The astrophysical odds of GW151216
MMNRAS , 1–6 (0000) Preprint 3 September 2020 Compiled using MNRAS L A TEX style file v3.0
The astrophysical odds of GW151216
Gregory Ashton , ,(cid:63) , Eric Thrane , , School of Physics and Astronomy, Monash University, Vic 3800, Australia, OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery, Clayton VIC 3800, Australia
ABSTRACT
The gravitational-wave candidate GW151216 is a proposed binary black hole event from thefirst observing run of the Advanced LIGO detectors. Not identified as a bona fide signal bythe LIGO–Virgo collaboration, there is disagreement as to its authenticity, which is quantifiedby p astro , the probability that the event is astrophysical in origin. Previous estimates of p astro from different groups range from 0.18 to 0.71, making it unclear whether this event shouldbe included in population analyses, which typically require p astro > .
5. Whether GW151216is an astrophysical signal or not has implications for the population properties of stellar-massblack holes and hence the evolution of massive stars. Using the astrophysical odds, a Bayesianmethod which uses the signal coherence between detectors and a parameterised model of non-astrophysical detector noise, we find that p astro = .
03, suggesting that GW151216 is unlikelyto be a genuine signal. We also analyse GW150914 (the first gravitational-wave detection)and GW151012 (initially considered to be an ambiguous detection) and find p astro values of1 and 0.997 respectively. We argue that the astrophysical odds presented here improve upontraditional methods for distinguishing signals from noise. Key words: gravitational waves – black hole mergers
Transient gravitational wave-astronomy has opened a new windowwith which to study black holes and neutron stars. The LIGO (Aasiet al. 2015) and Virgo (Acernese et al. 2015) collaborations havenow completed three observing runs and announced 13 binary co-alescence signals (Abbott et al. 2019a, 2020; The LIGO ScientificCollaboration et al. 2020). The data collected by these observato-ries is public allowing independent groups to reaffirm observationsand identify new candidates (Zackay et al. 2019; Nitz et al. 2019b;Venumadhav et al. 2019, 2020).In addition to astrophysical signals, gravitational-wave detectordata contains transient non-Gaussian noise artefacts, often referredto as glitches (Blackburn et al. 2008; Abbott et al. 2016a; Nuttallet al. 2015; Cabero et al. 2019; Powell 2018). Glitches degrade ourability to identify signals, i.e. the sensitivity of the detector; whenthe cause of the glitch is fully understood, the optimal solution isto remove the data containing the glitches which improves the sen-sitivity of the detector (Abbott et al. 2018a). However, the cause ofmany glitches is not understood and hence they cannot be removedfrom the data, but must be treated as part of the background noiseof the detector. Traditional search methods (see, e.g. Cannon et al.(2013); Usman et al. (2016) and Capano et al. (2017) for a reviewof the methods) deal with this by estimating the background usingbootstrap methods (Efron & Tibshirani 1993). Bootstrap methodsare defined by the use of an empirical distribution to estimate a (cid:63)
E-mail: [email protected] quantity of interest. Subsequently, candidates are assigned an as-trophysical probability, p astro , based on the empirical output of thesearch pipeline; see Abbott et al. (2016e,d, 2019a) for details. Forloud events such as the GW150914 Abbott et al. (2016c), the firstobserved binary black hole coalescence, p astro ≈
1. Meanwhile, formarginal candidates, p astro ∈ [ . , . ] . Different search pipelinesproduce different values of p astro due to differing assumptions. Forloud events, this is of little consequence, but as we will see, under-standing these assumptions can be crucial for marginal candidates.GW151216 was reported as a significant trigger in O1, the firstLIGO observing run, with p astro = .
71 by Zackay et al. (2019).The event was not included in the first LIGO–Virgo gravitational-wave transient catalogue covering the O1 and O2 observing runs(Abbott et al. 2019a). The candidate was also identified in Nitzet al. (2020), but with p astro = .
