Estimations of Planetary Occurrence Rates for Solar-type Stars with Data Release 25 from Kepler Q1–Q17 Observations

The detection of exoplanets in the past three decades has revealed the fact that planets are ubiquitous in the universe. In order to deeply study the ubiquity of habitable planets, on one hand, we need to understand the characteristics of habitable planets; on the other hand, we can analyze the the distribution characteristics of exoplanets have been found, and to calculate the probability of occurrence of such planets around stars. Among the exoplanets that have been found so far, most of them are discovered by the transit method. For example, the number of the planets detected by the Kepler space telescope is 2344. Kepler telescope officially retired in 2018, and the Kepler team released the final version of Kepler Data Release (DR25), including a total of 198709 stars observed quarterly Q1–Q17. Here 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 radius and orbital 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 $R_{\oplus }$ ($R_{\oplus }$ is one radius of the Earth) and orbital period range of 0.4–400 days by IDEM and ML, for which around F stars are respectively $0.36\pm 0.02$ and $0.47\pm 0.02$. The rates around G stars by IDEM and ML are respectively $1.62\pm 0.05$ and $1.23\pm 0.04$. The rates around K stars by IDEM and ML are respectively $2.61\pm 0.12$ and $2.73\pm 0.13$. And the overall occurrence rate of such planets around F, G, K stars by IDEM and ML are respectively $1.16\pm 0.03$ and $0.90\pm 0.02$. According to our estimation, we further show the results for the planet occurrence rates around stars with different spectral types by different methods, and discuss the reliability of the results in comparison with the previous studies.