  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.
