We have presented an idealized model of the noise and signal content in G W observations with a network of laser interferometric detectors. This model led us to the matched filter, the maximum likelihood estimator, and the network S N R as the simplest possible statistic for discriminating between the presence or absence of an astrophysical signal. Having defined S N R, we worked out the horizon distance of a G W detector. Next, we used the Fisher matrix formalism to calculate the sky resolution of a G W detector network. Previous approaches (Fairhurst 2009, etc.) have considered only arrival time measurements, but our computation also accounts for measurements of phase and amplitude on arrival. Despite this, our method as outlined in Section 2.6.3 is only slightly more complicated than the timing-only calculation. Though the Fisher matrix analysis cannot be applied to two-detector networks, we do expect it to accurately predict the sky localization accuracy of signals that are confidently detected by networks of three or more detectors of comparable sensitivity. We endorse it as the most sophisticated analysis worth carrying out, short of performing full Bayesian parameter estimation on a population of simulated signals. We advocate using it to revise the overly pessimistic sky resolution predictions for the 2019 and later scenarios in Aasi et al. (2013c).
The horizon distance, the observables and parameters in G W observations of compact binaries, the Fisher matrix, and estimates of sky resolution will recur in later chapters. In the next chapter, we will use all of these results to study the prospects for detecting and localizing B N S signals in near real-time, from hundreds of seconds before to seconds after merger.
Chapter 3
Early warning G W detection
Kipp Cannon1, Romain Cariou2, Adrian Chapman3, Mireia Crispin-Ortuzar4,
Nickolas Fotopoulos3, Melissa Frei5,6, Chad Hanna7, Erin Kara8, Drew Keppel9,10,
Laura Liao11, Stephen Privitera3, Antony Searle3, Leo Singer3, and Alan Weinstein3
1Canadian Institute for Theoretical Astrophysics, Toronto, ON, Canada 2D´epartement de Physique, ´Ecole Normale Sup´erieure de Cachan, Cachan, France
3LIGO Laboratory, California Institute of Technology, MC 100-36, 1200 E. California Blvd., Pasadena, CA, USA 4Facultat de F´ısica, Universitat de Val`encia, Burjassot, Spain
5Department of Physics, University of Texas at Austin, Austin, TX, USA
6Center for Computational Relativity and Gravitation and School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY, USA
7Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada
8Department of Physics and Astronomy, Barnard College, Columbia University, New York, NY, USA 9Albert-Einstein-Institut, Max-Planck-Institut f ¨ur Gravitationphysik, Hannover, Germany
10Institut f ¨ur Gravitationsphysik, Leibniz Universit¨at Hannover, Hannover, Germany 11Department of Chemistry and Biology, Ryerson University, Toronto, ON, Canada
This chapter is reproduced in part from Cannon et al. (2012), which was published in The Astrophysical Journal as “Toward early-warning detection of gravitational waves from compact binary coalescence,” copyright © 2012 The American Astronomical Society. Note that the author list is alphabetical because of the large number of contributors to this algorithm and codebase, initiated and organized by K.C., C.H., and D.K. My contributions to that code are related to the interpolation, decimation, and triggering stages. My contributions to the project include all of the calculations
related to “early warning” detection and localization, all of the accounting of the computational cost, and the measurement of the mismatch of the template bank. I prepared all of the figures and tables in this publication and about
In the first generation of ground-based laser interferometers, the G W community initiated a project to send alerts when potential G W transients were observed in order to trigger follow-up observations by E M telescopes. The typical latencies were 30 minutes (Hughey, 2011). This was an important achievement, but too late to catch any prompt (i.e., simultaneous with gamma-ray emission) optical flash and later than would be desirable to search for an on-axis optical afterglow (which fades rapidly as a power law in time; see for example Metzger & Berger 2012). Since the G W signal is in principle detectable even before the tidal disruption, one might have the ambition of reporting G W candidates not minutes after the merger, but seconds before. We explore one essential ingredient of this problem, a computationally inexpensive real-time filtering algorithm for detecting inspiral signals in G W data. We also consider the prospects for advanced G W detectors and discuss other areas of work that would be required for rapid analysis.
In October 2010, L I G O completed its sixth science run (S6) and Virgo completed its third science run (VSR3). While both L I G O detectors and Virgo were operating, several all-sky detection pipelines operated in a low-latency configuration to send astronomical alerts, namely, Coherent WaveBurst (cW B), Omega, and Multi-Band Template Analysis (M B TA; Abadie et al., 2012a,b). cW B and Omega are both unmodeled searches for bursts based on time-frequency decomposition of the G W data. M B TA is a novel kind of template-based inspiral search that was purpose- built for low latency operation. M B TA achieved the best G W trigger-generation latencies, of 2–5 minutes. Alerts were sent with latencies of 30–60 minutes, dominated by human vetting. Candidates were sent for E M follow-up to several telescopes; Swift, LOFAR, ROTSE, TAROT, QUEST, SkyMapper, Liverpool Telescope, Pi of the Sky, Zadko, and Palomar Transient Factory imaged some of the most likely sky locations (Abadie et al., 2012b; Evans et al., 2012; Aasi et al., 2014).
