  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.
