Stability and detectability of exomoons orbiting HIP 41378 f, a temperate Jovian planet with an anomalously low apparent density

Moons orbiting exoplanets ("exomoons") may hold clues about planet formation, migration, and habitability. In this work, we investigate the plausibility of exomoons orbiting the temperate ($T_\text{eq}=294$ K) giant ($R = 9.2$ R$_\oplus$) planet HIP 41378 f, which has been shown to have a low apparent bulk density of $0.09\,\text{g}\,\text{cm}^{-3}$ and a flat near-infrared transmission spectrum, hinting that it may possess circumplanetary rings. Given this planet's long orbital period ($P\approx1.5$ yr), it has been suggested that it may also host a large exomoon. Here, we analyze the orbital stability of a hypothetical exomoon with a satellite-to-planet mass ratio of 0.0123 orbiting HIP 41378 f. Combining a new software package, astroQTpy, with REBOUND and EqTide, we conduct a series of N-body and tidal migration simulations, demonstrating that satellites up to this size are largely stable against dynamical escape and collisions. We simulate the expected transit signal from this hypothetical exomoon and show that current transit observations likely cannot constrain the presence of exomoons orbiting HIP 41378 f, though future observations may be capable of detecting exomoons in other systems. Finally, we model the combined transmission spectrum of HIP 41378 f and a hypothetical moon with a low-metallicity atmosphere, and show that the total effective spectrum would be contaminated at the $\sim$10 ppm level. Our work not only demonstrates the feasibility of exomoons orbiting HIP 41378 f, but also shows that large exomoons may be a source of uncertainty in future high-precision measurements of exoplanet systems.