Asymptotic gravitational wave fluxes from a spinning particle in circular equatorial orbits around a rotating black hole

We present a new computation of the asymptotic gravitational wave energy fluxes emitted by a {\it spinning} particle in circular equatorial orbits about a Kerr black hole. The particle dynamics is computed in the pole-dipole approximation, solving the Mathisson-Papapetrou equations with the Tulczyjew spin-supplementary-condition. The fluxes are computed, for the first time, by solving the 2+1 Teukolsky equation in the time-domain using hyperboloidal and horizon-penetrating coordinates. Denoting by $M$ the black hole mass and by $\mu$ the particle mass, we cover dimensionless background spins $a\mathrm{/}M=(0,\pm 0.9)$ and dimensionless particle spins $-0.9\le S\mathrm{/}{\mu }^2\le +0.9$. Our results span orbits of Boyer-Lindquist coordinate radii $4\leq r/M \leq 30$; notably, we investigate the strong-field regime, in some cases even beyond the last-stable-orbit. We confirm, numerically, the Tanaka {\it et al.} [Phys.
Rev.\ D 54, 3762] 2.5th order accurate Post-Newtonian (PN) predictions for the gravitational wave fluxes of a spinning particle in circular equatorial orbit: we find an unambiguos trend of the PN-prediction towards the numerical results when $r$ is large. At $r\mathrm{/}M=30$ the fractional agreement between the full numerical flux, approximated as the sum over the modes $m=1,2,3$, and the PN prediction is $\lesssim 0.5\mathrm{\%}$ in all cases tested. This is close to our fractional numerical accuracy ($\sim 0.2\mathrm{\%}$). For smaller radii, the agreement between the 2.5PN prediction and the numerical result progressively deteriorates. Our numerical data will be essential to develop suitably resummed expressions of the 2.5PN analytical fluxes in order to improve their accuracy in the strong-field regime.