Jiayin Li, Wei Zhu

Compared to the commonly used planet occurrence rates, the multiplicity distribution of planets can be more useful in constraining the formation and evolution pathways of planetary systems. This work follows an earlier work of Zhu (2022) and derive the intrinsic multiplicity distribution of giant planets (with masses above Saturn mass) from two independent radial velocity (RV) surveys. In particular, we find that $(7.8\pm1.4\%, 2.3\pm1.2\%, 0.5^{+0.8}_{-0.3}\%)$ of Sun-like stars in the HARPS sample have $(1, 2, 3)$ giant planets within 10 au, whereas $(7.3\pm2.8\%, 7.2\pm2.3\%, <1.3\%, 1.0^{+1.0}_{-0.6}\%)$ of Sun-like stars in the California Legacy Survey (CLS) have $(1, 2, 3, 4)$ giant planets within 10 au. Here we have further cleaned the CLS sample and removed planet detections that were not discovered in the survey mode. The total fraction of Sun-like stars with giant planets within 10 au from the two samples are $10.6\pm1.2\%$ and $15.8\pm2.1\%$, respectively, and the difference may be accounted for by their different metallicity distributions. We briefly discuss the theoretical implications of our results. In particular, the inferred giant planet multiplicity distribution is inconsistent with most of the proposed theoretical models involving planet-planet scatterings, which predict either too many giant planets or too many systems with multiple giants.