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[abridged]CO rovibrational lines are efficient probes of warm molecular gasand can give unique insights into the inner 10 AU of proto-planetary disks.Recent studies have found a relation between the ratio of lines originatingfrom the second and first vibrationally excited state, denoted as $v2/v1$, andthe emitting radius of CO. In disks around Herbig Ae stars the vibrationalexcitation is low when CO lines come from close to the star, and high whenlines only probe gas at large radii (more than 5 AU). We aim to findexplanations for the observed trends between CO vibrational ratio, emittingradii, and NIR excess, and identify their implications in terms of the physicaland chemical structure of inner disks around Herbig stars. Slab models and fulldisk thermo chemical models are calculated. Simulated observations from themodels are directly compared to the data. Broad CO lines with low vibrationalratios are best explained by a warm (400-1300 K) inner disk surface withgas-to-dust ratios below 1000; no CO is detected within/at the inner dust rim,due to dissociation at high temperatures. In contrast, explaining the narrowlines with high vibrational ratios requires an inner cavity of a least 5 AU inboth dust and gas, followed by a cool (100-300 K) molecular gas reservoir withgas-to-dust ratios greater than 10000 at the cavity wall. In all cases the COgas must be close to thermalization with the dust. The high gas-to-dust ratiosneeded to explain high $v2/v1$ in narrow CO lines for a subset of group I diskscan naturally be interpreted as due to the dust traps that have been proposedto explain millimeter dust cavities. The broad lines seen in most group IIobjects indicate a very flat disk in addition to inner disk substructureswithin 10 AU that can be related to the substructures recently observed withALMA.

Probing planet formation and disk substructures in the inner disk of Herbig Ae stars with CO rovibrational emission