The Herbig Ae stars RR Tau, BF Ori and WW Vul are members of the small subclass of young stars with Algol-type brightness variability. There are reasons to assume that they are surrounded by young protoplanetary disk-like envelopes, oriented edge-on and that they are young progenitors of the star β Pictoris. In this paper we present spectroscopic evidences for this assumption. They are based on the observations of variable redshifted absorption components in the sodium Na I D resonance lines, similar to those found in the spectrum of UX Ori. The shortest time scale of their observed variability is one day (BF Ori, WW Vul). Their maximum radial velocities reach 200-300 km s-1, which corresponds to a distance from the star of a few stellar radii. As in the case of UX Ori we connect the formation of such absorption components with the evaporation of star-grazing bodies in the vicinity of young hot stars. The fact that high-velocity redshifted absorption components are systematically observed in the sodium Na I D lines in the spectra of several UX Ori type stars, excludes the interpretation of this phenomenon by a special orientation of star-grazing orbits relative to the observer. We connect such an asymmetry with the evaporation of small (meteor-like) bodies which dissipate completely before the periastron of their orbits are reached, in their movements towards the stars.