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

The LIGO--Virgo--KAGRA collaborations (LVK) recently produced a catalogue containing gravitational-wave (GW) observations from the first half of the third GW observing run (O3a). This catalogue, GWTC-2.1, includes for the first time a number of \emph{exceptional} GW candidates produced from merging black-hole-binaries with unequivocally unequal component masses. Since subdominant multipole moments and spin-induced orbital precession are more likely to leave measurable imprints on the emitted GW from unequal component mass binaries, these general relativistic phenomena may now be measurable. Indeed, both GW190412 and GW190814 have already shown conclusive evidence for subdominant multipole moments. This provides valuable insights into the dynamics of the binary. We calculate the evidence for subdominant multipole moments and spin-induced orbital precession for all merging black-hole-binaries in GWTC-2.1 that were observed during O3a and show that (a) no gravitational-wave candidate has measurable higher order multipole content beyond $\ell = 3$, (b) in addition to the already known GW190412 and GW190814, GW190519\_153544 shows significant evidence for the $(\ell, |m|) = (3, 3)$ subdominant multipole, (c) GW190521 may have measurable subdominant multipole content and (d) GW190412 may show evidence for spin-induced orbital precession.Comment: 18 pages, 6 figure

VARAHA: A Fast Non-Markovian sampler for estimating Gravitational-Wave posteriors

This article introduces VARAHA, an open-source, fast, non-Markovian sampler for estimating gravitational-wave posteriors. VARAHA differs from existing Nested sampling algorithms by gradually discarding regions of low likelihood, rather than gradually sampling regions of high likelihood. This alternative mindset enables VARAHA to freely draw samples from anywhere within the high-likelihood region of the parameter space, allowing for analyses to complete in significantly fewer cycles. This means that VARAHA can significantly reduce both the wall and CPU time of all analyses. VARAHA offers many benefits, particularly for gravitational-wave astronomy where Bayesian inference can take many days, if not weeks, to complete. For instance, VARAHA can be used to estimate accurate sky locations, astrophysical probabilities and source classifications within minutes, which is particularly useful for multi-messenger follow-up of binary neutron star observations; VARAHA localises GW170817 $\sim 30$ times faster than LALInference. Although only aligned-spin, dominant multipole waveform models can be used for gravitational-wave analyses, it is trivial to extend this algorithm to include additional physics without hindering performance. We envision VARAHA being used for gravitational-wave studies, particularly estimating parameters using expensive waveform models, analysing subthreshold gravitational-wave candidates, generating simulated data for population studies, and rapid posterior estimation for binary neutron star mergers

When will we observe binary black holes precessing?

After eleven gravitational-wave detections from compact-binary mergers, we are yet to observe the striking general-relativistic phenomenon of orbital precession. Measurements of precession would provide valuable insights into the distribution of black-hole spins, and therefore into astrophysical binary formation mechanisms. Using our recent two-harmonic approximation of precessing-binary signals~\cite{Fairhurst:2019_2harm}, we introduce the ``precession signal-to-noise ratio'', $\rho_p$. We demonstrate that this can be used to clearly identify whether precession was measured in an observation (by comparison with both current detections and simulated signals), and can immediately quantify the measurability of precession in a given signal, which currently requires computationally expensive parameter-estimation studies. $\rho_p$ has numerous potential applications to signal searches, source-property measurements, and population studies. We give one example: assuming one possible astrophysical spin distribution, we predict that precession has a one in $\sim 25$ chance of being observed in any detection.Comment: 5 pages, 2 Figures; resubmission following reviewers comment

Understanding how fast black holes spin by analysing data from the second gravitational-wave catalogue

