Axisymmetric galaxy models with central black holes, with an application to M32
Abstract
The contour integral method of Hunter & Qian is applied to axisymmetric galaxy models in which the distribution function (DF) is of the form f=f(E, L_z), where E and L_z are the classical integrals of motion in an axisymmetric potential. A practical way to construct the unique even part fe(E, L_z) of the twointegral DF for such systems is presented. It is applied to models, both oblate and prolate, in which the mass density is stratified on similar concentric spheroids. The spheroids with scalefree densities are discussed in detail. These provide useful approximations to the behaviour of more realistic models in the limit of small and large radii. The selfconsistent case is treated, as well as the case in which there are additional contributions to the potential from a central black hole or dark halo. The twointegral DFs for scalefree densities in a Kepler potential are particularly simple. These can be used to model powerlaw density cusps near a central black hole, or to model the outer parts of finitemass systems. The range of axial ratios and density profile slopes is determined for which spheroidal powerlaw cusps with a central black hole have a physical twointegral DF. More generally, the twointegral DFs are discussed for a set of spheroidal `(alpha,beta)models', characterized by a powerlaw density cusp with slope alpha at small radii, and a powerlaw density falloff with slope alpha + 2 beta at large radii. As an application, the DF is constructed for the (alpha,beta)model with a 1.8 x 10^6 M_solar black hole used by van der Marel et al.to interpret their high spatial resolution spectroscopic data for M32. The lineofsight velocity profiles are calculated. The results confirm that the model fits the data remarkably well. The model is used to calculate the predicted kinematic signatures of a central black hole in M32 in spectroscopic observations through small apertures, such as are now possible with the Faint Object Spectrograph on board the Hubble Space Telescope.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 1995
 DOI:
 10.1093/mnras/274.2.602
 arXiv:
 arXiv:astroph/9412067
 Bibcode:
 1995MNRAS.274..602Q
 Keywords:

 BLACK HOLE PHYSICS;
 CELESTIAL MECHANICS;
 STELLAR DYNAMICS;
 GALAXIES: INDIVIDUAL: M32;
 GALAXIES: KINEMATICS AND DYNAMICS;
 GALAXIES: STRUCTURE;
 Astrophysics
 EPrint:
 22 pages, uuencoded compressed PostScript, without the figures. Figures at ftp://eku.ias.edu/pub/marel/qianetalfig.uu