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Retired A Stars and Their Companions VI. A Pair of Interacting Exoplanet Pairs Around the Subgiants 24 Sextanis and HD200964

We report radial velocity measurements of the G-type subgiants 24 Sextanis (=HD90043) and HD200964. Both are massive, evolved stars that exhibit periodic variations due to the presence of a pair of Jovian planets. Photometric monitoring with the T12 0.80m APT at Fairborn Observatory demonstrates both stars to be constant in brightness to <= 0.002 mag, thus strengthening the planetary interpretation of the radial velocity variations. 24 Sex b,c have orbital periods of 453.8 days and 883~days, corresponding to semimajor axes 1.333 AU and 2.08 AU, and minimum masses (Msini) 1.99 Mjup and 0.86 Mjup, assuming a stellar mass 1.54 Msun. HD200964 b,c have orbital periods of 613.8 days and 825 days, corresponding to semimajor axes 1.601 AU and 1.95 AU, and minimum masses 1.85 Mjup and 0.90 Mjup, assuming M* = 1.44 Msun. We also carry out dynamical simulations to properly account for gravitational interactions between the planets. Most, if not all, of the dynamically stable solutions include crossing orbits, suggesting that each system is locked in a mean motion resonance that prevents close encounters and provides long-term stability. The planets in the 24 Sex system likely have a period ratio near 2:1, while the HD200964 system is even more tightly packed with a period ratio close to 4:3. However, we caution that further radial velocity observations and more detailed dynamical modelling will be required to provide definitive and unique orbital solutions for both cases, and to determine whether the two systems are truly resonant.