of the TOI-1347 system using Keck/HIRES and HARPS-N and found the USP to be unusually massive at $11.1 \pm 1.2$ M$_\oplus$. The measured mass and radius of TOI-1347 b imply an Earth-like bulk composition. A thin H/He envelope (>0.01% by mass) can be ruled out at high confidence. The system is between 1 and 1.8 Gyr old; therefore, intensive photoevaporation should have concluded. We detected a tentative phase curve variation (3$\sigma$) and a secondary eclipse (2$\sigma$) in TESS photometry, which if confirmed could indicate the presence of a high-mean-molecular-weight atmosphere. We recommend additional optical and infrared observations to confirm the presence of an atmosphere and investigate its composition.