  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.
