  White dwarfs are routinely observed to have polluted atmospheres, and
sometimes significant infrared excesses, that indicate ongoing accretion of
circumstellar dust and rocky debris. Typically this debris is assumed to be in
the form of a (circular) disc, and to originate from asteroids that passed
close enough to the white dwarf to be pulled apart by tides. However,
theoretical considerations suggest that the circularisation of the debris,
which initially occupies highly eccentric orbits, is very slow. We therefore
hypothesise that the observations may be readily explained by the debris
remaining on highly eccentric orbits, and we explore the properties of such
debris. For the generic case of an asteroid originating at several au from the
white dwarf, we find that all of the tidal debris is always bound to the white
dwarf and that the orbital energy distribution of the debris is narrow enough
that it executes similar elliptical orbits with only a narrow spread. Assuming
that the tidal field of the white dwarf is sufficient to minimise the effects
of self-gravity and collisions within the debris, we estimate the time over
which the debris spreads into a single elliptical ring, and we generate toy
spectra and lightcurves from the initial disruption to late times when the
debris distribution is essentially time steady. Finally we speculate on the
connection between these simple considerations and the observed properties of
these systems, and on additional physical processes that may change this simple
picture.
