Dynamical evolution and leading order gravitational wave emission of Riemann-S binaries

TL;DR

This paper introduces an approximate method to study the dynamical evolution and gravitational wave emission of binary systems of polytropic ellipsoids, accounting for stellar parameters and gravitational radiation effects.

Contribution

It presents a novel approach reducing hydrodynamics to ODEs for ellipsoidal stars and incorporates leading order gravitational wave emission in the analysis.

Findings

Stellar parameters significantly influence gravitational waveforms.

The method effectively models the evolution of extended binary systems.

Gravitational radiation reaction is incorporated in a quasi-static approximation.

Abstract

An approximate strategy for studying the evolution of binary systems of extended objects is introduced. The stars are assumed to be polytropic ellipsoids. The surfaces of constant density maintain their ellipsoidal shape during the time evolution. The equations of hydrodynamics then reduce to a system of ordinary differential equations for the internal velocities, the principal axes of the stars and the orbital parameters. The equations of motion are given within Lagrangian and Hamiltonian formalism. The special case when both stars are axially symmetric fluid configurations is considered. Leading order gravitational radiation reaction is incorporated, where the quasi-static approximation is applied to the internal degrees of freedom of the stars. The influence of the stellar parameters, in particular the influence of the polytropic index $n$, on the leading order gravitational waveforms is studied.