Measuring source properties and quasi-normal-mode frequencies of heavy massive black-hole binaries with LISA

The laser-interferometer space antenna (LISA) will be launched in the mid 2030s. It promises to observe the coalescence of massive black-hole (BH) binaries with signal-to-noise ratios (SNRs) reaching thousands. Crucially, it will detect some of these binaries with high SNR both in the inspiral and the merger-ringdown stages. Such signals are ideal for tests of General Relativity (GR) using information from the whole waveform. Here, we consider astrophysically motivated binary systems at the high-mass end of the population observable by LISA, and simulate their LISA signals using the newly developed parametrised, multipolar, aligned-spin effective-one-body model: pSEOBNRv5HM. The merger-ringdown signal in this model depends on the binary properties (masses and spins), and also on parameters that describe fractional deviations from the GR quasi-normal-mode frequencies of the remnant BH. Performing full Bayesian analyses, we assess to which accuracy LISA will be able to constrain deviations from GR in the ringdown signal when using information from the whole signal. We find that these deviations can typically be constrained to within $10\%$ and in the best cases to within $1\%$. We also show that we can measure the binary masses and spins with great accuracy even for very massive BH systems with low SNR in the inspiral: individual source-frame masses can typically be constrained to within $10\%$ and as precisely as $1\%$, and individual spins can typically be constrained to within $0.1$ and as precisely as $0.001$. Finally, we probe the accuracy of the SEOBNRv5HM waveform family by performing synthetic injections of GR numerical-relativity waveforms. For the source parameters considered, we measure erroneous deviations from GR due to systematics in the waveform model. These results confirm the need for improving waveform models to perform tests of GR with binary BHs at high SNR with LISA.Comment: 15 pages, 18 with appendices, 19 figure