Photodynamical analysis of the nearly resonant planetary system WASP-148. Accurate transit-timing variations and mutual orbital inclination

WASP-148 is a recently announced extra-solar system harbouring at least two giant planets. The inner planet transits its host star. The planets travel on eccentric orbits and are near the 4:1 mean-motion resonance, which implies significant mutual gravitational interactions. In particular, this causes transit-timing variations of a few minutes, which were detected based on ground-based photometry. This made WASP-148 one of the few cases where such a phenomenon was detected without space-based photometry. Here, we present a self-consistent model of WASP-148 that takes into account the gravitational interactions between all known bodies in the system. Our analysis simultaneously fits the available radial velocities and transit light curves. In particular, we used the photometry secured by the TESS space telescope and made public after the WASP-148 discovery announcement. The TESS data confirm the transit-timing variations, but only in combination with previously measured transit times. The system parameters we derived agree with those previously reported and have a significantly improved precision, including the mass of the non-transiting planet. We found a significant mutual inclination between the orbital planes of the two planets: I=41.0 +6.2 -7.6 deg based on the modelling of the observations, although we found I=20.8 +/- 4.6 deg when we imposed a constraint on the model enforcing long-term dynamical stability. When a third planet was added to the model - based on a candidate signal in the radial velocity - the mutual inclination between planets b and c changed significantly allowing solutions closer to coplanar. We conclude that more data are needed to establish the true architecture of the system. If the significant mutual inclination is confirmed, WASP-148 would become one of the only few candidate non-coplanar planetary systems. We discuss possible origins for this misalignment.