Multipole Density Research Articles

High zonal harmonics of rapidly rotating planets

A new perturbation expansion is derived for the structure of rotating bodies in hydrostatic equilibrium. The method uses an expansion of the density on Legendre polynomial functions of angle, and can be developed analytically in a manner analogous to the standard level-surface perturbation theory. The new theory proceeds from a prescribed pressure-density relation rather than from a prescribed density distribution, and is both simpler and more physically transparent than the level-surface approach. High zonal harmonics are shown to arise via a transfer function involving derivatives of the interior sound velocity, and via mixing of multipole density components in the outer shell of the planet. Sample calculations for polytropic sequences are presented, as well as standard gravity models for Jupiter and Saturn. Mathematical subleties of the theory are discussed in an appendix.

Covariant multipole polarization operators and density matrices for any spin

Covariant multipole polarization operators for a particle with finite nonzero mass and arbitrary spin are constructed by considering the usual multipole expansion of polarization matrices as the rest system operators. Then these multipole operators are used to write down the covariant density matrices and finally their properties are briefly discussed.