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

Abstract

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 dust-free 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. We can design a Phantom Spheroid (PS) for a nearby system which preserves the intrinsic mirror symmetry and projected surface brightness 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 ($D_0$) to the object and the amount ($γ$) of the superimposed PS density. The PS density, different from the well-known konuses of extragalactic systems, makes the luminosity of the system vary slightly with the distance $D_0$. The physical ranges for $γ$ and the major axis angles are constrained analytically by requiring a positive volume density everywhere. These models suggest that observations other than surface brightness maps are required to lift the degeneracy in the tilt angles and axis ratio of the central bar of the Milky Way.