Analysis framework for the prompt discovery of compact binary mergers in gravitational-wave data

We describe a stream-based analysis pipeline to detect gravitational waves from the merger of binary neutron stars, binary black holes, and neutron-star–black-hole binaries within $\sim 1$ min of the arrival of the merger signal at Earth. Such low-latency detection is crucial for the prompt response by electromagnetic facilities in order to observe any fading electromagnetic counterparts that might be produced by mergers involving at least one neutron star. Even for systems expected not to produce counterparts, low-latency analysis of the data is useful for deciding when not to point telescopes, and as feedback to observatory operations. Analysts using this pipeline were the first to identify GW151226, the second gravitational-wave event ever detected. The pipeline also operates in an offline mode, in which it incorporates more refined information about data quality and employs acausal methods that are inapplicable to the online mode. The pipeline’s offline mode was used in the detection of the first two gravitational-wave events, GW150914 and GW151226, as well as the identification of a third candidate, LVT151012.

Figure 1

Diagram of the offline search mode of the GstLAL-based inspiral pipeline. First, data are transferred from each observatory ($H,L,\dots$) to a central computing cluster (Sec. 2a). Next, data are read from the disk, and the PSD is estimated (Sec. 2b) in chunks of time $t_0,t_1,\dots ,t_N$ for each observatory. The median over the entire analysis time of each observatory PSD estimate is computed. The input template bank, which is generated upstream of the analysis, is split into regions of similar parameters ${\overline{\theta }}_0,{\overline{\theta }}_1,\dots ,{\overline{\theta }}_N$ (Sec. 2d) and then decomposed into a set of orthonormal filters weighted by the median PSD for each observatory. The data are filtered to produce a series of triggers characterized by the signal-to-noise ratio (SNR), $\rho$, signal consistency check, ${\xi }^2$ (Secs. 3a, 3b, and 3c), and coalescence time. Coincident triggers between detectors are identified and promoted to the status of events (Sec. 3d). Events are ranked according to their relative probability of arising from signal versus noise (Sec. 3e). The data are then reduced to the most highly ranked event in 8 s windows (Sec. 3f). In parallel, triggers not found in coincidence are used to construct the probability of obtaining a given event from noise, $P(\mathrm{\Lambda }|n)$. Finally, the event significance and false-alarm rate are estimated (Sec. 4a). Note that the arrows drawn between nodes in this diagram do not imply the output of one node is the input of the next node; they simply indicate the order in which tasks are performed.

Figure 2

Diagram of the low-latency search mode of the GstLAL-based inspiral pipeline. First, data are received over a network connection from each observatory to a data broadcaster in a central computing facility. The data are then broadcast over the entire cluster with an efficient multicast protocol. The online analysis uses precomputed bank decompositions for each observatory from reference PSDs as input to jobs that combine the filtering, vetoing, coincidence, ranking, and significance estimation steps from the offline pipeline. Unlike the offline case, the online analysis workflow cannot be described as a directed acyclic graph, and in fact, data from each filtering job are exchanged bidirectionally and asynchronously to a process that constantly evaluates the global background estimates for the entire analysis. Events that are identified by any one filtering job, and subsequently pass a predetermined significance threshold, are sent to the Gravitational-Wave Candidate Event Database (GraceDB) [29] within a matter of seconds of the data being recorded at the observatories.

Figure 3

PSD convergence properties. Estimating the PSD is a critical part of ensuring that events are detected and assigned the appropriate significance. This figure illustrates the convergence properties of the PSD estimation in terms of the impact on SNR. Within 20 s the PSD will have an $\mathcal{O}(10\%)$ impact on SNR, and within 200 s the impact drops to $\mathcal{O}(1\%)$, where it remains.

Figure 4

Data conditioning. In this two second block of LIGO S6 data, three noise transients (glitches) are visible. The glitch at time zero surpassed the threshold of 50 standard deviations ($\sigma$), triggering the gate to veto a $\pm 0.25\mathrm{s}$ window around the glitch by replacing the data with zeros (black). The gray trace shows what the data looked like prior to gating.

