Determining the requisite number of higher harmonics for massive black hole binary analysis with LISA

Previous work has demonstrated that parameter estimation on massive black hole binaries observed by the Laser Interferometer Space Antenna (LISA) will be severely biased if even one higher harmonic out of the ones currently modeled in state-of-the-art waveforms is excluded from the template used for analysis. For very massive sources, the biases in extrinsic parameters can be severe enough that the binary is severely mis-localized, with the parameter estimation finding a nearly-degenerate position in the sky with respect to the true position. In light of this, it is crucial to understand whether parameter estimation (including sky-localization) of massive black hole binaries observed with LISA would be dangerously biased if we were to use current waveforms, and based on this, how many and which additional harmonics will be necessary to model by the time LISA flies. To begin answering these questions, we construct approximate waveforms for higher-order modes using post-Newtonian-inspired expressions for the inspiral stitched to phenomenological amplitudes for the merger-ringdown. We can then examine whether the inference of massive binaries' properties is likely to be biased if these additional higher-order modes are not accurately modeled.