  We report on a sensitive search for H2 1-0 S(1), 1-0 S(0) and 2-1 S(1)
ro-vibrational emission at 2.12, 2.22 and 2.25 micron in a sample of 15 Herbig
Ae/Be stars employing CRIRES, the ESO-VLT near-infrared high-resolution
spectrograph, at R~90,000. We detect the H2 1-0 S(1) line toward HD 100546 and
HD 97048. In the other 13 targets, the line is not detected. The H2 1-0 S(0)
and 2-1 S(1) lines are undetected in all sources. This is the first detection
of near-IR H2 emission in HD 100546. The H2 1-0 S(1) lines observed in HD
100546 and HD 97048 are observed at a velocity consistent with the rest
velocity of both stars, suggesting that they are produced in the circumstellar
disk. In HD 97048, the emission is spatially resolved and it is observed to
extend at least up to 200 AU. We report an increase of one order of magnitude
in the H2 1-0 S(1) line flux with respect to previous measurements taken in
2003 for this star, which suggests line variability. In HD 100546 the emission
is tentatively spatially resolved and may extend at least up to 50 AU. Modeling
of the H2 1-0 S(1) line profiles and their spatial extent with flat keplerian
disks shows that most of the emission is produced at a radius >5 AU. Upper
limits to the H2 1-0 S(0)/ 1-0 S(1) and H2 2-1 S(1)/1-0 S(1) line ratios in HD
97048 are consistent with H2 gas at T>2000 K and suggest that the emission
observed may be produced by X-ray excitation. The upper limits for the line
ratios for HD 100546 are inconclusive. Because the H2 emission is located at
large radii, for both sources a thermal emission scenario (i.e., gas heated by
collisions with dust) is implausible. We argue that the observation of H2
emission at large radii may be indicative of an extended disk atmosphere at
radii >5 AU. This may be explained by a hydrostatic disk in which gas and dust
are thermally decoupled or by a disk wind caused by photoevaporation.
