  In 2013 a dearth of close-in planets around fast-rotating host stars was
found using statistical tests on Kepler data. The addition of more Kepler and
Transiting Exoplanet Survey Satellite (TESS) systems in 2022 filled this region
of the diagram of stellar rotation period (Prot) versus the planet orbital
period (Porb). We revisited the Prot extraction of Kepler planet-host stars, we
classify the stars by their spectral type, and we studied their Prot-Porb
relations. We only used confirmed exoplanet systems to minimize biases. In
order to learn about the physical processes at work, we used the star-planet
evolution code ESPEM (French acronym for Evolution of Planetary Systems and
Magnetism) to compute a realistic population synthesis of exoplanet systems and
compared them with observations. Because ESPEM works with a single planet
orbiting around a single main-sequence star, we limit our study to this
population of Kepler observed systems filtering out binaries, evolved stars,
and multi-planets. We find in both, observations and simulations, the existence
of a dearth in close-in planets orbiting around fast-rotating stars, with a
dependence on the stellar spectral type (F, G, and K), which is a proxy of the
mass in our sample of stars. There is a change in the edge of the dearth as a
function of the spectral type (and mass). It moves towards shorter Prot as
temperature (and mass) increases, making the dearth look smaller. Realistic
formation hypotheses included in the model and the proper treatment of tidal
and magnetic migration are enough to qualitatively explain the dearth of hot
planets around fast-rotating stars and the uncovered trend with spectral type.
