Ringdown overtones, black hole spectroscopy, and no-hair theorem tests

Abstract

Validating the black-hole no-hair theorem with gravitational-wave observations of compact binary coalescences provides a compelling argument that the remnant object is indeed a black hole as described by the general theory of relativity. This requires performing a spectroscopic analysis of the post-merger signal and resolving the frequencies of either different angular modes or overtones (of the same angular mode). For a nearly-equal mass binary black-hole system, only the dominant angular mode (l = m = 2) is sufficiently excited and the overtones are instrumental to perform this test. Here we investigate the robustness of modelling the post-merger signal of a binary black hole coalescence as a superposition of overtones. Further, we study the bias expected in the recovered frequencies as a function of the start time of a spectroscopic analysis and provide a computationally cheap procedure to choose it based on the interplay between the expected statistical error due to the detector noise and the systematic errors due to waveform modelling. Moreover, since the overtone frequencies are closely spaced, we find that resolving the overtones is particularly challenging and requires a loud ringdown signal. Rayleigh's resolvability criterion suggests that -in an optimistic scenario -a ringdown signal-to-noise ratio larger than ∼ 30 (achievable possibly with LIGO at design sensitivity and routinely with future interferometers such as Einstein Telescope, Cosmic Explorer, and LISA) is necessary to resolve the overtone frequencies. We then conclude by discussing some conceptual issues associated with black-hole spectroscopy with overtones.

Parametrized ringdown spin expansion coefficients: A data-analysis framework for black-hole spectroscopy with multiple events

“…Recent work tried to better quantify the contribution of additional overtones to the high-frequency signal for GW150914. Adding at least one overtone is necessary to obtain ringdown estimates of the mass and spin of the remnant which are in agreement (at the ∼ 20% level) with the values inferred by fitting the entire signal within GR [34,35] (see also [20,24,36]).…”

“…For a given (l, m), the overtones are in general relevant for parameter estimation [24,34,35,[78][79][80]. However, the frequencies of different overtones are very similar and hard to resolve [4, 36], and therefore it is hard to use them for direct BH spectroscopy. For this reason, in this paper we will not consider overtones.…”

“…In general, overtones are relevant for parameter estimation [24,34,35,[78][79][80]. However, the frequencies of different overtones are very closely spaced and hard to resolve [4, 36], and therefore -besides consistency tests with mass/spin inferred from the whole waveform [34,35] -it is hard to use them for direct BH spectroscopy. If the ringdown SNR is very high (as expected for 3G detectors and LISA) [36] the overtones may be resolved, and therefore they should be included in our model.…”

Quantum Black Holes in the Sky

“…The ringdown of the perturbations of the BH is regarded as a superposition of these QNMs, and thus can be used to test the accuracy of GR predictions and no-hair theorem (e.g., see [14]). As a result, precise detection of QNMs from the ringdown phase (from BH mergers or formation) in gravitational wave (GW) observations may enable us to test the classical and quantum modifications to GR (e.g., [15]).…”

Scope Out Multiband Gravitational-Wave Observations of GW190521-Like Binary Black Holes with Space Gravitational Wave Antenna B-DECIGO

“…These obstacles will be overcome if one includes higher overtones (n > 0) into the ringdown GW analysis [85], for which a much larger SNR than the single-mode analysis will be expected. Indeed, a superposition of overtones (n > 0) in a single harmonic mode will be observed [85,[118][119][120] in the high SNR events (with ET). Another step-functional improvement of the ringdown GW analysis will be offered by using completely different signal analysis methods than the traditional matched filtering analysis, which may not be always optimal for the ringdown GW signal.…”