There were a number of sources of latency associated with the search for C B C signals in S6/VSR3 (Hughey, 2011), listed here.
Data acquisition and aggregation (&100 ms) The L I G O data distribution system collects data in real time, but distributes it to computers in the control rooms 16 times a second, and archives it for immediate offsite replication in blocks of 16 s (Bork et al., 2001). Data are copied from all of the G W observatories to the analysis clusters over the Internet, which is capable of high
bandwidth but only modest latency. Altogether, it takes about 16 s to transmit the data to the analysis clusters, but with moderate changes in infrastructure could be reduced to∼100 ms if the data were streamed to the computing clusters in real-time without blocking it into 16 s chunks.
Data conditioning (∼1 min) Science data must be calibrated using the detector’s frequency response to gravitational radiation. Currently, data are calibrated in blocks of 16 s. Within
∼1 minute, data quality is assessed in order to create veto flags. These are both technical sources of latency that might be addressed with improved calibration and data quality software for advanced detectors.
Trigger generation (2–5 min) Low-latency data analysis pipelines deployed in S6/VSR3 achieved an impressive latency of minutes. However, second to the human vetting process, this dominated the latency of the entire E M follow-up process. Even if no other sources of latency existed, this trigger generation latency is too long to catch prompt or even extended emission. Low-latency trigger generation will become more challenging with advanced detectors because inspiral signals will stay in band up to 10 times longer. In this work, we will focus on reducing this source of latency.
Alert generation (2–3 min) S6/VSR3 saw the introduction of low-latency astronomical alerts, which required gathering event parameters and sky localization from the various online analyses, downselecting the events, and calculating telescope pointings. If other sources of latency improve, the technical latency associated with this infrastructure could dominate, so work should be done to improve it.
Human validation (10–20 min) Because the new alert system was commissioned during S6/VSR3, all alerts were subjected to quality control checks by human operators before they were dissemi- nated. This was by far the largest source of latency during S6/VSR3. Hopefully, confidence in the system will grow to the point where no human intervention is necessary before alerts are sent, so we give it no further consideration here.
This chapter will focus on reducing the latency of trigger production. Data analysis strategies for advance detection of C B C s will have to strike a balance between latency and throughput.
C B C searches consist of banks of matched filters, or cross-correlations between the data stream and a bank of nominal “template” signals. There are many different implementations of matched filters, but most have high throughput at the cost of high latency, or low latency at the cost of low throughput. The former are epitomized by the overlap-save algorithm for F D convolution, currently the preferred method in G W searches. The most obvious example of the latter is direct T D convolution, which can be done in real-time. However, its cost in floating point operations per second is linear in the length of the templates, so it is prohibitively expensive for long templates. The computational challenges of low-latency C B C searches are still more daunting for advanced detectors for which the inspiral signal remains in band for a large fraction of an hour (see Appendix B).
Fortunately, the morphology of inspiral signals can be exploited to offset some of the com- putational complexity of known low-latency algorithms. First, the signals evolve slowly in frequency, so that they can be broken into contiguous band-limited time intervals and processed at possibly lower sample rates. Second, inspiral filter banks consist of highly similar templates, admitting methods such as the singular value decomposition (S V D) (Cannon et al., 2010) or the Gram-Schmidt process (Field et al., 2011) to reduce the number of templates.
Several efforts that exploit one or both of these properties are under way to develop low-latency C B C search pipelines with tractable computing requirements. One example is M B TA (Marion & the Virgo Collaboration, 2003; Buskulic et al., 2010), which was deployed in S6/VSR3. M B TA consists of multiple, usually two, template banks for different frequency bands, one which is matched to the early inspiral and the other which is matched to the late inspiral. An excursion in the output of any filter bank triggers coherent reconstruction of the full matched filtered output. Final triggers are built from the reconstructed matched filter output. Another novel approach using networks of parallel, second-order infinite impulse response (I I R) filters is being explored by Hooper et al. (2010) and Luan et al. (2012).
We will use both properties to demonstrate that a very low latency detection statistic is possible with current computing resources. Assuming the other technical sources of latency can be reduced significantly, this could make it possible to send prompt (<1 minute) alerts to the astronomical community.
The chapter is organized as follows. First, we describe the standard, offline C B C detection process. Using a simple model of the detection and sky localization accuracy of this search, we
10−2 10−1 100 101 102 103
time before coalescence (s) 10−1 100 101 102 103 detections yr − 1
Figure 3.1 Expected number of N S–N S sources that could be detectable by Advanced L I G O a given number of seconds before coalescence. The heavy solid line corresponds to the most probable yearly rate estimate from Abadie et al. (2010b). The shaded region represents the 5%–95% confidence interval arising from substantial uncertainty in predicted event rates.
study the prospects for early-warning detection. Then, we provide an overview of our novel method for detecting C B C signals near real-time. We then describe a prototype implementation using open source signal processing software. To validate our approach we present a case study focusing on a particular subset of the N S–N S parameter space. We conclude with some remarks on what remains to be prepared for the advanced detector era.