The black hole uniqueness and the no-hair theorems imply that the quasinormal spectrum of any astrophysical black hole is determined solely by its mass and spin. The countably infinite number of quasinormal modes of a Kerr black hole are thus related
to each other and any deviations from these relations provide a strong hint for physics beyond the general theory of relativity. To test the no-hair theorem using ringdown signals, it is necessary to detect at least two quasinormal modes. In particular, one can detect the fundamental mode along with a subdominant overtone or with another angular mode, depending on the mass ratio and the spins of the progenitor binary. Also in the light of the recent discovery of GW190412, studying how the mass ratio affects the prospect of black hole spectroscopy using overtones or angular modes is pertinent, and this is the major focus of our study. First, we provide ready-to-use fits for the amplitudes and phases of both the angular modes and overtones as a function of mass ratio $qin[0,10]$. Using these fits we estimate the minimum signal-to-noise ratio for detectability, resolvability, and measurability of subdominant modes/tones. We find that performing black-hole spectroscopy with angular modes is preferable when the binary mass ratio is larger than $qapprox 1.2$ (provided that the source is not located at a particularly disfavoured inclination angle). For nonspinning, equal-mass binary black holes, the overtones seem to be the only viable option to perform a spectroscopy test of the no-hair theorem. However this would require a large ringdown signal-to-noise ratio ($approx 100$ for a $5%$ accuracy test with two overtones) and the inclusion of more than one overtone to reduce modelling errors, making black-hole spectroscopy with overtones impractical in the near future.
The ringdown is the late part of the post-merger signature emitted during the coalescence of two black holes and comprises of a superposition of quasi-normal-modes. Within general relativity, because of the no-hair theorems, the frequencies and dampi
ng times of these modes are entirely determined by the mass and angular momentum of the final Kerr black hole. A detection of multiple ringdown modes would potentially allow us to test the no-hair theorem from observational data. The parameters which determine whether sub-dominant ringdown modes can be detected are primarily the overall signal-to-noise ratio present in the ringdown signal, and on the amplitude of the subdominant mode with respect to the dominant mode. In this paper, we use Bayesian inference to determine the detectability of a subdominant mode in a set of simulated analytical ringdown signals. Focusing on the design sensitivity of the Advanced LIGO detectors, we systematically vary the signal-to-noise ratio of the ringdown signal, and the mode amplitude ratio in order to determine what kind of signals are promising for performing black hole spectroscopy.
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 require
s 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. Rayleighs resolvability criterion suggests that in an optimistic scenario a ringdown signal-to-noise ratio larger than $sim 30$ (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.
The final stage of a binary black hole merger is ringdown, in which the system is described by a Kerr black hole with quasinormal mode perturbations. It is far from straightforward to identify the time at which the ringdown begins. Yet determining th
is time is important for precision tests of the general theory of relativity that compare an observed signal with quasinormal mode descriptions of the ringdown, such as tests of the no-hair theorem. We present an algorithmic method to analyze the choice of ringdown start time in the observed waveform. This method is based on determining how close the strong field is to a Kerr black hole (Kerrness). Using numerical relativity simulations, we characterize the Kerrness of the strong-field region close to the black hole using a set of local, gauge-invariant geometric and algebraic conditions that measure local isometry to Kerr. We produce a map that associates each time in the gravitational waveform with a value of each of these Kerrness measures; this map is produced by following outgoing null characteristics from the strong and near-field regions to the wave zone. We perform this analysis on a numerical relativity simulation with parameters consistent with GW150914- the first gravitational wave detection. We find that the choice of ringdown start time of $3,mathrm{ms}$ after merger used in the GW150914 study to test general relativity corresponds to a high dimensionless perturbation amplitude of $ sim 7.5 times 10^{-3}$ in the strong-field region. This suggests that in higher signal-to-noise detections, one would need to start analyzing the signal at a later time for studies that depend on the validity of black hole perturbation theory.
Motivated by the recent discoveries of binary black-hole mergers by the Advanced Laser Interferometer Gravitational-wave Observatory (Advanced LIGO), we investigate the prospects of ground-based detectors to perform a spectroscopic analysis of signal
s emitted during the ringdown of the final Kerr black-hole formed by a stellar mass binary black-hole merger. If we assume an optimistic rate of 240 Gpc$^{-3}$yr$^{-1}$, about 3 events per year can be measured by Advanced LIGO. Further, upgrades to the existing LIGO detectors will increase the odds of measuring multiple ringdown modes significantly. New ground-based facilities such as Einstein Telescope or Cosmic Explorer could measure multiple ringdown modes in about thousand events per year. We perform Monte-Carlo injections of $10^{6}$ binary black-hole mergers in a search volume defined by a sphere of radius 1500 Mpc centered at the detector, for various proposed ground-based detector models. We assume a uniform random distribution in component masses of the progenitor binaries, sky positions and orientations to investigate the fraction of the population that satisfy our criteria for detectability and resolvability of multiple ringdown modes. We investigate the detectability and resolvability of the sub-dominant modes $l=m=3$, $l=m=4$ and $l=2, m=1$. Our results indicate that the modes with $l=m=3$ and $l=2, m=1$ are the most promising candidates for sub-dominant mode measurability. We find that for stellar mass black-hole mergers, resolvability is not a limiting criteria for these modes. We emphasize that the measurability of the $l=2, m=1$ mode is not impeded by the resolvability criterion.
Coalescing binaries of neutron stars (NS) and black holes (BH) are one of the most important sources of gravitational waves for the upcoming network of ground based detectors. Detection and extraction of astrophysical information from gravitational-w
ave signals requires accurate waveform models. The Effective-One-Body and other phenomenological models interpolate between analytic results and $10-30$ orbit numerical relativity (NR) merger simulations. In this paper we study the accuracy of these models using new NR simulations that span $36-88$ orbits, with mass-ratios and black hole spins $(q,chi_{BH}) = (7, pm 0.4), (7, pm 0.6)$, and $(5, -0.9)$. We find that: (i) the recently published SEOBNRv1 and SEOBNRv2 models of the Effective-One-Body family disagree with each other (mismatches of a few percent) for black hole spins $geq 0.5$ or $leq -0.3$, with waveform mismatch accumulating during early inspiral; (ii) comparison with numerical waveforms indicate that this disagreement is due to phasing errors of SEOBNRv1, with SEOBNRv2 in good agreement with all of our simulations; (iii) Phenomenological waveforms disagree with SEOBNRv2 over most of the NSBH binary parameter space; (iv) comparison with NR waveforms shows that most of the models dephasing accumulates near the frequency interval where it switches to a phenomenological phasing prescription; and finally (v) both SEOBNR and post-Newtonian (PN) models are effectual for NSBH systems, but PN waveforms will give a significant bias in parameter recovery. Our results suggest that future gravitational-wave detection searches and parameter estimation efforts targeted at NSBH systems with $qlesssim 7$ and $chi_mathrm{BH} approx [-0.9, +0.6]$ will benefit from using SEOBNRv2 templates. For larger black hole spins and/or binary mass-ratios, we recommend the models be further investigated as suitable NR simulations become available.
