**AAS 199th meeting, Washington, DC, January 2002**

*Session 53. Galaxies - Evolution*

Display, Tuesday, January 8, 2002, 9:20am-6:30pm, Exhibit Hall
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## [53.05] On van Kampen Modes of Oscillation in Galaxies

*P. O. Vandervoort (Univ. Chicago)*

This paper describes a theory of the modes of oscillation of
a galaxy with a continuous spectrum of real frequencies.
Such modes in an inhomogeneous system are generalizations of
the van Kampen modes in the theory of plasma oscillations.
In the present case, the characteristic value problem
governing the modes is solved with the aid of a generalized
version of the matrix method of Kalnajs. The Eulerian
perturbations of the densities and the gravitational
potentials are represented as superpositions of the elements
of a biorthonormal set of basis densities and potentials.
The linearized collisionless Boltzmann equation is solved in
terms of action-angle variables. As in the case of the van
Kampen modes in a homogeneous plasma, the solutions for the
Eulerian perturbations of the distribution function are
expressed in terms of generalized functions. The condition
for the self-consistency of a mode requires that the density
perturbation of the response of the system to the
perturbation of the gravitational potential is equal to the
density perturbation that is the source of the perturbation
of the potential. The condition of self-consistency reduces
to an inhomogeneous system of linear, algebraic equations
governing the constant coefficients in the superpostions of
basis functions representing the perturbation. In general,
there is no characteristic equation governing the
frequencies in the continuous spectrum. However, isolated
frequencies in the continuous spectrum do satisfy a
characteristic equation which, for inhomogeneous systems, is
a counterpart of the dispersion relation derived by Vlasov
for plasma oscillations.

The author(s) of this abstract have provided an email address
for comments about the abstract:
voort@oddjob.uchicago.edu

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