## Abstract

Gravitational waves emitted by binary systems in the inspiral phase carry a complicated structure, consisting in a superposition of different harmonics of the orbital frequency, the amplitude of each of them taking the form of a post-Newtonian series. In addition to that, spinning binaries experience spin-orbit and spin-spin couplings which induce a precession of the orbital angular momentum and of the individual spins. With one exception, previous analyses of the measurement accuracy of gravitational wave experiments for comparable-mass binary systems have neglected either spin-precession effects or subdominant harmonics and amplitude modulations. Here we give the first explicit description of how these effects combine to improve parameter estimation. We consider supermassive black hole binaries as expected to be observed with the planned space-based interferometer LISA, and study the measurement accuracy for several astrophysically interesting parameters obtainable taking into account the full 2PN waveform for spinning bodies, as well as spin-precession effects. We find that for binaries with a total mass in the range 105M⊙<M<107M⊙ at a redshift of 1, a factor ∼1.5 is in general gained in accuracy, with the notable exception of the determination of the individual masses in equal-mass systems, for which a factor ∼5 can be gained. We also find, as could be expected, that using the full waveform helps increasing the upper mass limit for detection, which can be as high as M=108M⊙ at a redshift of 1, as well as the redshift limit where some information can be extracted from a system, which is roughly z≳10 for M≤107M⊙, 1.5–5 times higher than with the restricted waveform. We computed that the full waveform allows us to use supermassive black hole binaries as standard sirens up to a redshift of z≈1.6, about 0.4 larger than what previous studies allowed. We found that for lower unequal-mass binary systems, the measurement accuracy is not as drastically improved as for other systems. This suggests that for these systems, adding parameters such as eccentricity or alternative gravity parameters could be achieved without much loss in the accuracy.