GW190412: measuring a black-hole recoil direction through higher-order gravitational-wave modes

General relativity predicts that gravitational waves (GWs) carry linear momentum. Consequently, the remnant black hole of a black-hole merger can inherit a recoil velocity or ``kick'' of crucial implications in, e.g, black-hole formation scenarios. While the kick magnitude is determined by the mass ratio and spins of the source, estimating its direction requires a measurement of the two orientation angles of the source. While the orbital inclination angle is commonly reported in GW observations, the azimuthal one has been to date ignored. We show how the presence of more than one GW emission mode allows constraining this angle and, consequently, determines the kick direction in a real GW event. %We show that the higher-order mode content GW190412 enables the determination of both these angles and, consequently, the kick direction. We analyse the GW190412 signal, which contains higher-order modes, with a numerical-relativity surrogate waveform model for black-hole mergers. We find that while GW190412 is barely informative about the kick magnitude, we can constrain its direction. This forms angles $\theta_{KL}^{\text{-100M}}=28^{+23}_{-11}\,\deg$ with the orbital angular momentum defined at a reference time $t_{\rm ref}=-100\,M$ before merger (being preferentially kicked upwards), $\theta_{KN}=37^{+15}_{-12}\,\deg$ with the line-of-sight and $\phi_{KN}^{\text{-100M}}=46^{+32}_{-41}\,\deg$ with the projection of the latter onto the former, all at the $68\%$ credible level. We briefly discuss the potential application of this type of measurement for multi-messenger observations of black-hole mergers occurring in Active Galactic Nuclei.Comment: 8 pages, 4 figure

Impact of Bayesian Priors on the Inferred Masses of Quasi-Circular Intermediate-Mass Black Hole Binaries

Observation of gravitational waves from inspiralling binary black holes has offered a unique opportunity to study the physical parameters of the component black holes. To infer these parameters, Bayesian methods are employed in conjunction with general relativistic waveform models that describe the source's inspiral, merger, and ringdown. The results depend not only on the accuracy of the waveform models but also on the underlying fiducial prior distribution used for the analysis. In particular, when the pre-merger phase of the signal is barely observable within the detectors' bandwidth, as is currently the case with intermediate-mass black hole binary signals in ground-based gravitational wave detectors, different prior assumptions can lead to different interpretations. In this study, we utilise the gravitational-wave inference library, $\texttt{Parallel Bilby}$, to evaluate the impact of mass prior choices on the parameter estimation of intermediate-mass black hole binary signals. While previous studies focused primarily on analysing event data, we offer a broader, more controlled study by using simulations. Our findings suggest that the posteriors in total mass, mass ratio and luminosity distance are contingent on the assumed mass prior distribution used during the inference process. This is especially true when the signal lacks sufficient pre-merger information and/or has inadequate power in the higher-order radiation multipoles. In conclusion, our study underscores the importance of thoroughly investigating similarly heavy events in current detector sensitivity using a diverse choice of priors. Absent such an approach, adopting a flat prior on the binary's redshifted total mass and mass ratio emerges as a reasonable choice, preventing biases in the detector-frame mass posteriors.Comment: 16 Pages, 7 figure

Searching for the full symphony of black hole binary mergers

Current searches for the gravitational-wave signature of compact binary mergers rely on matched-filtering data from interferometric observatories with sets of modelled gravitational waveforms. These searches currently use model waveforms that do not include the higher-order mode content of the gravitational-wave signal. Higher-order modes are important for many compact binary mergers and their omission reduces the sensitivity to such sources. In this work we explore the sensitivity loss incurred from omitting higher-order modes. We present a new method for searching for compact binary mergers using waveforms that include higher-order mode effects, and evaluate the sensitivity increase that using our new method would allow. We find that, when evaluating sensitivity at a constant rate-of-false alarm, and when including the fact that signal-consistency tests can reject some signals that include higher-order mode content, we observe a sensitivity increase of up to a factor of 2 in volume for high mass ratio, high total-mass systems. Our new search method is also directly applicable in searches for generic compact binaries

Solving the Teukolsky equation with physics-informed neural networks

We use physics-informed neural networks (PINNs) to compute the first quasi-normal modes of the Kerr geometry via the Teukolsky equation. This technique allows us to extract the complex frequencies and separation constants of the equation without the need for sophisticated numerical techniques, and with an almost immediate implementation under the \texttt{PyTorch} framework. We are able to compute the oscillation frequencies and damping times for arbitrary black hole spins and masses, with accuracy typically below the percentual level as compared to the accepted values in the literature. We find that PINN-computed quasi-normal modes are indistinguishable from those obtained through existing methods at signal-to-noise ratios (SNRs) larger than 100, making the former reliable for gravitational-wave data analysis in the mid term, before the arrival of third-generation detectors like LISA or the Einstein Telescope, where SNRs of ${\cal O}(1000)$ might be achieved.Comment: 12 pages, 7 figure