The Intrinsic Multiplicity Distribution of Exoplanets Revealed from the Radial Velocity Method. II. Constraints on Giant Planet Multiplicity from Different Surveys

Abstract

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.

Figures (7)

• Figure 1: The distribution of 822 HARPS sample stars in the minimum mass vs. semi--major axis plane. Planets with different observed multiplicities are differentiated with different labels and colors. The contours represent the survey completeness, with lighter shades indicating higher sensitivity and darker shades indicating lower sensitivity. Both based on the data from Mayor:2011. The vertical dashed line indicates the outer boundary (10 au) that is considered in this work, and the horizontal dashed line indicates the upper mass limit (13 M$_{\mathrm{J}}$). The positions of Jupiter and Saturn are also shown. The regions of different planet categories defined in Section 3 are outlined by the black boxes. The red solid and dashed lines denote the RV semi-amplitudes of 3 and 1 m s$^{-1}$, respectively.
• Figure 2: This figure shows in blue dots the planets detected in the HARPS sample whose properties fall within our chosen parameter space. The values within each grid cell give the number of such planets per 100 stars. Error bars correspond to the 68% confidence interval, whereas for grid cells with fewer than two planet only the 95% upper limit is shown. The integrated planet frequencies are $\bar{n}_{\mathrm{p}} = 0.036, \approx 0.104, \approx 0.140$ for our definitions of close-in, cold, and all giant planets, respectively.
• Figure 3: The distribution of the remaining 351 CLS sample stars in the minimum mass vs. semimajor axis plane after selection. The meanings of the markers, background contours, and various lines are the same as described in the caption of Figure \ref{['fig:harps-sample']}.
• Figure 4: This figure shows in blue dots the planets detected in the less biased CLS sample whose properties fall within our chosen parameter space. The values shown in the grid and their meanings are the same as described in the caption of Figure \ref{['fig:harps-rate']}.
• Figure 5: Illustrations of the derived intrinsic planet multiplicity distributions for the three chosen planet classes from the cleaned CLS (blue) and HARPS (orange) datasets. The maximum-likelihood solutions and 1$\sigma$--3$\sigma$ confidence intervals are indicated by the colored bars with increasing transparency.