11-orbit inspiral of a mass ratio 4:1 black-hole binary

We analyse an 11-orbit inspiral of a non-spinning black-hole binary with mass ratio q = M-1/M-2 = 4. The numerically obtained gravitational waveforms are compared with post-Newtonian (PN) predictions including several subdominant multipoles up to multipolar indices (l = 5, m = 5). We find that (i) numerical and post-Newtonian predictions of the phase of the (2, 2) mode accumulate a phase difference of about 0.35 rad at the PN cut-off frequency M omega = 0.1 for the Taylor T1 approximant when numerical and PN waveforms are matched over a window in the early inspiral phase; (ii) in contrast to previous studies of equal mass and specific spinning binaries, we find the Taylor T4 approximant to agree less well with numerical results, provided the latter are extrapolated to infinite extraction radius; (iii) extrapolation of gravitational waveforms to infinite extraction radius is particularly important for subdominant multipoles with l not equal m; (iv) 3PN terms in post-Newtonian multipole expansions significantly improve the agreement with numerical predictions for subdominant multipoles.