The Hubble Space Telescope UV Legacy Survey of Galactic Globular Clusters -- XI. The horizontal branch in NGC\,6388 and NGC\,6441

The Hubble Space Telescope UV Legacy survey of Galactic Globular Clusters (GC) is characterising many different aspects of their multiple stellar populations. The "Grundahl-jump" (G-jump) is a discontinuity in ultraviolet brightness of blue horizontal branch (HB) stars, signalling the onset of radiative metal levitation. The HB Legacy data confirmed that the G-jump is located at the same T$_{eff}$ ($\simeq$11,500 K) in nearly all clusters. The only exceptions are the metal-rich clusters NGC 6388 and NGC 6441, where the G-jump occurs at T$_{eff}\simeq$13-14,000K. We compute synthetic HB models based on new evolutionary tracks including the effect of helium diffusion, and approximately accounting for the effect of metal levitation in a stable atmosphere. Our models show that the G-jump location depends on the interplay between the timescale of diffusion and the timescale of the evolution in the T$_{eff}$ range 11,500 K$\lessapprox$T$_{eff}\lessapprox$14,000 K. The G-jump becomes hotter than 11,500 K only for stars that have, in this T$_{eff}$ range, a helium mass fraction Y>0.35. Similarly high Y values are also consistent with the modelling of the HB in NGC 6388 and NGC 6441. In these clusters we predict that a significant fraction of HB stars show helium in their spectra above 11,500 K, and full helium settling should only be found beyond the hotter G-jump.