Non-parametric Triaxial Deprojection of Elliptical Galaxies
  We present a grid-based non-parametric approach to obtain a triaxial
three-dimensional luminosity density from its surface brightness distribution.
Triaxial deprojection is highly degenerate and our approach illustrates the
resulting difficulties. Fortunately, for massive elliptical galaxies, many
deprojections for a particular line of sight can be discarded, because their
projection along other lines of sight does not resemble elliptical galaxies.
The near-elliptical isophotes of these objects imply near ellipsoidal intrinsic
shapes. In fact, deprojection is unique for densities distributed on
ellipsoidal shells. The constrained non-parametric deprojection method we
present here relaxes this constraint and assumes that the contours of the
luminosity density are boxy/discy ellipsoids with radially varying axis ratios.
With this approach we are able to reconstruct the intrinsic triaxial densities
of our test models, including one drawn from an $N$-body simulation. The method
also allows to compare the relative likelihood of deprojections at different
viewing angles. We show that the viewing orientations of individual galaxies
with nearly ellipsoidal isophotal shapes can be constrained from photometric
data alone.
