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-VLTs 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 disks 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 disks 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.
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