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

Gravitational wave (GW) detection has enabled us to test General Relativity in an entirely new regime. A prominent role in tests of General Relativity takes the detection of the Quasi-normal modes (QNMs) that arise as the highly distorted remnant formed after the merger emits GWs until it becomes a regular Kerr BH. According to the no-hair theorem, the frequencies and damping times of these QNMs are determined solely by the mass and spin of the remnant BH. Therefore, detecting the 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 binary black hole (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 using the resonant mode where the detection band is optimized to the frequencies of the QNMs predicted from the inspiral-merger phase. We find that using the regular broadband mode allows constraining the parameters of the BBH with relative errors of at most 10^-6 from the ringdown while the frequencies and the damping times of the QNMs can be determined with total errors below 0.2 Hz and 115 μ s, respectively. Furthermore, we find that using the resonant mode can improve the parameter estimation for the BBH from the ringdown by up to one order of magnitude. Utilizing the resonant mode significantly limits the detection of the frequency of the QNMs but improves the detection error of the damping times by one to four orders of magnitude.