  Metal pollution onto white dwarfs is a wide-spread phenomenon that remains
puzzling. Some of these white dwarfs also harbour gaseous debris disks.
Emission lines from these disks open a unique window to the physical properties
of the polluting material, lending insights to their origin. We model the
emission line kinematics for the gas disk around SDSS J1228+1040, a system that
has been monitored for over two decades. We show that the disk mass is strongly
peaked at 1 solar radius (modulo the unknown inclination), and the disk
eccentricity decreases from a value of 0.44 at the inner edge, to nearly zero
at the outer edge. This eccentricity profile is exactly what one expects if the
disk is in a global eccentric mode, precessing rigidly under general relativity
and gas pressure. The precession period is about two decades. We infer that the
mass of the gas disk is roughly equivalent to that of a 50-km rocky body, while
the mass of the accompanying dust disk is likely insignificant. The disk
eccentricity confirms an origin in tidal disruption, while the short disk
diffusion time suggests that the disruption event happened a few centuries ago.
Moreover, we argue that the initial orbit for the disrupted body, and that of
its putative planetary perturber, fall within an AU around the white dwarf. The
total mass of the source population is likely orders of magnitude more massive
than our own Asteroid belt, and does not seem to exist around main-sequence
stars.
