Measuring rest-frame ultraviolet rotational transitions from the Lyman and Werner bands in absorption against a bright background continuum is one of the few ways to directly measure molecular hydrogen (H2). Here we report the detection of Lyman-Werner absorption from H2 at z=0.56 in a sub-damped Ly-alpha system with neutral hydrogen column density N(HI) = 10^(19.5 +/- 0.2) cm^-2. This is the first H2 system analysed at a redshift < 1.5 beyond the Milky Way halo. It has a surprisingly high molecular fraction: log f(H2) > -1.93 +/- 0.36 based on modelling the line profiles, with a robust model-independent lower limit of f(H2) > 10^-3. This is higher than f(H2) values seen along sightlines with similar N(HI) through the Milky Way disk and the Magellanic clouds. The metallicity of the absorber is 0.19 +0.21 -0.10 solar, with a dust-to-gas ratio < 0.36 times the value in the solar neighbourhood. Absorption from associated low-ionisation metal transitions such as OI and FeII is observed in addition to OVI. Using Cloudy models we show that there are three phases present; a ~100 K phase giving rise to H2, a ~10^4 K phase where most of the low-ionisation metal absorption is produced; and a hotter phase associated with OVI. Based on similarities to high velocity clouds in the Milky Way halo showing H2 and the presence of two nearby galaxy candidates with impact parameters of ~10 kpc, we suggest that the absorber may be produced by a tidally-stripped structure similar to the Magellanic Stream.
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