  We present an analysis of the debris disc around the nearby K2 V star HIP
17439. In the context of the Herschel DUNES key programme the disc was observed
and spatially resolved in the far-IR with the Herschel PACS and SPIRE
instruments. In a first model, Ertel et al. (2014) assumed the size and radial
distribution of the circumstellar dust to be independent power laws. There, by
exploring a very broad range of possible model parameters several scenarios
capable of explaining the observations were suggested. In this paper, we
perform a follow-up in-depth collisional modelling of these scenarios trying to
further distinguish between them. In our models we consider collisions, direct
radiation pressure, and drag forces, i.e. the actual physical processes
operating in debris discs. We find that all scenarios discussed in Ertel et al.
are physically sensible and can reproduce the observed SED along with the PACS
surface brightness profiles reasonably well. In one model, the dust is produced
beyond 120au in a narrow planetesimal belt and is transported inwards by
Poynting-Robertson and stellar wind drag. A good agreement with the observed
radial profiles would require stellar winds by about an order of magnitude
stronger than the solar value, which is not supported, although not ruled out,
by observations. Another model consists of two spatially separated planetesimal
belts, a warm inner and a cold outer one. This scenario would probably imply
the presence of planets clearing the gap between the two components. Finally,
we show qualitatively that the observations can be explained by assuming the
dust is produced in a single, but broad planetesimal disc with a surface
density of solids rising outwards, as expected for an extended disc that
experiences a natural inside-out collisional depletion. Prospects of
discriminating between the competing scenarios by future observations are
discussed.
