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Characterizing the WASP-4 system with TESS and radial velocity data: Constraints on the cause of the hot Jupiter's changing orbit and evidence of an outer planet

Orbital dynamics provide valuable insights into the evolution and diversity of exoplanetary systems. Currently, only one hot Jupiter, WASP-12b, is confirmed to have a decaying orbit. Another, WASP-4b, exhibits hints of a changing orbital period that could be caused by orbital decay, apsidal precession, or the acceleration of the system towards the Earth. We have analyzed all data sectors from NASA's Transiting Exoplanet Survey Satellite together with all radial velocity (RV) and transit data in the literature to characterize WASP-4b's orbit. Our analysis shows that the full RV data set is consistent with no acceleration towards the Earth. Instead, we find evidence of a possible additional planet in the WASP-4 system, with an orbital period of ~7000 days and $M_{c}sin(i)$ of $5.47^{+0.44}_{-0.43} M_{Jup}$. Additionally, we find that the transit timing variations of all of the WASP-4b transits cannot be explained by the second planet but can be explained with either a decaying orbit or apsidal precession, with a slight preference for orbital decay. Assuming the decay model is correct, we find an updated period of 1.338231587$\pm$0.000000022 days, a decay rate of -7.33$\pm$0.71 msec/year, and an orbital decay timescale of 15.77$\pm$1.57 Myr. If the observed decay results from tidal dissipation, we derive a modified tidal quality factor of $Q^{'}_{*}$ = 5.1$\pm$0.9$\times10^4$, which is an order of magnitude lower than values derived for other hot Jupiter systems. However, more observations are needed to determine conclusively the cause of WASP-4b's changing orbit and confirm the existence of an outer companion.