Dearth of short-period Neptunian exoplanets - a desert in period-mass and period-radius planes

A few studies have reported a significant dearth of exoplanets with Neptune mass and radius with orbital periods below $2$--$4$ d. This cannot be explained by observational biases because many Neptunian planets with longer orbital periods have been detected. The existence of this desert is similar to the appearance of the so-called brown-dwarf desert that suggests different formation mechanisms of planets and stellar companions with short orbital periods. Similarly, the Neptunian desert might indicate different mechanisms of formation and evolution for hot Jupiters and short-period super-Earths. We here follow a previous study and examine the location and shape of the desert in both the period-mass and period-radius planes, using the currently available large samples of planets. The desert in the period-mass plane has a relatively sharp upper edge, with a planetary mass that is inversely proportional to the planetary orbital period, while the lower, somewhat blurred, boundary is located along masses that are apparently linearly proportional to the period. The desert in the period-radius plane of the transiting planets is less clear. It seems as if the radius along the upper boundary is inversely proportional to the period to the power of one-third, while the lower boundary shows a radius that is proportional to the period to the power of two-thirds. The combination of the two upper bounds of the desert, in the period-mass and period-radius planes, yields a planetary mass-radius relation of $R_{\rm p}/R_{\rm Jup}\simeq (1.2\pm0.3)(M_{\rm p}/M_{\rm Jup})^{0.27\pm0.11}\,$ for $ 0.1\lesssim M_{\rm p}/M_{\rm Jup}\lesssim 1$. The derived shape of the desert, which might extend up to periods of $5$--$10$ d, could shed some light on the formation and evolution of close-in planets.