The Advanced LIGO and Virgo detectors have now observed approximately 50 black-hole-binary mergers, from which we can begin to infer how rapidly astrophysical black holes spin. The LIGO-Virgo Collaboration (LVC) analysis of detections up to the end of the first half of the third observing run (O3a) appeared to uncover a distribution of spin magnitudes that peaks at $\sim$0.2. This is surprising: is there a black-hole formation mechanism that prefers a particular, non-zero spin magnitude, or could this be the cumulative effect of multiple formation processes? We perform an independent analysis of the most recent gravitational-wave catalogue, and find that (a) the support for the LVC spin-magnitude is tenuous; in particular, adding or removing just one signal from the catalogue can remove the statistical preference for this distribution, and (b) we find potential evidence for two spin sub-populations in the observed black holes; one with extremely low spins and one with larger spin magnitudes. We make the connection that these spin sub-populations could be correlated with the mass of the binary, with more massive binaries preferring larger spin magnitudes, and argue that this may provide evidence for hierarchical mergers in the second gravitational-wave catalogue.Comment: 12 pages, 6 figures. Update to match published versio

Two-harmonic approximation for gravitational waveforms from precessing binaries

Binary-black-hole orbits precess when the black-hole spins are mis-aligned with the binary's orbital angular momentum. The apparently complicated dynamics can in most cases be described as simple precession of the orbital angular momentum about an approximately fixed total angular momentum. However, the imprint of the precession on the observed gravitational-wave signal is yet more complicated, with a non-trivial time-varying dependence on black-hole dynamics, the binary's orientation and the detector polarization. As a result, it is difficult to predict under which conditions precession effects are measurable in gravitational-wave observations, and their impact on both signal detection and source characterization. We show that the observed waveform can be simplified by decomposing it as a power series in a new precession parameter $b = \tan(\beta/2)$, where $\beta$ is the opening angle between the orbital and total angular momenta. The power series is made up of five harmonics, with frequencies that differ by the binary's precession frequency, and individually do not exhibit amplitude and phase modulations. In many cases, the waveform can be well approximated by the two leading harmonics. In this approximation we are able to obtain a simple picture of precession as caused by the beating of two waveforms of similar frequency. This enables us to identify regions of the parameter space where precession is likely to have an observable effect on the waveform, and to propose a new approach to searching for signals from precessing binaries, based upon the two-harmonic approximation.Comment: 23 pages, 9 figures. Accepted for publication in PR

An evaluation of a personalised text message reminder compared to a standard text message on postal questionnaire response rates: an embedded randomised controlled trial

Abstract Background: Research outcome data is commonly collected using postal questionnaires; however, poor response can introduce bias and reduce statistical power. Text messaging is simple, cost-effective, and can be customised to the individual. Personalised, reminder text messages may improve response rates. Methods: A two-arm, parallel group ‘Study within a Trial’ (SWAT) was embedded within the Occupational Therapist Intervention Study (OTIS), a randomised controlled trial of a home assessment for falls prevention in older people. OTIS participants who provided a mobile phone number were randomly allocated (1:1) to receive either a personalised text message (Title, Surname, plus York Trials Unit (YTU) text) or the standard YTU text alone, prior to receiving their four-month post-randomisation follow-up postal questionnaire. The primary outcome measure was the proportion of participants who returned the questionnaire. Secondary outcomes were: time to response, completeness of response, requirement of a reminder letter, and cost-effectiveness. Binary data were compared using logistic regression and time to response by Cox Proportional Hazards regression. Results: A total of 403 participants were randomised: 201 to the personalised text and 202 to the standard text. Of the 283 participants included in the final analysis, 278 (98.2%) returned their questionnaire; 136 (97.8%) for the personalised text versus 142 (98.6%) for the standard text (adjusted odds ratio 0.64, 95% CI 0.10 to 3.88, p=0.63). The median time to response was nine days in both groups. In total, 271 (97.5%) participants returned a complete questionnaire; 133 (97.8%) in the personalised text versus 138 (97.2%) for the standard text. In total, 21 reminder letters were sent. The additional cost of personalised text messages was £0.04 per participant retained. Conclusions: Personalised texts were not superior to standard texts in any outcome assessed in our study. Further SWATs are needed to perform a meta-analysis and obtain more evidence. Registration: ISRCTN22202133; SWAT 35 Keywords: SWAT, Randomised Controlled Trial, personalised, SMS text, postal questionnaire, reminde

Simple parameter estimation using observable features of gravitational-wave signals

Using simple, intuitive arguments, we discuss the expected accuracy with which astrophysical parameters can be extracted from an observed gravitational wave signal. The observation of a chirplike signal in the data allows for measurement of the component masses and aligned spins, while measurement in three or more detectors enables good localization. The ability to measure additional features in the observed signal—the existence or absence of power in (i) the second gravitational wave polarization, (ii) higher gravitational wave multipoles or (iii) spin-induced orbital precession—provide new information which can be used to significantly improve the accuracy of parameter measurement. We introduce the simple-pe algorithm which uses these methods to generate rapid parameter estimation results for binary mergers. We present results from a set of simulations, to illustrate the method, and compare results from simple-pe with measurements from full parameter estimation routines. The simple-pe routine is able to provide initial parameter estimates in a matter of CPU minutes, which could be used in real-time alerts and also as input to significantly accelerate detailed parameter estimation routines

Preoperative botulinum neurotoxin A for children with bilateral cerebral palsy undergoing major hip surgery: a randomized double-blind placebo-controlled trial.

AIM: To assess whether preoperative botulinum neurotoxin A (BoNT-A) affects pain after major hip surgery for children with bilateral cerebral palsy (CP). METHOD: This was a randomized, parallel arms, placebo-contolled trial. Children with hypertonic CP aged 2 to 15 years awaiting bony hip surgery at a tertiary hospital were randomized to receive either BoNT-A or placebo injections into the muscles of the hip on a single occasion immediately before surgery. The primary outcome was the paediatric pain profile (PPP), which was assessed at baseline and weekly for 6 weeks. Treatment allocation was by minimization. Participants, clinicians, and outcome assessors were masked to group assignment. RESULTS: Twenty-seven participants (17 males, 10 females; mean 8y 8mo [SD 3y 9mo], range 3y 4mo-15y 10mo) were allocated to BoNT-A and 27 participants (14 males, 13 females; mean 8y 11mo [SD 3y 5mo], range 4y 1mo-15y 2mo) to placebo. Mean (SD) PPP at 6 weeks for the BoNT-A group (n=24 followed up) was 10.96 (7.22) and for the placebo group (n=26) was 10.04 (8.54) (p=0.69; 95% confidence interval [CI] -4.82, 3.18). There were 16 serious adverse events in total during 6 months of follow-up (n=6 in BoNT-A group). INTERPRETATION: Use of BoNT-A immediately before bony hip surgery for reducing postoperative pain for children with CP was not supported. WHAT THIS PAPER ADDS: Botulinum neurotoxin A (BoNT-A) does not reduce postoperative pain following bony hip surgery. BoNT-A also does not affect postoperative quality of life

Identifying when precession can be measured in gravitational waveforms

In binary-black-hole systems where the black-hole spins are misaligned with the orbital angular momentum, precession effects leave characteristic modulations in the emitted gravitational waveform. Here, we investigate where in the parameter space we will be able to accurately identify precession, for likely observations over coming LIGO-Virgo-KAGRA observing runs. Despite the large number of parameters that characterize a precessing binary, we perform a large scale systematic study to identify the impact of each source parameter on the measurement of precession. We simulate a fiducial binary at moderate mass-ratio, signal-to-noise ratio (SNR), and spins, such that precession will be clearly identifiable, then successively vary each parameter while holding the remaining parameters fixed. As expected, evidence for precession increases with signal-to noise-ratio (SNR), higher in-plane spins, more unequal component masses, and higher inclination, but our study provides a quantitative illustration of each of these effects, and informs our intuition on parameter dependencies that have not yet been studied in detail, for example, the effect of varying the relative strength of the two polarizations, the total mass, and the aligned-spin components. We also measure the “precession SNR” ρ p , to quantify the signal power associated with precession. By comparing ρ p with both Bayes factors and the recovered posterior distributions, we find it is a reliable metric for measurability that accurately predicts when the detected signal contains evidence for precession