Updated Mass, Eccentricity, and Tidal Heating Constraints for the Earth-sized Planet LP 791-18 d

Abstract: LP 791-18 d is a temperate Earth-sized planet orbiting a late M dwarf, surrounded by an interior super-Earth (LP 791-18 b, $R_P$ = 1.2 $R_{\oplus}$, $P=0.95$ days) and an exterior sub-Neptune (LP 791-18 c, $R_P$ = 2.5 $R_{\oplus}$, $P=4.99$ days). Dynamical interactions between LP 791-18 d and c produce transit timing variations (TTVs) that can be used to constrain the planet masses and eccentricities. These interactions can also force a non-zero eccentricity for LP 791-18 d, which raises its internal temperature through tidal heating and could drive volcanic outgassing. We present three new transit observations of LP 791-18 c with Palomar/WIRC, including the most precise TTV measurements ($<$ 6 seconds) of this planet to date. We fit these times with a TTV model to obtain updated constraints on the mass, eccentricity, and tidal heat flux of LP 791-18 d. We reduce the mass uncertainty by more than a factor of two ($M_d$ = 0.91 $\pm$ 0.19 $M_{\oplus}$). We perform an updated fit assuming tidally damped free eccentricities and find $e_d = 0.0011^{+0.0010}_{-0.0008}$ and $e_c = 0.0001 \pm 0.0001$, consistent with circular orbits. We find that the observed TTVs are not sensitive to $e \leq$ $\sim$0.01. Without a tidally damped eccentricity prior, $e_d = 0.056^{+0.015}_{-0.014}$, much higher than the eccentricity predicted by n-body simulations incorporating the effects of dynamical excitation and tidal damping. We predict the timing of upcoming JWST secondary eclipse observations for LP 791-18 d, which could tightly constrain the eccentricity and tidal quality factor of this Earth-sized exoplanet.