A dichotomy in group II Herbig disks: ALMA gas disk height measurements show both shadowed large vertically extended disks and compact flat disks

Herbig stars can be classified into group I and group II depending on the shape of the far-IR excess from the spectral energy distribution. This separation may be evolutionary and related to the vertical structure of these disks. We aim to determine the emission height of Herbig disks and compare the resulting vertical extent of both groups. ALMA Band 6 observations of 12CO emission lines at sufficient velocity and spatial resolution of eight Herbig disks (four group I and four group II sources) are used to determine the emission heights from the channel maps via geometrical methods developed in other works. We find that all group I disks are vertically extended with a height to radius ratio of at least 0.25, and for three of the disks the gas emission profile can be traced out to 200-500 au. The group II disks are divided between MWC 480 and HD 163296 which have similar emission height profiles as the group I disks, and AK Sco and HD 142666 which are very flat (not exceeding a height of 10 au) and more compact (<200 au in size). The brightness temperatures show no differences between the disks when the luminosity of the host star is accounted for. Our findings agree with previous work suggesting that group I disks are vertically extended and that group II disks are either large and self-shadowed or compact. Both MWC 480 and HD 163296 could be precursors of group I disks, which we see now before a cavity has formed that would allow irradiation of the outer parts of the disk. The very flat disks AK Sco and HD 142666 could be due to significant settling because of the advanced age of these disks (~20 instead of <10 Myr). These large differences in vertical structures are not reflected in the spectral energy distributions of these disks. More and deeper observations at higher spatial and velocity resolution are necessary to further characterize the Herbig sub-groups.