Existence of slowly rotating bipolytropes with prolate cores

TL;DR

This paper demonstrates the theoretical existence of slowly rotating bipolytropic bodies with prolate cores and oblate envelopes, revealing new equilibrium configurations in astrophysical models.

Contribution

It introduces the first known hydrostatic equilibrium states for bipolytropes with prolate cores and oblate envelopes, supported by numerical experiments.

Findings

Prolate cores can exist in equilibrium with faster-spinning oblate envelopes.

No equilibrium solutions found with prolate envelopes.

Prolate cores can be at rest in some configurations.

Abstract

We report the existence of hydrostatic equilibrium states for a composite body made of two rigidly rotating, homogeneous layers bounded by spheroidal surfaces, where the core has a prolate shape. These new configurations require an oblate envelope that spins faster than the core. No solution with a prolate envelope is found. For some parameters, the prolate core can even be at rest. Numerical experiments based on the self-consistent field method support this result in the case of heterogeneous layers with polytropic equations of state. The possible cancellation of the first gravitational moment, $J_2$, is discussed.