Towards the routine use of subdominant harmonics in gravitational-wave inference: Reanalysis of GW190412 with generation X waveform models

Abstract

We re-analyse the gravitational-wave event GW190412 with state-of-the-art phenomenological waveform models. This event, which has been associated with a black hole merger, is interesting due to the significant contribution from subdominant harmonics. We use both frequency-domain and time-domain waveform models. The PhenomX waveform models constitute the fourth generation of frequency-domain phenomenological waveforms for black hole binary coalescence; they have more recently been complemented by the time-domain PhenomT models, which open up new strategies to model precession and eccentricity, and to perform tests of general relativity with the phenomenological waveforms approach. Both PhenomX and PhenomT have been constructed with similar techniques and accuracy goals, and due to their computational efficiency this "generation X" model family allows the routine use of subdominant spherical harmonics in Bayesian inference. We show the good agreement between these and other state-of-the-art waveform models for GW190412, and discuss the improvements over the previous generation of phenomenological waveform models. We also discuss practical aspects of Bayesian inference such as run convergence, variations of sampling parameters, and computational cost.

Evidence for subdominant multipole moments and precession in merging black-hole-binaries from GWTC-2.1

“…Indeed, the observed distribution for the population, shown in Figure 1, shows a clear high-SNR tail that indicates the observation of the (3,3) multipole. Higher multipoles have previously been identified in both GW190814 and GW190412, with their observability and their impact on parameter estimates discussed at length in previous works [27,28,[40][41][42]. Unsurprisingly, we see that among all events in O3a, GW190412 and GW190814 have the largest SNR in the (3, 3) multipole, with ρ 33 = 6.2 +1.3 −1.5 for GW190814 and ρ 33 = 3.5 +0.8 −1.2 for GW190412.…”

“…Previous studies have identified evidence for subdominant multipole moments by either a) calculating Bayes factors, the difference in Bayesian evidences, through multiple parameter estimation studies [e.g. 16,40,41] or via likelihood re-weighting [15], b) statistically comparing posteriors obtained with waveform models which included higher order multipoles and those which excluded higher order multipoles beyond = 2 [46], c) analysing time-frequency tracks in the GW strain data [27,47], d) identifying if there is a loss in the observed coherent signal energy when comparing the output from the cWB detection pipeline [48] with predictions from a waveform model which excludes subdominant multipole moments [28], or e) directly calculating the SNR of each ( , m) multipole ρ m [20,27,28,49]. Here, we identify whether multipoles other than the dominant (2,2) multipole have been observed by calculating the orthogonal SNR of each ( , m) multipole.…”

“…Previous studies have identified evidence for spininduced orbital precession by either a) calculating Bayes factors [e.g. 27,28,40,51], b) statistically comparing posterior distributions for parameters characterizing precession to their prior distributions [e.g. 9, 46] or c) directly calculating the precession SNR, described as the contribution to the total SNR of the system that can be attributed to precession [18, 27-29, 36, 44, 46].…”

“…The unequal mass ratio resulted in more significant higher order multipoles, and for the first time, imprints of subdominant multipole radiation oscillating at three times the orbital frequency -the ( , m) = (3, 3) multipole 1 -were visible. Similarly, it was the first time that the amount of precession in the system was constrained away from the prior [27,38,[40][41][42]. Several months later GW190814 was detected with highly asymmetric component masses (∼9:1) and a secondary component with a mass larger than any previously discovered neutron star and lighter than any black hole [28].…”

“…Similarly, by comparing the posterior and prior distributions for parameters characterising spin-induced orbital precession, it has previously been shown that no event in O3a unambiguously exhibits spin-induced orbital precession [37], although there is evidence that the observed population of BBHs have spins which are misaligned with the orbital angular momentum [43]. Other studies have investigated the evidence for higher order multipoles and precession for GW190412 and GW190814 [27,28,[40][41][42], but there has not yet been a study which identifies the evidence for precession and higher order multipoles for the latest gravitational-wave observations on an event by event basis.…”