Non-parametric Deprojection of Surface Brightness Profiles of Galaxies
  in Generalised Geometries
  We present a new Bayesian non-parametric deprojection algorithm DOPING
(Deprojection of Observed Photometry using and INverse Gambit), that is
designed to extract 3-D luminosity density distributions $\rho$ from observed
surface brightness maps $I$, in generalised geometries, while taking into
account changes in intrinsic shape with radius, using a penalised likelihood
approach and an MCMC optimiser. We provide the most likely solution to the
integral equation that represents deprojection of the measured $I$ to $\rho$.
In order to keep the solution modular, we choose to express $\rho$ as a
function of the line-of-sight (LOS) coordinate $z$. We calculate the extent of
the system along the ${\bf z}$-axis, for a given point on the image that lies
within an identified isophotal annulus. The extent along the LOS is binned and
density is held a constant over each such $z$-bin. The code begins with a seed
density and at the beginning of an iterative step, the trial $\rho$ is updated.
Comparison of the projection of the current choice of $\rho$ and the observed
$I$ defines the likelihood function (which is supplemented by Laplacian
regularisation), the maximal region of which is sought by the optimiser
(Metropolis Hastings). The algorithm is successfully tested on a set of test
galaxies, the morphology of which ranges from an elliptical galaxy with varying
eccentricity to an infinitesimally thin disk galaxy marked by an abruptly
varying eccentricity profile. Applications are made to faint dwarf elliptical
galaxy Ic~3019 and another dwarf elliptical that is characterised by a central
spheroidal nuclear component superimposed upon a more extended flattened
component. The result of deprojection of the X-ray image of triaxial cluster
A1413 is also presented.
