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7.16. A possibility of direct determination of the star phase density in the Galactic nuclear cluster

Published online by Cambridge University Press:  25 May 2016

A.M. Fridman
Affiliation:
Institute of Astronomy, Russian Academy of Science, Pyatnitskaya 48, Moscow, 109017 Russia
E.V. Polyachenko
Affiliation:
Institute of Astronomy, Russian Academy of Science, Pyatnitskaya 48, Moscow, 109017 Russia
V.L. Polyachenko
Affiliation:
Institute of Astronomy, Russian Academy of Science, Pyatnitskaya 48, Moscow, 109017 Russia

Extract

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Line-of-sight and proper motions data for stars near the Galactic center have evolved in recent years (see, e.g. Eckart & Genzel). The data were used for determining the star velocity dispersions in different directions (with a result that the velocity distribution is isotropic to within the observational error). Here we note that there exists a possibility for determining the star phase density itself from such data. The method is based on the solution of the corrensponding integral equations with their left sides being calculated from radial velocities and proper motions. Remind that discussion of the problems connected with reconstruction of the phase density from the radial velocity data was started by Merritt. There is some difference in applying this approach to self-gravitating systems (open and globular clusters) and clusters within external gravitational field. Among the latter is, for example, the inner parts of the Galactic nuclear cluster: they are governed by the field of the central black hole. It follows from the proper motions data estimates for a mass within a radius of 0.16 pc and within 0.083 pc given by Eckart & Genzel (cited above). In the case of the cluster in the field of the black hole we have no need of information about the densities σ(s) (s is the projected radius) and ρ(r) (since the method uses only the gravitational potential Φ(r), which here is foregone: Φ(r) = −GMh/r). Unfortunately, the data on the stars around the central black hole are yet inadequate to derive the distribution function with satisfactory accuracy. (Obviously the necessary data will be available before long.) So we restrict ourselves to only testing the computer algorithms used on the example of the simplest (Plummer) model, for which f(E) ∞ (–E)7/2.

Type
Part II. Nuclear Interstellar Medium
Copyright
Copyright © Kluwer 1998 

References

Eckart, , and Genzel, , (1996) Nature 383, p. 415.Google Scholar
Merritt, D., (1993) Astrophys. J. 413, p. 79.Google Scholar
Tikhonov, A.N., Goncharskij, A.V., Stepanov, V.V. and Yagola, A.G. (1990) Numerical methods of solution of ill-posed problems, Moscow, Nauka.Google Scholar