Figure 5

Top: Time domain representation of the whitening filter computed from a PSD estimated in an analysis of one week of S6 data. The $\sim 0.98$ of the filter’s square magnitude is contained enclosed within $\pm 10\mathrm{ms}$ of the peak. Bottom: The PSD used to compute the whitening filter.

Figure 6

An illustration of how the physical parameter space is tiled into regions in which the LLOID decomposition is done. The physical parameter space is projected onto the $\mathcal{M}$, $\chi$ plane. Tiles of equal template number, $2N_T$, are constructed and overlapped in the $\mathcal{M}$ direction by $\mathcal{O}(10\%)$. Above a specified chirp mass, ${\mathcal{M}}_c$, waveforms that use the full inspiral-merger-ringdown description are used. Below ${\mathcal{M}}_c$, waveforms that model only the inspiral phase are used. Tiles of similar chirp mass are then grouped together to define a one-dimensional family of similar parameters, $\overline{\theta }$, used in the evaluation of the likelihood-ratio ranking statistic (Sec. 3e).

Figure 7

An example of the LLOID decomposition [24]. In this example, $N_T=195$ binary inspiral waveforms (390 including the two possible phases) with a chirp mass between 0.87 and 0.88 are first “whitened” by dividing them by a realistic noise amplitude spectral density from advanced LIGO (aLIGO). The line features in the spectrum are responsible for the amplitude modulation of the waveforms. The waveforms, which are prepended with zeros when necessary so that all of the templates in a given decomposition have the same number of sample points, were decomposed into 30 time slices at sample rates ranging between 128 Hz and 2048 Hz (only the last 10 slices are shown). A basis filter set from the waveforms in each time slice was constructed using the SVD [46]. Only 6–10 basis waveforms per slice were needed to reconstruct both phases of the 195 input waveforms to an accuracy of better than 99.9%.

Figure 8

Ingredients in the autocorrelation-based least-squares test as described in (26). The two panels show the SNR time series near a simulated signal in initial LIGO data (black lines) along with the predicted SNR computed from the template autocorrelation. Subtracting these two time series and integrating their squared magnitude provides a signal consistency test, ${\xi }^2$, at the time of a given trigger that can be used to reject nonstationary noise transients.

Figure 9

PDFs used in the likelihood ratio calculation, generated by histogramming, then smoothing, and normalizing the triggers. The plots shown are from an analysis of S6 data beginning at September 14, 2010, at 23∶58:48 UTC and ending at September 21, 2010, at 23∶58:48 UTC, which includes the blind injection known as the Big Dog. The warm colormap corresponds to the natural logarithm of marginalized probability density function estimated from noncoincident triggers only; the cool-colormap region was computed by adding coincident triggers to the histograms before smoothing and normalizing. Regions of the cool-colormap model consistent with the warm-colormap model were then masked. The location of the Big Dog in the $(\rho ,{\xi }^2)$ plane is marked with a black X.

Figure 10

Instances of two of the distributions included in the calculation of the likelihood-ratio numerator, generated from an analysis of S6 data beginning at September 14, 2010, at 23∶58:48 UTC and ending at September 21, 2010, at 23∶58:48 UTC. Top: The joint SNR PDF used to enforce amplitude consistency across observatories. The location of the measured Big Dog parameters is marked with a black X. Bottom: The $(\rho ,{\xi }^2)$ signal distribution used in the numerator of the likelihood ratio. The locations of the measured Big Dog parameters are marked with a black X for Hanford and a $\mathrm{black}+\text{for Livingston}$.

Figure 11

Number of observed events as a function of the log likelihood ratio in an analysis of S6 data beginning on September 14, 2010, at 23∶58:48 UTC and ending at September 21, 2010, at 23∶58:48 UTC. The Big Dog injection, found with a false alarm probability of $5.4\times {10}^{-9}$ ($5.7\sigma$), is marked on the observed distribution (green). The black line represents the predicted number of events when observed events are included in the background model, while the blue line is the predicted number when the observed events are not included in the background model.