A transit timing variation observed for the long-period extremely low-density exoplanet HIP 41378 f

HIP 41378 f is a temperate 9.2 ± 0.1 R_⊕ planet with period of 542.08 d and an extremely low density of 0.09 ± 0.02 g cm^-3. It transits the bright star HIP 41378 (V = 8.93), making it an exciting target for atmospheric characterization including transmission spectroscopy. HIP 41378 was monitored photometrically between the dates of 2019 November 19 and 28. We detected a transit of HIP 41378 f with NGTS, just the third transit ever detected for this planet, which confirms the orbital period. This is also the first ground-based detection of a transit of HIP 41378 f. Additional ground-based photometry was also obtained and used to constrain the time of the transit. The transit was measured to occur 1.50 h earlier than predicted. We use an analytic transit timing variation (TTV) model to show the observed TTV can be explained by interactions between HIP 41378 e and HIP 41378 f. Using our TTV model, we predict the epochs of future transits of HIP 41378 f, with derived transit centres of T_{C, 4} = $2459\,355.087^{+0.031}_{-0.022}$ (2021 May) and T_{C, 5} = $2459\,897.078^{+0.114}_{-0.060}$ (2022 November).