Context : Gaseous metal discs around single white dwarfs have been discovered recently .
They are thought to develop from disrupted planetary bodies .

Aims : Spectroscopic analyses will allow us to study the composition of extrasolar planetary material .
We investigate in detail the first object for which a gas disc was discovered ( SDSS J122859.93+104032.9 ) .

Methods : We perform non-LTE modelling of viscous gas discs by computing the detailed vertical structure and line spectra .
The models are composed of carbon , oxygen , magnesium , silicon , calcium , and hydrogen with chemical abundances typical for Solar System asteroids .
Line asymmetries are modelled by assuming spiral-arm and eccentric disc structures as suggested by hydrodynamical simulations .

Results : The observed infrared Ca ii emission triplet can be modelled with a hydrogen-deficient metal gas disc located inside of the tidal disruption radius , with T _ { eff } \approx 6 000 K and a surface mass density of \mathit { \Sigma } \approx 0.3 g/cm ^ { 2 } .
The inner radius is well constrained at about 0.64 R _ { \odot } .
The line profile asymmetry can be reproduced by either a spiral-arm structure or an eccentric disc , the latter being favoured by its time variability behaviour .
Such structures , reaching from 0.64 to 1.5 R _ { \odot } , contain a mass of about 3–6 \cdot 10 ^ { 21 } g , the latter equivalent to the mass of a 135-km diameter Solar System asteroid .

Conclusions :