18, less than the 0.5 threshold usedto determine inclusion in the catalogue. In the original analysis,Zackay et al. noted the large effective spin of the candidate, whichled to a range of implications; e.g. Piran & Piran (2020); Fragione& Kocsis (2020); De Luca et al. (2020)). However, in a systematicstudy (Huang et al. 2020), it was shown that support for the effectivespin was sensitive to the choice of prior. We summarise the varioussignificance estimates for all events analysed in this work in Table 1.In this work, we study the significance of GW151216 usingthe astrophysical odds (Ashton et al. 2019a). This method is dif-ferent from traditional methods in that it eschews bootstrap noiseestimation. Instead, it directly models and fits for the populationproperties of glitches as they appear projected onto the parameterspace of compact binary coalescence signals. By combining the © 0000 The Authors a r X i v : . [ a s t r o - ph . H E ] S e p G. Ashton & E. Thrane notion of glitches as incoherent signals (Veitch & Vecchio 2010; Isiet al. 2018), and using contextual data to measure the populationproperties of glitches, the astrophysical odds can elevate the sig-nificance of marginal candidates based on their coherence betweendetectors and their properties in the context of typical glitches. Theodds is a Bayesian ratio of probabilities comparing a signal andnoise hypothesis complete with prior probability; it can be used todirectly weight posteriors in the context of a population analysis, dis-posing of the need for arbitrary thresholds for inclusion (Galaudageet al. 2019; Gaebel et al. 2019) and can be employed directly to theanalysis of multi-messenger events using the framework laid out inAshton et al. (2018).In order to give the results for GW151216 context, and tovalidate our method, we also analyse two other binary black holesignals: GW150914, the first and most significant signal in O1 andGW151012, first reported as a “trigger” (Abbott et al. 2016b) andsubsequently upgraded in significance to a candidate (Abbott et al.2019a; Nitz et al. 2019a). In the future, we expect more candidatesto be identified in the open data by independent pipelines (see, e.g.Venumadhav et al. (2020)). While we focus here on GW151216,our broader goal is to establish a unified catalogue, sourced frommultiple groups, each event with a single, reliable value of p astro .The p astro in this unified catalogue will not depend on the searchpipeline used to first identify each trigger. Following Ashton et al. (2019a), we use a Bayesian framework tocalculate the astrophysical odds, O . The odds answers the question:what is the ratio of probability that a ∆ t = . d i spans the coalescence time of an astrophysical signalversus the probability that it contains noise? The noise can be eitherGaussian or it can include glitch. The odds for a signal in datasegment d i in a larger data set d are O S i /N i ( d ) ≈ (cid:104) ξ (cid:105)L( d i |S i ) ∫ L( d i |N i , Λ N ) π ( Λ N | d i (cid:44) k , I ) d Λ N . (1)Here, ξ is the probability of a signal in d i and its expectation value (cid:104) ξ (cid:105) , marginalised over the uncertainty in the astrophysical distri-bution, is the prior odds; we discuss this more below. The term L( d i |S i ) is the Bayesian evidence (marginal likelihood) for d i given the signal hypothesis. This is the likelihood function com-monly used to estimate the parameters of merging binaries, (Veitchet al. 2015). Meanwhile, L( d i |N i , Λ N ) is the likelihood of the datagiven the noise hypothesis. The noise hypothesis is that the datacontain either Gaussian noise or non-Gaussian glitches, modelledby uncorrelated (between detectors) binary mergers (Veitch & Vec-chio 2010; Isi et al. 2018; Ashton et al. 2019a). The noise likelihoodis marginalized over Λ N , a set of hyper-parameters that describethe distributions of glitch parameters.Finally, π ( Λ N | d i (cid:44) k , I ) is the noise parameter prior informedby conditional data d i (cid:44) k and any other cogent information I ; theimportance of this will be made clear later on. We refer to thisdistribution as the glitch population properties. Our present purposeis to describe how we calculate O for the three events consideredin this paper, so we take Eq. 1 as given and refer readers to Ashton The coalescence time is defined differently for different waveforms, butit is approximately synonymous with time of peak gravitational-wave am-plitude. While a gravitational waveform can span several segments, thecoalescence time always falls in just one segment. et al. (2019a) for more information including a derivation of O anda discussion of the motivation for our noise model.Equation 1 differs slightly from the expression in Ashton et al.(2019a) because of two simplifying assumptions. First, we assumethat the prior signal probability ξ is independent of the glitch hyper-parameters Λ N . Second we assume that the prior signal probability ξ (cid:28) π S i /N i ( d i (cid:44) k , I ) and approximate them by π S i /N i ( d i (cid:44) k , I ) = ∫ ξπ ( ξ | d i (cid:44) k , I ) d ξ ∫ ( − ξ ) π ( ξ | d i (cid:44) k , I ) d ξ ≈ (cid:104) ξ (cid:105) , (2)where (cid:104) ξ (cid:105) is the expectation of value of ξ . We omitted I in Ash-ton et al. (2019a) as all inferences were made from the contextualdata alone. In this work, we will make good use of cogent priorinformation and hence re-introduce it in order to show where thisinformation is important. With this formalism out of the way, weturn our attention to the evaluation of O using data from O1.The first step is to define the contextual data. The contextualdata is drawn from a span of time near to the candidate of interest.Ideally, one would like to include as much contextual data as pos-sible, though, not so much that the detector performance is likelyto have changed. A comprehensive study of transient noise in O1was performed by Abbott et al. (2016a). Using the single-detectorburst identification algorithm Omicron (Abbott et al. 2016a; Chat-terji et al. 2004), the rate of all glitches with signal to noise ra-tio (SNR) > . − . However, louder glitches with SNR > .
