Probing planet formation and disk substructures in the inner disk of
  Herbig Ae stars with CO rovibrational emission
  [abridged]CO rovibrational lines are efficient probes of warm molecular gas
and can give unique insights into the inner 10 AU of proto-planetary disks.
Recent studies have found a relation between the ratio of lines originating
from the second and first vibrationally excited state, denoted as $v2/v1$, and
the emitting radius of CO. In disks around Herbig Ae stars the vibrational
excitation is low when CO lines come from close to the star, and high when
lines only probe gas at large radii (more than 5 AU). We aim to find
explanations for the observed trends between CO vibrational ratio, emitting
radii, and NIR excess, and identify their implications in terms of the physical
and chemical structure of inner disks around Herbig stars. Slab models and full
disk thermo chemical models are calculated. Simulated observations from the
models are directly compared to the data. Broad CO lines with low vibrational
ratios are best explained by a warm (400-1300 K) inner disk surface with
gas-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 narrow
lines with high vibrational ratios requires an inner cavity of a least 5 AU in
both dust and gas, followed by a cool (100-300 K) molecular gas reservoir with
gas-to-dust ratios greater than 10000 at the cavity wall. In all cases the CO
gas must be close to thermalization with the dust. The high gas-to-dust ratios
needed to explain high $v2/v1$ in narrow CO lines for a subset of group I disks
can naturally be interpreted as due to the dust traps that have been proposed
to explain millimeter dust cavities. The broad lines seen in most group II
objects indicate a very flat disk in addition to inner disk substructures
within 10 AU that can be related to the substructures recently observed with
ALMA.
