On the non-existence of some heterogeneous equivalents of ellipsoidal Dedekind figures

Details On the non-existence of some heterogeneous equivalents of ellipsoidal Dedekind figures On the non-existence of some heterogeneous equivalents of ellipsoidal Dedekind figures

Dec 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994a%26a...292...76c&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 292, no. 1, p. 76-81

Statistics

Computation

10

Computational Astrophysics, Ellipsoids, Elliptical Galaxies, Fluid Flow, Hydrodynamics, Incompressible Flow, Kinematics, Stellar Models, Anisotropy, Boundary Conditions, Gravitational Effects, Poisson Equation, Pressure, Stellar Mass, Theorems, Velocity Distribution

Scientific paper

This paper investigates whether a class of heterogeneous equivalents of triaxial ellipsoidal Dedekind equilibrium figures can exist. The self-gravitating mass is made up with concentric ellipsoidal shells which are similar at least in planes containing the velocity field. The velocity field is supposed to be everywhere perpendicular to an axis of the ellipsoids; the flow is incompressible and permanent. By means of the hydrodynamic equations for a perfect fluid we show that if the density is a monotonic function of the radius, no such figures do exist. An equivalent to Dedekind's theorem is also given in the more general case of anisotropic pressure.

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