We perform detailed spectroscopic analysis and numerical modelling of an H _ { 2 } -bearing damped Lyman- \alpha absorber ( DLA ) at z _ { abs } = 2.05 towards the quasar FBQS J2340-0053 .
Metal absorption features arise from fourteen components spread over \Delta v _ { 90 } = 114 km s ^ { -1 } , seven of which harbour H _ { 2 } .
Column densities of atomic and molecular species are derived through Voigt profile analysis of their absorption lines .
We measure total N ( \ion Hi ) , N ( H _ { 2 } ) and N ( HD ) to be 20.35 \pm 0.05 , 17.99 \pm 0.05 and 14.28 \pm 0.08 ( log cm ^ { -2 } ) respectively .
H _ { 2 } is detected in the lowest six rotational levels of the ground vibrational state .
The DLA has metallicity , Z = 0.3 Z _ { \sun } ( [ S/H ] = -0.52 \pm 0.06 ) and dust-to-gas ratio , \kappa = 0.34 \pm 0.07 .
Numerical models of the H _ { 2 } components are constrained individually to understand the physical structure of the DLA .
We conclude that the DLA is subjected to the metagalactic background radiation and cosmic ray ionization rate of \sim 10 ^ { -15.37 } s ^ { -1 } .
Dust grains in this DLA are smaller than grains in the Galactic interstellar medium .
The inner molecular regions of the H _ { 2 } components have density , temperature and gas pressure in the range 30–120 cm ^ { -3 } , 140–360 K and 7,000–23,000 cm ^ { -3 } K respectively .
Micro-turbulent pressure is a significant constituent of the total pressure , and can play an important role in these innermost regions .
Our H _ { 2 } component models enable us to constrain component-wise N ( \ion Hi ) , and elemental abundances of sulphur , silicon , iron and carbon .
We deduce the line-of-sight thickness of the H _ { 2 } -bearing parts of the DLA to be 7.2 pc .