  Gaseous metal discs around single white dwarfs have been discovered recently.
They are thought to develop from disrupted planetary bodies. 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). Therefor 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. 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 an effective
temperature of about 6000 K and a surface mass density of 0.3 g/cm^2. The inner
radius is well constrained at about 0.64 Solar radii. 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 Solar radii, contain a mass of about 3 to
6*10^21 g, the latter equivalent to the mass of a 135-km diameter Solar System
asteroid.
