Combining TTVs, RVs, and astrometry to characterize distant giant companions of transiting hot Jupiters: Application to WASP-4

Authors: J. -V. Harre, Louise D. Nielsen, A. M. S. Smith

arXiv: 2611.16782v1 (astro-ph.EP)
Submitted to arXiv on 12 Nov. 2026
License: CC BY 4.0
Abstract

The origins and architectures of hot Jupiter (HJ) systems remain unclear, with potential explanations for the tight orbits being in-situ formation, disk-migration, or high-eccentricity migration. These mechanisms can leave different imprints on the orbital architecture, but tidal interactions act to erase these imprints for HJs, leading to orbital circularization, realignment, and potentially orbital decay. The latter can be mimicked by the introduction of light travel-time effects (LTTE) caused by an outer giant companion, as for WASP-4$\,$b. We examine the WASP-4 system using newly obtained ESO$\,$3.6/HARPS radial velocity (RV) observations and archival transit-timing data, leveraging the LTTE. Furthermore, we present a novel approach of analyzing HJ systems in sight of $\textit{Gaia}$'s Data Release 4. We propose combining RV, transit-timing, and astrometry data, making use of the LTTE as a proxy for the orbital motion of a possible outer companion. We combine and fit all currently available data and simulate $\textit{Gaia}$ DR4 and DR5 astrometric measurements of WASP-4 and perform an injection and recovery procedure to estimate their impact on the recovered planetary parameters of WASP-4$\,$c. The procedure employs a combined model that describes RVs, transit timing variations (TTVs) via the LTTE, and astrometry simultaneously. Analyzing the existing data, we improve the planetary parameters of WASP-4$\,$c, finding a minimum mass of $9.3\pm1.7\,M_\mathrm{Jup}$ with an orbital period of $10\,600^{+1100}_{-1000}\,$d, or about $29\,$yr. Furthermore, we find that there is no significant orbital decay taking place for WASP-4$\,$b. In simulations of $\textit{Gaia}$ DR5, our three-pronged approach reduces the error bars of WASP-4$\,$c's parameters by about $10\%$, $25\%$, and $33\%$ for its orbital period, time of inferior conjunction, and RV semi-amplitude, respectively. (abridged)

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    Abstract

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  3. Close Another approach to the problem
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  4. Close Broader context
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    Abstract

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    In short

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  7. Close Broader context
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    Abstract

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  8. Close Broader context
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    Abstract

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