01 and0 .
001 s − . Given this rate, a coincident-observing 24 h period willcontain several thousand quiet glitches and a few hundred loudglitches: a sufficient number to estimate typical population proper-ties. Thus, we use 24 h of contextual data, which is long enough toprovide adequate estimates of the population properties of glitches,but short enough to control computational costs. We define d i (cid:44) k tobe the set of Omicron triggers in the contextual data.The next step is to calculate the expectation value of ξ . Thisis often referred to as the “duty cycle” (Smith & Thrane 2018). Itis the expectation value for the fraction of segments containing thecoalescence time of a gravitational-wave signal. The duty cycle isstraightforwardly related to the local merger rate R and the averagetime between mergers in the Universe τ : ξ ∼ R ∼ τ − .By assuming a plausible cosmological model, Abbott et al.(2018b) obtained τ = + − s based on a local merger rate of R = . + − Gpc − yr − . Since then, Abbott et al. (2019b) updatedthe estimated local merger rate to be R = . + . − . Gpc − yr − .Combining these results, we obtain a point estimate of (cid:98) ξ ≈ . × − (cid:18) ∆ T . (cid:19) (cid:18) R
59 Gpc − yr − (cid:19) . (3)We approximate the posterior for merger rate as a log-normal dis-tributions, centred on (cid:98) ξ , with shape parameters estimated by fittingthe 90% credible intervals given above. Using these fits, we Monte-Carlo sample the distribution π ( ξ | I ) in Eq. 2 (we are dropping thecontextual data d i (cid:44) k in deference to the information I used above)and find that (cid:104) ξ (cid:105) = . × − . Thus, roughly one in 1 /(cid:104) ξ (cid:105) ≈ except (cid:104) ξ (cid:105) ) must be larger than these prior odds. These error bars don’t include systematic uncertainty associated with thecosmological model, which might increase the uncertainty by a factor of ∼000
59 Gpc − yr − (cid:19) . (3)We approximate the posterior for merger rate as a log-normal dis-tributions, centred on (cid:98) ξ , with shape parameters estimated by fittingthe 90% credible intervals given above. Using these fits, we Monte-Carlo sample the distribution π ( ξ | I ) in Eq. 2 (we are dropping thecontextual data d i (cid:44) k in deference to the information I used above)and find that (cid:104) ξ (cid:105) = . × − . Thus, roughly one in 1 /(cid:104) ξ (cid:105) ≈ except (cid:104) ξ (cid:105) ) must be larger than these prior odds. These error bars don’t include systematic uncertainty associated with thecosmological model, which might increase the uncertainty by a factor of ∼000 , 1–6 (0000) he astrophysical odds of GW151216 The next step is to estimate the glitch population proper-ties π ( Λ N | d i (cid:44) k , I ) . We write the set of glitch hyper-parametersas Λ N ≡ { ξ h g , ξ l g , λ N } where ξ h g and ξ l g are the prior proba-bility for a glitch in the LIGO Hanford and Livingston detec-tors and λ N is the remaining set of hyper-parameters describingthe glitch population properties. Making the simplifying assump-tion that these are independent, we can write π ( Λ N | d i (cid:44) k , I ) = π ( ξ h g | d i (cid:44) k , I ) π ( ξ l g | d i (cid:44) k , I ) π ( λ N | d i (cid:44) k , I ) .A computationally efficient means to infer λ N is to use theSNR>5 Omicron triggers present in the 24 h span of contextualdata as a representative sample of glitches (we pre-filter this list toonly include triggers with frequencies between 20 and 1000 Hz).By using only these Omicron triggers, we can save the time thatwould otherwise be spent analysing data segments consistent withGaussian noise; they do not teach us about the properties of glitches.The inferred distribution of ξ h g and ξ l g given this contextual data isconsistent with unity. This is not surprising since the Omicronpipeline is designed to identify non-Gaussian noise.For calculations of the astrophysical odds, we approximate thedistribution of ξ h g and ξ l g using a point estimates ˆ ξ h g and ˆ ξ l g given bythe ratio of the number of Omicron triggers, for each detector, to theavailable data span. That is, we assume π ( ξ g | d i (cid:44) k , I ) = δ (cid:16) ξ g − ˆ ξ g (cid:17) .The values of these point estimates are reported in Table 1. To verifythat these point estimates are appropriate, we additionally analysean auxiliary set of conditional data: 1000 randomly selected timesnear to GW151216. This contextual data has too few glitches togive reasonable inferences about λ N , but gives a good measure ofthe glitch probability with medians and 90% credible intervals ξ h g = . + . − . and ξ l g = . + . − . . The Omicron rate estimates(Table 1) lie at the 80% and 96% percentiles for the Hanford andLivingston detectors respectively. We conclude that the Omicrontriggers provide reliable point estimates, but that they are slightlyconservative; by slightly overestimating ξ G , there is a modest biasagainst the astrophysical hypothesis. In Sec. 5 we show that theresults are robust to this conservative choice.When writing out the prior previously, each term was con-ditional on both the contextual data as well as I . However, byusing the Omicron triggers to infer λ N , but point estimates toinfer ξ h g and ξ l g we see that we are calculating π ( Λ N | d i (cid:44) k , I ) = π ( ξ h g | I ) π ( ξ l g | I ) π ( λ N | d i (cid:44) k ) .Having described details of our calculation, we now recapthe procedure from start to finish. There are three steps. First, weidentify a 24 h period of data passing the standard data-qualityvetoes and absent of injected signals and the analysis segment itself.Second, we filter the available data against Omicron triggers toproduce a list of contextual data segments known to contain glitches.Third, we analyse the loudest N of these triggers and estimate theglitch hyper-parameters λ N . In this step we vary N by a factor oftwo and check that the resulting glitch population posteriors areinvariant: this demonstrates that we have captured the typical glitchpopulation properties without analysing the entire available dataset. Finally, we calculate the astrophysical odds, Eq. (1), using thedistribution of hyper-parameters found in the second step, the priorodds (cid:104) ξ (cid:105) = . × − , and the point estimates ˆ ξ h g and ˆ ξ l g . We use the aligned-spin waveform model
IMRPhenomD (Husa et al.2016; Khan et al. 2016) for the signal model and for the incoherent- between-detectors glitch model. In the future, it is desirable to ex-tend this analysis to use more sophisticated waveforms includingprecession of the orbital plane and marginalization over systematicwaveform uncertainties (Ashton & Khan 2020). However, we electto use
IMRPhenomD because it is fast and no published candidateevents exhibit strong evidence of precession.We use data from the Gravitational Wave Open Science Cen-tre (The LIGO Scientific Collaboration et al. 2019) spanning20 −
512 Hz. We estimate the noise properties, the power spec-tral density (PSD), from the median average of 31 non-overlapping4 s periodograms using gwpy (Macleod et al. 2019; Macleod et al.2020). The data used for estimating the PSD is off-source and im-mediately before the analysis segment in each instance. We do notinclude the effects of calibration uncertainty (Cahillane et al. 2017).For signals, we use uniform priors in the chirp mass and massratio over the ranges [ ,
100 M (cid:12) and [ . , ] respectively; forthe component spin prior we use the “ z -prior” (see Eq. (A7) ofLange et al. (2018)) which places much of the prior support at smallspins; this is equivalent to the aligned-spin prior (Config. B) used inHuang et al. (2020). For the remaining parameters we use standardpriors (see Romero-Shaw et al. (2020)), which are informed by theastrophysical nature of expected signals. In the future, it is worthemploying more realistic population models for mass and spin,though, this is outside our present scope; see Fishbach et al. (2020);Galaudage et al. (2019).The informative prior distributions used for signals are not nec-essarily appropriate for the glitch model in which we project glitchesinto the compact binary coalescence signal parameter space. Theastrophysical odds framework is designed to use knowledge abouttypical glitches by marginalizing over the contextual data. It doesso by “recycling” posteriors obtained with an initial prior (see Ap-pendix B of Ashton et al. (2019a)). This process is inefficient if theglitch posteriors strongly disagree with the initial prior. We find,in agreement with Davis et al. (2020), that glitches tend to haveposterior support in regions of parameter space unusual for typicalastrophysical signals, e.g., large negative spins and extreme massratios. To counter this inefficiency, we apply, a glitch prior uniformin the component spin χ ∈ [− , ] and χ ∈ [− , ] . In testing,we find this improved the efficiency of the astrophysical odds inproperly classifying glitches. One might worry that, by applyinga different prior for glitches and signals, we are biasing the odds.However, posterior samples are ultimately recycled using hierarchi-cal inference, and so these prior choices do not affect our resultsexcept to improve computational efficiency.We also find that the astrophysically motivated co-moving vol-umetric prior (Romero-Shaw et al. 2020) for luminosity distancecan also decrease the efficiency of recycling as most glitches tendto occur around ∼
100 Mpc. To be clear, glitches have no phys-ical distance; we refer here to the effective distance obtained byfitting glitches to binary merger waveforms. We therefore employ auniform-in-luminosity distance prior for both signals and glitches,which ensures efficient recycling.In testing, we find that it is important to include uncertaintyin our estimate of the PSD estimation. Failing to take this intoaccount yields false-positive signals ( O >
1) in time-slide checks inwhich the H1 data is offset from L1 to destroy the coherence of realgravitational-wave signals in the data. The solution is to marginaliseover uncertainty in the noise PSD as in Talbot & Thrane (2020);Banagiri et al. (2020). Using the median Student- t method fromTalbot & Thrane (2020)), the astrophysical odds calculated for theset of time-slid Omicron triggers behaves properly: all triggersresult in an odds disfavouring an astrophysical interpretation (see MNRAS , 1–6 (0000)
G. Ashton & E. Thrane
Fig. 1). We conclude that marginalizing over uncertainty in the PSDis necessary for a reliable odds, and so we apply this to all the resultsdiscussed below.
