Revisiting Orbital Evolution in HAT-P-2 b and Confirmation of HAT-P-2 c

One possible formation mechanism for Hot Jupiters is that high-eccentricity gas giants experience tidal interactions with their host star that cause them to lose orbital energy and migrate inwards. We study these types of tidal interactions in an eccentric Hot Jupiter called HAT-P-2 b, which is a system where a long-period companion has been suggested, and hints of orbital evolution (de Wit et al. 2017) were detected. Using five additional years of radial velocity (RV) measurements, we further investigate these phenomena. We investigated the long-period companion by jointly fitting RVs and Hipparcos-Gaia astrometry and confirmed this long-period companion, significantly narrowed down the range of possible periods ($P_2 = 8500_{-1500}^{+2600}$ days), and determined that it must be a substellar object ($10.7_{-2.2}^{+5.2}$ $M_j$). We also developed a modular pipeline to simultaneously model rapid orbital evolution and the long-period companion. We find that the rate and significance of evolution are highly dependent on the long-period companion modeling choices. In some cases the orbital rates of change reached $de/dt = {3.28}_{-1.72}^{+1.75} \cdot 10^{-3}$/year, $d\omega/dt = 1.12 \pm 0.22 ^{\circ}$/year which corresponds to a $\sim 321$ year apsidal precession period. In other cases, the data is consistent with $de/dt = 7.67 \pm 18.6 \cdot 10^{-4}$/year, $d\omega/dt = 0.76\pm 0.24 ^{\circ}$/year. The most rapid changes found are significantly larger than the expected relativistic precession rate and could be caused by transient tidal planet-star interactions. To definitively determine the magnitude and significance of potential orbital evolution in HAT-P-2 b, we recommend further monitoring with RVs and precise transit and eclipse timings.