基于 f(E,Lz) 的星系建模：M32 中的一颗黑洞

presented a technique for constructing axisymmetric distribution functions for individual galaxies. It starts from the observed surface brightness distribution, which is deprojected to gain the axisymmetric luminosity density, from which follows the stars' gravitational potential. After adding dark mass components, such as a central black hole, the two-integral distribution function (2I-DF) f(E,Lz), which depends only on the classical integrals of motion in an axisymmetric potential, is constructed using the Richardson-Lucy algorithm. This algorithm proved to be very efficient in finding f(E,Lz) provided the integral equation to be solved has been properly modified. Once the 2I-DF is constructed, its kinematics can be computed and compared with those observed. Many discrepancies may be remedied by altering the assumed inclination angle, mass-to-light ratio, dark components, and odd part of the 2I-DF. Remaining discrepancies may indicate, that the distribution function depends on the non-classical third integral, or is non-axisymmetric. The method has been applied to the nearby elliptical galaxy M32. A 2I-DF with ~55 degrees inclination and a central black hole (or other compact dark mass inside ~1pc) of 1.6-2*10^6 Msun fits the high-spatial-resolution kinematic data of van der Marel et al. remarkably well. 2I-DFs with a significantly less or more massive central dark mass or with edge-on inclination can be ruled out for M32. Predictions are made for HST-observations: spectroscopy using its smallest square aperture of 0.09"*0.09" should yield a non-gaussian central velocity profile with broad wings, true and gaussian-fit velocity dispersion of 150-170km/s and 120-130km/s, respectively.