The SPHERE infrared survey for exoplanets (SHINE). III. The demographics
  of young giant exoplanets below 300 au with SPHERE
  The SHINE project is a 500-star survey performed with SPHERE on the VLT 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 that are representative of the full SHINE
sample. Our goal is to constrain the frequency of substellar companions with
masses between 1 and 75 MJup and semimajor axes between 5 and 300 au. 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 MCMC 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 $23.0_{-9.7}^{+13.5}\%$, $5.8_{-2.8}^{+4.7}\%$, and
$12.6_{-7.1}^{+12.9}\%$ for BA, FGK, and M stars, respectively. We also
demonstrate that a planet-like formation pathway probably dominates the mass
range from 1-75 MJup 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 $5.7_{-2.8}^{+3.8}\%$, 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.
