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We report on a sensitive search for mid-infrared molecular hydrogen emission from protoplanetary disks. 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 H$\,_2~0{-}0~S(2)~(J=4{-}2)$emission at 12.278 micron and H$\,_2~0{-}0~S(1)~(J=3{-}1)$emission at 17.035 micron with VISIR, ESO-VLT's high-resolution mid-infrared spectrograph. None of the sources present evidence for molecular hydrogen emission at the wavelengths observed. Stringent 3σupper limits to the integrated line fluxes and the mass of optically thin warm gas ($T=$150, 300 and 1000 K) in the disks are derived. The disks contain less than a few tenths of Jupiter mass of optically thin H2gas at 150 K, and less than a few Earth masses of optically thin H2gas at 300 K and higher temperatures. We compare our results to a Chiang & Goldreich (1997, ApJ, 490, 368, CG97) two-layer disk model of masses 0.02 $M_{\odot}$and 0.11 $M_{\odot}$. 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 expected to be in the surface layer. If the two-layer approximation to the structure of the disk is correct, our non-detections are consistent with the low flux levels expected from the small amount of H2gas in the surface layer. We present a calculation of the expected thermal H2emission from optically thick disks, assuming a CG97 disk structure, a gas-to-dust ratio of 100 and Tgas= Tdust. We show that the expected H2thermal emission fluxes from typical disks around Herbig Ae/Be stars are of the order of 10-16to 10-17erg s-1cm-2for a distance of 140 pc. This is much lower than the detection limits of our observations (5 $\times$10-15erg s-1cm-2). H2emission levels are very sensitive to departures from the thermal coupling between the molecular gas and dust in the surface layer. Additional sources of heating of gas in the disk's surface layer could have a major impact on the expected H2disk emission. Our results suggest that 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.

The process of turbulent radial mixing in protoplanetary disks has strong relevance to the analysis of the spatial distribution of crystalline dust species in disks around young stars and to studies of the composition of meteorites and comets in our own solar system. A debate has gone on in the recent literature on the ratio of the effective viscosity coefficient ν(responsible for accretion) to the turbulent diffusion coefficient D(responsible for mixing). Numerical magneto-hydrodynamic simulations have yielded values between $\nu/D\simeq 10$(Carballido et al. 2005, MNRAS, 358, 1055) and $\nu/D\simeq 0.85$(Johansen & Klahr 2005, ApJ, 634, 1353). Here we present two analytic arguments for the ratio $\nu/D=1/3$which are based on elegant, though strongly simplified assumptions. We argue that whichever of these numbers comes closest to reality may be determined observationallyby using spatially resolved mid-infrared measurements of protoplanetary disks around Herbig stars. If meridional flows are present in the disk, then we expect less abundance of crystalline dust in the surface layers, a prediction which can likewise be observationally tested with mid-infrared interferometers.

Context. The disk-outflow connection is thought to play a key role in extracting excess angular momentum from a forming proto-star. Although jet rotation has been observed in a few objects, no rotation of molecular outflows has been unambiguously reported so far.Aims. We report new millimeter-interferometric observations of the edge-on T?Tauri?star ? disk system in the isolated Bok globule CB?26. The aim of these observations was to study the disk-outflow relation in this 1?Myr old low-mass young stellar object.Methods. The IRAM PdBI array was used to observe 12CO(2?1) at 1.3?mm in two configurations, resulting in spectral line maps with 1.5???resolution. We use an empirical parameterized steady-state outflow model combined with 2-D line radiative transfer calculations and ?2-minimization in parameter space to derive a best-fit model and constrain parameters of the outflow.Results. The data reveal a previously undiscovered collimated bipolar molecular outflow of total length ?2000?AU, escaping perpendicular to the plane of the disk. We find peculiar kinematic signatures that suggest that the outflow is rotating with the same orientation as the disk. However, we could not ultimately exclude jet precession or two misaligned flows as possible origins of the observed peculiar velocity field. There is indirect indication that the embedded driving source is a binary system, which, together with the youth of the source, could provide a clue to the observed kinematic features of the outflow.Conclusions. CB?26 is so far the most promising source in which to study the rotation of a molecular outflow. Assuming that the outflow is rotating, we compute and compare masses, mass flux, angular momenta, and angular momentum flux of the disk and outflow and derive disk dispersal timescales of 0.5 ...1?Myr, comparable to the age of the system.