Gravitational helicity flux density from two-body systems

Abstract: The helicity flux density is a novel quantity which characterizes the angle-dependence of the helicity of radiative gravitons and it may be tested by gravitational wave experiments in the future. We derive a quadrupole formula for the helicity flux density due to gravitational radiation in the slow motion and the weak field limit. We apply the formula to the bound and unbound orbits in two-body systems and find that the total radiative helicity fluxes are always zero. However, the radiative helicity flux density, which is $\mathcal{O}(G^3)$ in the Newtonian limit, still has non-trivial dependence on the angle. Furthermore, we also find a formula for the total helicity flux by including all contributions of the higher multipoles.