Radial Velocity Observations of a Gas Giant Candidate in Companion to a TESS Discovered sub-Neptune

We present a TESS discovered planetary system with a short-period sub-Neptune, HD 307842 (or TOI 784), to confirm and characterize its distant gas giant companion using radial velocity (RV) observations. Observational and statistical studies indicate that long-period gas giants are more common around stars hosting super-Earths or sub-Neptunes. In addition, simulations show that the growth of a Jupiter-mass planet in a protoplanetary disk may drive the instability of the disk and in turn influence inner small planet formation. Observations and simulations both hint in correlations between inner planet properties and the presence or absence of an outer companion. Our program investigates such links between the long-period giants and inner small planets by systematically search and characterize giant planets in systems with known transiting planets. HD 307842 is a V = 9.4 solar-type mid-G star observed by TESS. Transiting data shows that around HD 307842, there is one planet candidate TOI 784.01 with period P = 2.8 days and R = 1.86 R_{Earth}. The radial velocity measurements by the Magellan/PFS suggest that there is likely an additional long-period planet in the system. In this work, we aim to confirm the outer long-period planet or at least give constraints on its properties. The preliminary RV fitting results suggest an orbital period ~110 days and a minimum mass of ~90 M_{Earth}. Next, we will collect more RV data from Magellan/PFS and LCOGT/NRES to map out the entire orbit of the giant planet candidate