Spatially resolving the inner dust cavity of the transitional disks is a key
to understanding the connection between planetary formation and disk dispersal.
The disk around the Herbig star HD 139614 is of particular interest since it
presents a pretransitional nature with an au-sized gap, in the dust, that was
spatially resolved by mid-IR interferometry. Using new NIR interferometric
observations, we aim to characterize the 0.1-10~au region of the HD~139614 disk
further and identify viable mechanisms for the inner disk clearing. We report
the first multiwavelength radiative transfer modeling of the interferometric
data acquired on HD~139614 with PIONIER, AMBER, and MIDI, complemented by
Herschel/PACS photometries. We confirm a gap structure in the um-sized dust,
extending from about 2.5 au to 6 au, and constrained the properties of the
inner dust component: e.g., a radially increasing surface density profile, and
a depletion of 10^3 relative to the outer disk. Since self-shadowing and
photoevaporation appears unlikely to be responsible for the au-sized gap of
HD~139614, we thus tested if dynamical clearing could be a viable mechanism
using hydrodynamical simulations to predict the gaseous disk structure. Indeed,
a narrow au-sized gap is expected when a single giant planet interacts with the
disk. Assuming that small dust grains are well coupled to the gas, we found
that a ~ 3~Mjup planet located at 4.5 au from the star could, in less than 1
Myr, reproduce most of the aspects of the dust surface density profile, while
no significant depletion in gas occurred in the inner disk, in contrast to the
dust. However, the dust-depleted inner disk could be explained by the expected
dust filtration by the gap and the efficient dust growth/fragmentation in the
inner disk regions. Our results support the hypothesis of a giant planet
opening a gap and shaping the inner region of the HD~139614 disk.Comment: Version accepted in A&A, with typos corrections in the tex