an injection recovery test to check the sensitivity of our RV data. Using the RVSearch python package (Rosenthal et al. 2021) to inject 3000 synthetic planets drawn from a log-uniform period (1-1000 days) and RV amplitude (1-500 m/s) distribution into our RV data. We then used the ∆BIC periodogram search implemented in RVSearch to see if we could recover these planets. The resulting completeness maps are shown in Appendix B. Based on these completeness maps, we can only rule out the existence of giant planet companions
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[Figure: Fig. 2. Posterior distributions for the eccentricity and argument of periastron for TOI-2147 (top) and TOI-6019 (bottom). The black contours are the result of the fitting of the TESS light curves only, while the green contours are derived from the combined fitting of RV and photometry.]

The gray region shows constant angular momentum tracks which follow a final = a(1 −e2) as expected for planets undergoing high-eccentricity migration. Planets inside this region are considered proto-HJs as their orbits will shrink over time, bringing the planet close to its host star (a < 0.1 AU). TOI-6019 b lies just inside this gray region and is predicted to have a final semi-major axis of 0.093 ± 0.007 AU after circularizing (i.e., a period of 10 ± 1 days). The broad eccentricity distribution of WJs is indicative of multiple origin channels. Low-eccentricity WJs likely migrated via disk migration or might have even formed in situ. On the other hand, the high-eccentricity WJs have likely undergone a more dynamical migration mechanism, such as planet-planet scattering or Zeipel-Lidov-Kozai (ZLK) oscillation. Another indicator for the dynamical history of a giant planet is the existence (Mp ≥100 M⊕)

[Figure: Fig. 3. Results of the juliet fit for TOI-2147 (left) and TOI-6019 (right). First panel: Time-series radial velocity curve with the best-fit Keplerian model in black. Second panel: RVs phase-folded to the period of the planets. The dark blue data points represent the MaHPS RV data binned at 0.05 phases. Third Panel: Residuals after subtracting the eccentric model of the planet.]

with a period up to 100 days. Additionally, we looked for transit timing variations in the TESS light curves of both planets. For this, we fit the transits separately using Juliet to get a transit mid time for each individual transit and then subtracted the expected mid transit time from our combined fit. The resulting O-C diagrams are shown in Figure C.1. The measured transit times show some small scatter with an amplitude of ∼5 minutes. To look for periodic signals suggesting the presence of undetected companions, we performed a periodogram analysis with a Lomb-Scargle periodogram, which revealed no periodicities, indicating that the scatter might be coming from sources other than a planet (e.g., systematics, stellar activity). Although this has been attributed to the small number of transits, no definitive inferences can be made. The elevated eccentricities and absence of companion planets are consistent with our two planets undergoing high-eccentricity migration; however, due to the limited sensitivity of our RV (and TTV) data, we cannot rule out the existence of smaller companions, which would imply a more quiescent migration.

[Figure: Fig. 4. Density as a function of period for giant planets (Mp > 0.3 MJ) with mass and radius measured to a precision of 33% or better, taken from the NASA Exoplanet Archive (Christiansen et al. 2025). TOI-6019 b and TOI-2147 b are highlighted in black. The vertical dotted line indicates the separation between the hot and warm Jupiter populations.]

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