We infer the properties of the glitch population by analysing thetop 100 Omicron triggers from Hanford and Livingston in a 24 hperiod around each of the events. Our glitch model consists ofcompact binary coalescence signals with uncorrelated parametersin each detector (Ashton et al. 2019a). As such, we are projectingthe properties of glitches (for which we do not have a first-principlemodel) onto the parameter space of astrophysical signals. We findbroadly consistent features in the glitch populations surroundingeach of the three events. Namely, glitches tend to have large anti-aligned spins χ ∼ − We present the astrophysical odds for the three events analysedin this work in Table 1. For GW151216, we find p astro = . O = .
03, are larger than the prior odds 7 . × − , showing that thissegment is 40 times more likely than average to contain a signal.Our result suggests that the astrophysical implications inferred fromGW151216 may be premised on a terrestrial event (Piran & Piran2020; Fragione & Kocsis 2020; De Luca et al. 2020).In Table 1, we also provide several Bayesian estimates of sig-nificance. These are the signal vs. Gaussian noise Bayes factor asmeasured directly B G S / N , the signal vs. Gaussian noise Bayes factorafter marginalizing over uncertainty in the PSD; B S / N , the coher-ent vs. incoherent Bayes factor B coh , inc (Veitch et al. 2015), andthe Bayesian coherence ratio (BCR) (Isi et al. 2018). The astro-physical odds builds on each of these concepts, as such, we cansee each as a special case. B coh , inc , does not include the prior-oddsand gives only the evidence for a signal vs. a glitch (i.e. the non-Gaussian component of the noise in our noise model). The BCRis an odds comparing the signal and noise hypotheses used in thiswork, but does not include the glitch hyper model marginalization.In (Isi et al. 2018) the prior-odds and glitch probabilities are used to tune the statistic to maximise the detection power of the statisticin a bootstrap framework. In this work, we instead apply the usualdirect interpretation for the tuning parameters as prior probabili-ties. In this sense, the astrophysical odds in the absence of a glitchhyper-model are equivalent to the BCR up to the choice of tuningparameters/prior probabilities. The difference between ln BCR andln O in Tab. 1 quantifies the effect of the glitch hyper model.The astrophysical odds, as with any significance estimate, de-pends on the choice of priors and on the noise model. It is thereforeuseful to consider which aspects of the analysis are most importantfor the conclusion that GW151216 is not astrophysical in origin.From Table 1, it is clear that GW151216 is a less significant triggerthan the other two candidates from B G S / N alone; it has a lower signal-to-noise ratio. However, the critical factor in our analysis responsiblefor reducing the significance of this event is the marginalization overthe uncertainty in the PSD (see Sec. 3). In Table 1, we see that thesignal/noise Bayes factor falls from B G S / N = . B S / N = .
