What empties the hot Neptune desert?
In plain words
Planets the size and mass of Neptune are rare on orbits shorter than a few days, even though both smaller and larger planets are found there. Starlight stripping their gas, and the way giant planets arrive in such close orbits, are proposed causes.
Precise statement
Neptune-mass and Neptune-radius planets are depleted at $P$ below $\sim 2-4\,\mathrm{d}$, with the upper desert boundary following mass decreasing with period and a differently shaped lower boundary (Mazeh, Holczer and Faigler 2016, A&A 589, A75). Determine whether photoevaporation of irradiated sub-Neptunes sets the lower boundary and the tidal-disruption limit of high-eccentricity migration sets the upper one (Owen and Lai 2018, arXiv:1807.00012), or whether formation-location or tidal decay effects dominate. The answer is a mechanism reproducing both boundaries versus stellar type and age.
What would settle it
Masses, radii, ages and measured escape rates (helium $10830\,\mathrm{Angstrom}$ and Lyman-alpha transits) for planets in and near the desert from TESS follow-up, compared with each boundary's predicted dependence on host properties.