The orbital distribution of giant planets is crucial for understanding how terrestrial planets form and predicting yields of exoplanet surveys. Here, we derive giant planets occurrence rates as a function of orbital period by taking into account the detection efficiency of the Kepler and radial velocity (RV) surveys. The giant planet occurrence rates for Kepler and RV show the same rising trend with increasing distance from the star. We identify a break in the RV giant planet distribution between ∼2-3 au -close to the location of the snow line in the Solar System -after which the occurrence rate decreases with distance from the star. Extrapolating a broken power-law distribution to larger semi-major axes, we find good agreement with the ∼ 1% planet occurrence rates from direct imaging surveys. Assuming a symmetric power law, we also estimate that the occurrence of giant planets between 0.1−100 au is 26.6 +7.5 −5.4 % for planets with masses 0.1-20 M J and decreases to 6.2 +1.5 −1.2 % for planets more massive than Jupiter. This implies that only a fraction of the structures detected in disks around young stars can be attributed to giant planets. Various planet population synthesis models show good agreement with the observed distribution, and we show how a quantitative comparison between model and data can be used to constrain planet formation and migration mechanisms.

Context. Previous theoretical works on planet formation around low-mass stars have often been limited to large planets and individual systems. As current surveys routinely detect planets down to terrestrial size in these systems, models have shifted toward a more holistic approach that reflects their diverse architectures. Aims. Here, we investigate planet formation around low-mass stars and identify differences in the statistical distribution of modeled planets. We compare the synthetic planet populations to observed exoplanets and we discuss the identified trends. Methods. We used the Generation III Bern global model of planet formation and evolution to calculate synthetic populations, while varying the central star from Solar-like stars to ultra-late M dwarfs. This model includes planetary migration, N-body interactions between embryos, accretion of planetesimals and gas, and the long-term contraction and loss of the gaseous atmospheres. Results. We find that temperate, Earth-sized planets are most frequent around early M dwarfs (0.3 M⊙–0.5 M⊙) and that they are more rare for Solar-type stars and late M dwarfs. The planetary mass distribution does not linearly scale with the disk mass. The reason behind this is attributed to the emergence of giant planets for M⋆ ≥ 0.5 M⊙, which leads to the ejection of smaller planets. Given a linear scaling of the disk mass with stellar mass, the formation of Earth-like planets is limited by the available amount of solids for ultra-late M dwarfs. For M⋆ ≥ 0.3 M⊙, however, there is sufficient mass in the majority of systems, leading to a similar amount of Exo-Earths going from M to G dwarfs. In contrast, the number of super-Earths and larger planets increases monotonically with stellar mass. We further identify a regime of disk parameters that reproduces observed M-dwarf systems such as TRAPPIST-1. However, giant planets around late M dwarfs, such as GJ 3512b, only form when type I migration is substantially reduced. Conclusions. We are able to quantify the stellar mass dependence of multi-planet systems using global simulations of planet formation and evolution. The results fare well in comparison to current observational data and predict trends that can be tested with future observations.

The SpHere INfrared Exoplanet (SHINE) project is a 500-star survey performed with SPHERE on the Very Large Telescope for the purpose of directly detecting new substellar companions and understanding their formation and early evolution. Here we present an initial statistical analysis for a subsample of 150 stars spanning spectral types from B to M that are representative of the full SHINE sample. Our goal is to constrain the frequency of substellar companions with masses between 1 and 75 M Jup and semimajor axes between 5 and 300 au. For this purpose, we adopt detection limits as a function of angular separation from the survey data for all stars converted into mass and projected orbital separation using the BEX-COND-hot evolutionary tracks and known distance to each system. Based on the results obtained for each star and on the 13 detections in the sample, we use a Markov chain Monte Carlo tool to compare our observations to two different types of models. The first is a parametric model based on observational constraints, and the second type are numerical models that combine advanced core accretion and gravitational instability planet population synthesis. Using the parametric model, we show that the frequencies of systems with at least one substellar companion are 23.0 +13.5 −9.7 %, 5.8 +4.7 −2.8 %, and 12.6 +12.9 −7.1 % for BA, FGK, and M stars, respectively. We also demonstrate that a planet-like formation pathway probably dominates the mass range from 1-75 M Jup for companions around BA stars, while for M dwarfs, brown dwarf binaries dominate detections. In contrast, a combination of binary star-like and planet-like formation is required to best fit the observations for FGK stars. Using our population model and restricting our sample to FGK stars, we derive a frequency of 5.7 +3.8 −2.8 %, consistent with predictions from the parametric model. More generally, the frequency values that we derive are in excellent agreement with values obtained in previous studies.