In front of the LMC molecular hydrogen is found in absorption near 0 km/s, being local disk gas, near +60 km/s in an intermediate velocity cloud, and near +120 km/s, in a high velocity halo cloud. The nature of the gas is discussed based on four ORFEUS far UV spectra of LMC stars and including data from the ground and from the IUE satellite. The local gas is cool and, given a span of sight lines of only 2.5 deg, rather fluffy. The fractional abundance of H_2 varies from log(f)=-5.4 to -3.3. Metal depletions (up to -1.7 dex for Fe) are typical for galactic disk gas. In the IV and HV gas an apparent underabundance of neutral oxygen points to an ionization level of the gas of about 90%. H_2 is detected in IV and HV gas toward HD 269546. In the IV gas we find an H_2 column density of log(N)simeq15.6. The H_2 excitation indicates that the line of sight samples a cloud at a temperature below 150 K. Column densities are too small to detect the higher UV pumped excitation levels. The high velocity H_2 (log(N)simeq15.6) is highly excited and probably exposed to a strong radiation field. Its excitation temperature exceeds 1000 K. Due to the radial velocity difference between the halo gas and the Milky Way disk, the unattenuated disk radiation is available for H_2 excitation in the halo. We do not find evidence for an intergalactic origin of this gas; a galactic as well as a Magellanic Cloud origin is possible.
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