Black hole spectroscopy with ground-based atom interferometer and space-based laser interferometer gravitational wave detectors

Gravitational wave (GW) detection allows us to test general relativity in entirely new regimes. A prominent role takes the detection of quasi-normal modes (QNMs), which are emitted after the merger of a binary black hole (BBH) when the highly distorted remnant emits GWs to become a regular Kerr black hole (BH). The BH uniqueness theorems of Kerr black hole solutions in general relativity imply that the frequencies and damping times of QNMs are determined solely by the mass and spin of the remnant BH. Therefore, detecting QNMs offers a unique way to probe the nature of the remnant BH and to test general relativity. We study the detection of a merging BBH in the intermediate-mass range, where the inspiral-merger phase is detected by space-based laser interferometer detectors TianQin and LISA, while the ringdown is detected by the ground-based atom interferometer (AI) observatory AION. The analysis of the ringdown is done using the regular broadband mode of AI detectors as well as the resonant mode optimizing it to the frequencies of the QNMs predicted from the inspiral-merger phase. We find that the regular broadband mode allows constraining the parameters of the BBH with relative errors of the order 10 - 1 and below from the ringdown. Moreover, for a variety of systems considered, the frequencies and the damping times of the QNMs can be determined with relative errors below 0.1 and 0.2, respectively. We further find that using the resonant mode can improve the parameter estimation for the BBH from the ringdown by a factor of up to three. Utilizing the resonant mode significantly limits the detection of the frequency of the QNMs but improves the detection error of the damping times by around two orders of magnitude.