On the uncertainties of the central density in axisymmetric galaxies resulting from deprojection

• Published in: Monthly notices of the Royal Astronomical Society 1997-05, Vol.287 (3), p.543-555, Article 543
• Main Author: van den Bosch, F. C.
• Format: Article
• Language: English
• Subjects: galaxies: elliptical and lenticular; galaxies: fundamental parameters; galaxies: individual: M32; galaxies: kinematics and dynamics; galaxies: nuclei; galaxies: photometry
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/287.3.543

The deprojection of the surface brightness of axisymmetric galaxies is indeterminate unless the galaxy is seen edge-on. In practice, this problem is often circumvented by making ad hoc assumptions about the density distribution. However, one can redistribute the density and still project to the same surface brightness. This is similar to adding so-called konus densities to the assumed density distribution. In this paper we investigate the maximum konus density that one can add to elliptical galaxies. In particular we focus on the uncertainties in the central densities of axisymmetric, elliptical galaxies arising from the non-uniqueness of the deprojection. For Stäckel potentials a sufficient condition for positivity of the phase-space distribution function exists, which is used as a criterion for determining the maximum konus density that one can add to a perfect oblate spheroid. For small inclination angles we find an uncertainty in the central density of up to a factor 2. Elliptical galaxies in general have a central density cusp. We therefore also investigate the maximum konus densities of cusped ellipticals. For these models we use an approximate criterion, which we have tested on the perfect oblate spheroid models. For sufficiently small scalelengths, the central density of the maximum konus density that can be added to a cusped elliptical is very high. In order to estimate the dynamical influence of konus densities on the central region, we calculate the mass fraction Mkon/Mgal they can add to the centre. We show that this mass fraction is at most a few per cent. We also investigate the dynamical effect of cusped konus densities that have ρ(r) ∝ r−α at small radii. We show that konus densities can only be moderately cusped (α < 1), and that an increase in cusp slope α results in a decrease of the mass fraction added to the centre by the konus density. We illustrate all this by the specific example of M32, and show that the uncertainty in the central mass due to deprojection is negligible compared with the inferred mass of the central black hole (BH) in this galaxy.