Multimode black hole spectroscopy

The first two LIGO/Virgo observing runs have detected several black hole binary mergers. One of the most exciting prospects of future observing runs is the possibility to identify the remnants of these mergers as Kerr black holes by measuring their (complex) quasinormal mode frequencies. This idea-similar to the identification of atomic elements through their spectral lines-is sometimes called black hole spectroscopy. Third-generation Earth-based detectors and the space-based interferometer LISA could measure multiple spectral lines from different multipolar components of the radiation, and therefore provide qualitatively better tests of the Kerr hypothesis. In this paper we quantify the redshift out to which the various modes would be detectable (or, conversely, the number of detectable modes at any given redshift) as a function of the intrinsic parameters of the merging binary. LISA could detect so many modes that current numerical relativity simulations do not have enough resolution (or do not contain enough higher harmonics) to extract all available science from the data.