The Investigation Of Planetary Occurrence Rate Based On Kepler Data

One of the most fundamental and important scientific questions in the study of exoplanets is whether there are habitable worlds beyond Earth.In nearly 30 years of detection,until January 24th 2022,4946 exoplanets have been confirmed,including 810 multi-planet systems.These discoveries show that planets are common in the universe.On this basis,in order to study the occurrence rate of habitable planets,we need to understand the characteristics of habitable planets and analyze the distribution characteristics of discovered exoplanets to deduce the actual distribution of planetary populations in the universe.Until now,the only known habitable planet is Earth.Because of the importance of liquid water to life,the concept of the habitable zones has been proposed,which is the region around a star,in where water on planet’s surface can be kept liquid.A habitable planet should have an atmosphere,and the planet’s surface temperature is largely controlled by an input of external power from the star.The radiation is inversely proportional to the planet’s distance from its host star.Based on studies of the climate of early Venus and Mars,the presence of liquid water on both early Venus and Mars could help us delineate the empirical habitable zones of the solar system and extend the habitable zones beyond the solar system.Though being in the habitable zone is not a sufficient condition for a planet being habitable,it could help us narrow our focus.Exoplanets discovered by the Transit method are the most among the discovered exoplanets,especially the 2,344 exoplanets detected by the Kepler Space Telescope.In 2018,the Kepler Space Telescope was officially decommissioned,and the Kepler team released the final Kepler Data Release(DR25),which included 198,709 stars from Q1 to Q17.In this paper,we analyze the Kepler data by using two different methods,Inverse Detection Efficiency Method(IDEM)and Maximum Likelihood Analysis(ML),to estimate planet occurrence rates in the space of the parameters of exoplanet radius and period.At the same time,the samples were classified according to the spectral types of stars,and the planet occurrence rates around F,G and K Kepler stars as well as its overall formation rate were estimated respectively.We estimate the planetary occurrence rates for planets among radius range of 1-20 R⊕ and orbital period range of 0.4-400 days by IDEM,for which around F,G,K star is nIDEM_F=0.36±0.02,nIDEM_G=1.62±0.05,nIDEM_K=2.61±0.12.And the overall occurrence rate of such planets around FGK stars is nIDEM=1.16±0.03.By using ML for planets with the same range,we estimate the planetary occurrence rates around F,G,K star is nML_F=0.47±0.02,nML_G=1.23±0.04,nML_K=2.73±0.13.And the overall occurrence rate of such planets around FGK stars is nML=0.90±0.02.According to the Estimation,we analyze the results for the planet occurrence rates around star with different spectral types by different calculation methods,and discuss the reliability of the estimated results based on previous studies.