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

Deriving the 3-dimensional volume density distribution from a 2-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 are given as functions of the distance (D0) to the object and the amount (γ) 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.