On the Mass-Period Distributions and Correlations of Extrasolar Planets

In addition to fitting the data of 233 extrasolar planets with power laws, for the first time in this field we construct a correlated mass-period distribution function of extrasolar planets. An algorithm to generate a pair of positively correlated β-distributed random variables is introduced and used for the construction of correlated distribution functions. We investigate the mass-period correlations of extrasolar planets both in linear and logarithmic spaces, determine the confidence intervals of the correlation coefficients, and confirm that there is a positive mass-period correlation for extrasolar planets. In addition to the paucity of massive close-in planets, which are the main contribution to this correlation, there are other fine structures in the data in the mass-period plane.