Post-Newtonian expansion of gravitational waves from a particle in circular orbit around a rotating black hole: Up to O(v(8)) beyond the quadrupole formula

Extending a method developed by Sasaki in the Schwarzschild case and by Shibata, Sasaki, Tagoshi, and Tanaka in the Kerr case, we calculate the post-Newtonian expansion of the gravitational wave luminosities from a test particle in circular orbit around a rotating black hole up to O(upsilon(8)) beyond the quadrupole formula. The orbit of a test particle is restricted on the equatorial plane. We find that spin-dependent terms appear in each post-Newtonian order, and that at O(upsilon(6)) they have a significant effect on the orbital phase evolution of coalescing compact binaries. By comparing the post-Newtonian formula of the luminosity with numerical results we find that, for 30M less than or equal to r less than or equal to 100M, the spin-dependent terms at O(upsilon(6)) and O(upsilon(7)) improve the accuracy of the post-Newtonian formula significantly, but those at O(upsilon(8)) do not improve.