On the Implications of the nth-Order Virial Equations for Heterogeneous and Concentric Jacobi, Dedekind, and Riemann Ellipsoids

Details On the Implications of the nth-Order Virial Equations for Heterogeneous and Concentric Jacobi, Dedekind, and Riemann Ellipsoids On the Implications of the nth-Order Virial Equations for Heterogeneous and Concentric Jacobi, Dedekind, and Riemann Ellipsoids

Apr 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996apj...460..762f&link_type=abstract

Astrophysical Journal v.460, p.762

Astronomy and Astrophysics

Astronomy

2

Stars: Interiors, Stars: Rotation

Scientific paper

The implications of the nth-order virial equations are analyzed for concentric heterogeneous ellipsoids with a density distribution of the form ρ = ρcf(m2), where m2 = Σ31 =1χ2i, 0 ≤ m2 ≤ 1, and αi are the semiaxes of the external ellipsoid corresponding to m2 = 1. Solutions analogous to Jacobi ellipsoids (with constant angular velocity Ω, without vorticity), to Dedekind ellipsoids (with nonuniform vorticity Ζ and zero angular velocity), and to Riemann ellipsoids (with constant angular velocity and nonuniform vorticity) are explored. It is shown that only the second- and fourth-order virial equations give nontrivial results: all the odd-order virial equations are identically satisfied for ellipsoids rotating around a principal axis of symmetry. The even-order virial equations (sixth, eighth, etc.) are shown to be a consequence of the lowest order equations. The entire family of homogeneous and heterogeneous concentric ellipsoids allowed by the virial equations is presented, confronted, and contrasted with the known cases in the literature.

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