70 using the Student- t likelihood.Naively combining this Bayes factor (ignoring the effect ofglitches) with a prior odds of ln (cid:104) ξ (cid:105) = − . ξ -distribution. In this work, we usean astrophysical prior based on the rate of binary black hole eventsin the O1 and O2 observing runs. The factorisation of the priorodds in Eq. (1) allows us to update the odds based on differing priorassumptions. In order to change the conclusions for GW151216,one would need to increase (cid:104) ξ (cid:105) by a factor of ∼
36 Translating thisinto an updated merger rate, this would require a merger rate of R (cid:48) ∼ − yr − , much larger than the current uncertainty onthe merger rate (Abbott et al. 2019a). Similarly, a merger rate whichwould make GW151012 not of astrophysical origin (based on anupdated prior odds) would also require a merger rate well outsideof the current uncertainty. This demonstrates that our results are notsensitive to the choice of prior odds, given the current uncertainty.Technically, the odds for GW151012 and GW150914 are biasedbecause the data from these events is used to estimate the rate.However, we expect the error from this double-counting to be neg-ligible. The other potential bias from our prior assumptions is thechoice of point estimates for ξ h g and ξ l g . To check how sensitive ourresults are to this choice, we rerun the analysis of GW151216 using ξ h g = ξ l g = O = − .
5. This small shift from ourcalculated value confirms that our conclusion, that p astro = .
03, isrobust to the choice of glitch hyper prior.For GW150914 and GW151012, the astrophysical odds pro-vide unequivocal evidence that these events are of astrophysical ori-gin. Comparing the BCR and the O in Table 1 allows to assess theeffect of the glitch hyper-model. For GW151012 and GW151216,only a small effect is observed, but for GW150914 the astrophysicalodds is larger than the BCR by a factor of ≈
7. This demonstratesthe ability of the astrophysical odds to increase our confidence in a
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MNRAS000 , 1–6 (0000) he astrophysical odds of GW151216 Table 1.
Significance estimates and associated quantities. The first five columns give 1 − p astro for the GstLAL and PyCBC pipelines reported in Abbott et al.(2019a), the PyCBC pipeline as reported in 1-OGC (Nitz et al. 2019a) and 2-OGC (Nitz et al. 2020), and results from the Institute for Advanced Study (IAS)(Zackay et al. 2019; Venumadhav et al. 2020). The next three columns give the prior probabilities for signals and glitches; see Sec. 2. The next five columns givethe natural logarithm of: B G S / N , the signal vs. Gaussian-noise Bayes factor; B S / N , the signal vs. Gaussian-noise Bayes factor marginalizing over uncertainty inthe PSD (see Sec. 3); B coh , inc , the coherent vs. incoherent Bayes factor (Veitch & Vecchio 2010)); BCR, the Bayes coherence ratio (Isi et al. 2018); and, in thesecond-to-last column, the astrophysical odds, O , (this work) marginalizing over prior probabilities (columns five to seven) and the χ , χ glitch hyper-model.The final column is the remaining terrestrial probability where p astro ≡ O/( + O) , this can be directly compared to the output of the search pipelines.Event GstLAL PyCBC 1-OGC 2-OGC IAS (cid:104) ξ (cid:105) ˆ ξ h g ˆ ξ l g ln B G S / N ln B S / N ln B coh , inc ln BCR ln O − p astro GW150914 < − < − < × − < − – 7 . × − × − GW151012 0 .
001 0.04 0 . < − – 7 . × − . × − . Figure 1.
Visualisation of candidates and triggers considered in this work forthree Bayesian significance estimates: B coh , inc , the coherent vs. incoherentBayes factor (Veitch & Vecchio 2010); the “Bayes Coherence Ratio” (BCR)an odds comparing a signal with both incoherent glitches and Gaussian noise(Isi et al. 2018); and finally the astrophysical odds, Eq. (1). We label the threeevents analysed in this work in the figure and provide the numerical valuesfor each in Tab. 1. Blue circles and connecting curves are drawn for each ofthe Omicron triggers used to characterise the background. Pink crosses anddashed connecting curves mark the values for time-shifted Omicron triggerresults—a background where we can be sure there are no coherent signals. signal based on how unlike the glitch population it is. We can alsocompare the BCR values derived in this work with that of Isi et al.(2018). For GW150914 and GW151012, they find ln BCR values of19.6 and 8.5 respectively; larger than the values found in this work(see Tab. 1). This difference is caused by an unknown combinationof the choice of tuning parameters, the narrower source parameterpriors, the use of a precessing waveform, or the marginalization overthe PSD applied in this work. Given the significant impact of themarginalization over the PSD, we suspect this is likely to dominate,but we cannot determine this without further investigation.To visualise our results for the three candidates and variousrealisations of a background, in Fig. 1, we show the evolutionof candidates through three stages of Bayesian significance esti-mates. Individual candidates are labeled by their ID. In blue, arethe Omicron triggers identified for each of the three epochs aroundeach event; we show these together as no differences in behaviourper-epoch were found. All the significance estimates use evidenceobtained by marginalizing over the uncertainty in the PSD. For theOmicron trigger candidates, we see two distinct clusters: those with ln ( B coh , inc ) ∼ ( B coh , inc ) < −
1. These can be un-derstood as a cluster of candidates where the data is reasonablyGaussian in both detectors (thus tricking the coherent Bayes factorwhich only compares signal evidence against glitch evidence) and acluster of candidates with a strong glitch in one detector resulting ina Bayes factor favouring the glitch hypothesis. When subsequentlyanalysed with the BCR metric (Isi et al. 2018), the Gaussian clusteris weighted down because the BCR includes Gaussian noise in its al-ternative hypothesis. Finally, when applying the glitch hyper-priora small correction is applied based on the likeness of the candi-dates to the glitch population. For the candidates initially in theln ( B coh , inc ) < − We find that the marginal gravitational wave candidate GW151216is not of astrophysical origin, p astro = .
