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The motion of a passively gravitating body inside an inhomogeneous elliptical galaxy

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Abstract

The spatial motion of a passively gravitating body (a star or the center of mass of a globular cluster) inside an inhomogeneous, rotating elliptical galaxy with a homothetic density distribution is considered. A so-called “astrophysical law” is adopted for the density distribution of the luminous part of the elliptical galaxy. The gravitation of the luminous part of the galaxy, taken to be an ellipsoidal body with a homothetic density distribution, is taken into account in the motion of the star (or center of mass of a globular cluster), as well as perturbations due to the gravitation of a homeoid corresponding to an ellipsoidal layer filled with dark matter between the luminous part of the galaxy and the galactic halo. An analog for the Jacobi integral is found, the region of possible motions of the star (or globular-cluster center of mass) determined, and zero-velocity surfaces constructed. The Lyapunov stability of the resulting stationary solutions—libration points—is established. The results are applied to the elliptical galaxies NGC 4472 (M49), NGC 4636, and NGC 4374, which contain large numbers of globular clusters. The results for these galaxies show that exact expressions for the potentials of the luminous part of the elliptical galaxy and the homeoid should be used to find the libration points and investigate their stability, rather than approximate expressions.

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Authors and Affiliations

  1. Sternberg Astronomical Institute, Lomonosov Moscow State University, Moscow, 119991, Russia

    S. A. Gasanov

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  1. S. A. Gasanov
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Correspondence to S. A. Gasanov.

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Original Russian Text © S.A. Gasanov, 2015, published in Astronomicheskii Zhurnal, 2015, Vol. 92, No. 3, pp. 270–288.

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Gasanov, S.A. The motion of a passively gravitating body inside an inhomogeneous elliptical galaxy. Astron. Rep. 59, 238–255 (2015). https://doi.org/10.1134/S106377291502002X

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  • DOI: https://doi.org/10.1134/S106377291502002X

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