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 signals using the newly developed multipolar effective-one-body model: \texttt{pSEOBNRv5HM}. The merger-ringdown signal in this model depends on the binary properties, and also on parameters that describe fractional deviations from the GR quasi-normal-mode (complex) 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 with this model we can measure the binary masses and spins with great accuracy even for very massive BH systems with low SNR in the inspiral. We also probe the accuracy of the \texttt{SEOBNRv5HM} waveform family by performing synthetic injections of GR numerical-relativity waveforms. Using a novel method that we develop here to quantify the impact of systematic errors, we show that already for sources with SNR $\mathcal{O}(100)$, we would measure erroneous deviations from GR due to waveform model inaccuracies. One of the main sources of error is the mismodelling of the relative alignment between harmonics. Our results confirm the need for improving waveform models to perform tests of GR with high SNR binary BHs observed by LISA.