03. Our p astro estimateis smaller than that of the original detection claim p astro = . p astro = .
18 (Nitzet al. 2020). Taken together with (Huang et al. 2020), we urgethe community to use caution when considering the astrophysicalimplications of this event. We also analyse GW150914, the loudestsignal in the first advanced-LIGO observing run, and GW151012, acandidate first marked as marginal, but subsequently upgraded. Wefind overwhelming support that these are astrophysical signals.This work lays out the framework for applying the astrophysicalodds (Ashton et al. 2019a) to a growing catalogue of gravitational-wave transients. In doing so, we seek to provide a single p astro forcandidate events from multiple groups. Our results do not rely onthe output of a search pipeline, and it is easy to see the assump-tions that go into our calculations. It is also straightforward to up-date our significance estimates to keep pace with advances in noisemodelling. Unlike traditional search methods, it does not use boot-strap realisations of the noise, but models the noise as incoherent-between-detector signals. In future work, we anticipate a numberof improvements including: adding additional alternative models, MNRAS , 1–6 (0000)
G. Ashton & E. Thrane for example, sine-Gaussians; improved waveforms; improved meth-ods of estimating the noise PSD; and the addition of calibrationuncertainty.
The authors are grateful to Jess McIver, Will Farr, Laura Nutall,Sebastian Khan, Max Isi, Thomas Massinger, Thomas Dent, ouranonymous referee for useful comments during the developmentof this work. The authors are grateful for computational resourcesprovided by the LIGO Laboratory and supported by National Sci-ence Foundation Grants PHY-0757058 and PHY-0823459. We ac-knowledge the support of the Australian Research Council throughgrants CE170100004, FT150100281, and DP180103155. We usethe bilby (Ashton et al. 2019b) inference package and the dynesty (Speagle 2020) Nested Sampling algorithm.
This research has made use of data, and web tools obtainedfrom the Gravitational Wave Open Science Center (GWOSC: ), a service of LIGO Lab-oratory, the LIGO Scientific Collaboration and the Virgo Collabo-ration. LIGO is funded by the U.S. National Science Foundation.Virgo is funded by the French Centre National de Recherche Scien-tifique (CNRS), the Italian Istituto Nazionale della Fisica Nucleare(INFN) and the Dutch Nikhef, with contributions by Polish andHungarian institutes. The data underlying this article are availablefrom GWOSC (The LIGO Scientific Collaboration et al. (2019)) at https://doi.org/10.7935/K57P8W9D . REFERENCES
Aasi J., et al., 2015, Class. Quantum Gravity, 32, 074001Abbott B. P., et al., 2016a, Class. Quantum Gravity, 33, 134001Abbott B. P., et al., 2016b, Phys. Rev. D, 93, 122003Abbott B. P., et al., 2016c, Phys. Rev. Lett., 116, 061102Abbott B. P., et al., 2016d, ApJS, 227, 14Abbott B. P., et al., 2016e, ApJ, 833, L1Abbott B. P., et al., 2018a, Classical and Quantum Gravity, 35, 065010Abbott B. P., et al., 2018b, Phys. Rev. Lett., 120, 091101Abbott B. P., et al., 2019a, Phys. Rev. X, 9, 031040Abbott B. P., et al., 2019b, ApJ, 882, L24Abbott B. P., et al., 2020, ApJ, 892, L3Acernese F., et al., 2015, Class. Quantum Gravity, 32, 024001Ashton G., Khan S., 2020, Phys. Rev. D, 101, 064037Ashton G., et al., 2018, ApJ, 860, 6Ashton G., Thrane E., Smith R. J. E., 2019a, Phys. Rev. D, 100, 123018Ashton G., et al., 2019b, ApJS, 241, 27Banagiri S., Coughlin M. W., Clark J., Lasky P. D., Bizouard M. A., TalbotC., Thrane E., Mandic V., 2020, MNRAS, 492, 4945Biscoveanu S., Haster C.