Deprojection of light distributions of nearby systems: perspective effect and non-uniqueness

Deriving the three-dimensional volume density distribution from a two-dimensional light distribution of a system yields generally non-unique results. The case for nearby systems is studied, taking into account the extra constraints from the perspective effect. It is shown analytically that a new form of non-uniqueness exists. The phantom spheroid (PS) for a nearby system preserves the intrinsic mirror symmetry and projected asymmetry of the system while changing the shape and the major-axis orientation of the system. A family of analytical models is given as functions of the distance (D-o) to the object and the amount (gamma) of the PS density superimposed. The range of the major-axis angles is constrained analytically by requiring a positive density everywhere. These models suggest that observations other than surface brightness maps are required to lift the degeneracy in the major-axis angle and axis ratio of the central bar of the Milky Way.