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 ( H _ { 2 } ) .
Here we report the detection of absorption from H _ { 2 } at z = 0.56 in a sub-damped Ly \alpha system with neutral hydrogen column density N _ { \textsc { H i } } = 10 ^ { 19.5 \pm 0.2 } cm ^ { -2 } .
This is the first H _ { 2 } system analysed at a redshift < 1.5 beyond the Milky Way halo .
It has a surprisingly high molecular fraction : log _ { 10 } f _ { \textrm { H } _ { 2 } } > -1.93 \pm 0.36 based on modelling the line profiles , with a robust model-independent lower limit of f _ { \textrm { H } _ { 2 } } > 10 ^ { -3 } .
This is higher than f _ { \textrm { H } _ { 2 } } values seen along sightlines with similar N _ { \textsc { H i } } 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 of the value in the solar neighbourhood .
Absorption from associated low-ionisation metal transitions such as O i and Fe ii is observed in addition to O vi .
Using Cloudy models we show that there are three phases present ; a \sim 100 K phase giving rise to H _ { 2 } , a \sim 10 ^ { 4 } K phase where most of the low-ionisation metal absorption is produced ; and a hotter phase associated with O vi .
Based on similarities to high velocity clouds in the Milky Way halo showing H _ { 2 } , and the presence of two nearby galaxy candidates with impact parameters of \sim 10 kpc , we suggest that the absorber may be produced by a tidally-stripped structure similar to the Magellanic Stream .