-J., Vitale S., Davies J., 2020, arXiv e-prints, p.arXiv:2004.05149Blackburn L., et al., 2008, Class. Quantum Gravity, 25, 184004Cabero M., et al., 2019, Class. Quantum Gravity, 36, 155010Cahillane C., et al., 2017, Phys. Rev. D, 96, 102001Cannon K., Hanna C., Keppel D., 2013, Phys. Rev. D, 88, 024025Capano C., Dent T., Hanna C., Hendry M., Messenger C., Hu Y. M., VeitchJ., 2017, Phys. Rev. D, 96, 082002Chatterji S., Blackburn L., Martin G., Katsavounidis E., 2004, Class. Quan-tum Gravity, 21, S1809 Chatziioannou K., Haster C.-J., Littenberg T. B., Farr W. M., Ghonge S.,Millhouse M., Clark J. A., Cornish N., 2019, Phys. Rev. D, 100, 104004Davis D., White L. V., Saulson P. R., 2020, arXiv e-prints, p.arXiv:2002.09429De Luca V., Franciolini G., Pani P., Riotto A., 2020, arXiv e-prints, p.arXiv:2003.02778Efron B., Tibshirani R., 1993, An Introduction to the Bootstrap. Chapman& Hall, London, UKFishbach M., Farr W. M., Holz D. E., 2020, ApJ, 891, L31Fragione G., Kocsis B., 2020, MNRAS, 493, 3920Gaebel S. M., Veitch J., Dent T., Farr W. M., 2019, MNRAS, 484, 4008Galaudage S., Talbot C., Thrane E., 2019, arXiv e-prints, p.arXiv:1912.09708Huang Y., et al., 2020, arXiv e-prints, p. arXiv:2003.04513Husa S., et al., 2016, Phys. Rev. D, 93, 044006Isi M., et al., 2018, Phys. Rev. D, 98, 042007Khan S., et al., 2016, Phys. Rev. D, 93, 044007Lange J., O’Shaughnessy R., Rizzo M., 2018, arXiv e-prints, p.arXiv:1805.10457Littenberg T. B., Cornish N. J., 2015, Phys. Rev. D, 91, 084034Macleod D., et al., 2019, GWpy: Python package for studying data fromgravitational-wave detectors (ascl:1912.016)Macleod D., et al., 2020, gwpy/gwpy: 1.0.1, doi:10.5281/zenodo.3598469, https://doi.org/10.5281/zenodo.3598469
Nitz A. H., Dent T., Dal Canton T., Fairhurst S., Brown D. A., 2017, ApJ,849, 118Nitz A. H., Capano C., Nielsen A. B., Reyes S., White R., Brown D. A.,Krishnan B., 2019a, ApJ, 872, 195Nitz A. H., Nielsen A. B., Capano C. D., 2019b, ApJ, 876, L4Nitz A. H., et al., 2020, ApJ, 891, 123Nuttall L. K., et al., 2015, Classical and Quantum Gravity, 32, 245005Piran Z., Piran T., 2020, ApJ, 892, 64Powell J., 2018, Class. Quantum Gravity, 35, 155017Romero-Shaw I. M., et al., 2020, arXiv e-prints, p. arXiv:2006.00714Smith R., Thrane E., 2018, Phys. Rev. X, 8, 021019Speagle J. S., 2020, MNRAS, 493, 3132Talbot C., Thrane E., 2020, arXiv e-prints, p. arXiv:2006.05292The LIGO Scientific Collaboration the Virgo Collaboration et al., 2019,arXiv e-prints, p. arXiv:1912.11716The LIGO Scientific Collaboration the Virgo Collaboration et al., 2020,arXiv e-prints, p. arXiv:2004.08342Usman S. A., et al., 2016, Classical and Quantum Gravity, 33, 215004Veitch J., Vecchio A., 2010, Phys. Rev. D, 81, 062003Veitch J., et al., 2015, Phys. Rev. D, 91, 042003Venumadhav T., et al., 2019, Phys. Rev. D, 100, 023011Venumadhav T., Zackay B., Roulet J., Dai L., Zaldarriaga M., 2020, Phys.Rev. D, 101, 083030Zackay B., Venumadhav T., Dai L., Roulet J., Zaldarriaga M., 2019, Phys.Rev. D, 100, 023007This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS000