We observed the Herbig Ae/Be stars UX Ori, HD 34282, HD 100453, HD 101412, HD
104237 and HD 142666, and the T Tauri star HD 319139 and searched for H2 0-0
S(2) emission at 12.278 micron and H2 0-0 S(1) emission at 17.035 micron with
VISIR, ESO-VLT's high-resolution MIR spectrograph. None of the sources present
evidence for H2 emission. Stringent 3sigma upper limits to the integrated line
fluxes and the mass of optically thin warm gas in the disks are derived. The
disks contain less than a few tenths of Jupiter mass of optically thin H2 gas
at 150 K at most, and less than a few Earth masses of optically thin H2 gas at
300 K and higher temperatures. We compare our results to a Chiang and Goldreich
(1997, CG97) two-layer disk model. The upper limits to the disk's optically
thin warm gas mass are smaller than the amount of warm gas in the interior
layer of the disk, but they are much larger than the amount of molecular gas in
the surface layer. We present a calculation of the expected thermal H2 emission
from optically thick disks, assuming a CG97 disk structure, a gas-to-dust ratio
of 100 and Tgas = Tdust. The expected H2 thermal emission fluxes from typical
disks around Herbig Ae/Be stars (10^-16 to 10^-17 erg/s/cm2 at 140 pc) are much
lower than the detection limits of our observations (5*10^-15 erg/s/cm2). H2
emission levels are very sensitive to departures from the thermal coupling
between the molecular gas and dust. Additional sources of heating of gas in the
disk's surface layer could have a major impact on the expected H2 disk
emission. In the observed sources the molecular gas and dust in the surface
layer have not significantly departed from thermal coupling (Tgas/Tdust< 2) and
that the gas-to-dust ratio in the surface layer is very likely lower than 1000.Comment: 16 pages, 9 figures, accepted by A&A. v2: typo in footnote **
corrected, v3: corrections of the A&A language editor included, typo in title
of Fig. 1. correcte