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LASER INTERFEROMETER GRAVITATIONAL WAVE OBSERVATORY- LIGO -

CALIFORNIA INSTITUTE OF TECHNOLOGYMASSACHUSETTS INSTITUTE OF TECHNOLOGY

Document Type 2002/11/13

S1 Burst Search Report

Distribution of this draft:

California Institute of Technology Massachusetts Institute of TechnologyLIGO Project - MS 51-33 LIGO Project - MS 20B-145

Pasadena CA 91125 Cambridge, MA 01239Phone (626) 395-2129 Phone (617) 253-4824

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Processed with LATEX on 2002/11/13

Abstract

Executive summary here.This is an early and incomplete draft. It contains no data or results. Sections which seem

complete may not be. Please comment early, often and in writing.

Contents

1 Introduction 41.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2 S1 run and data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3.1 Excess events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3.2 The Babylonian sky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.3 Gravitational waves from GRBs . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Outline of the remainder of the report . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Analysis pipeline overview 62.1 Event triggers and their generation . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.2 TFClusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.3 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.4 BlockNormal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Vetos and their generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Veto triggers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Epoch vetos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Coincidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.1 Temporal Coincidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.2 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.3 Frequency Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.4 Amplitude Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Determination of detection efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 102.4.1 Fidelity of simulation pipeline to data pipeline . . . . . . . . . . . . . . . 102.4.2 Detector response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4.3 Efficiency of multiple interferometer coincidence . . . . . . . . . . . . . . 11

2.5 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5.1 Events from multiple ETGs . . . . . . . . . . . . . . . . . . . . . . . . . 122.5.2 Excess events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5.3 Distribution analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5.4 Model-dependent analyses . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5.5 Babylonian analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5.6 Astrophysical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

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3 Methods 143.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1.1 Playground vs. production . . . . . . . . . . . . . . . . . . . . . . . . . . 143.1.2 Iterative nature of the process . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Preliminary studies: veto channel candidates . . . . . . . . . . . . . . . . . . . . . 143.3 Preliminary studies: event trigger generators . . . . . . . . . . . . . . . . . . . . . 15

3.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3.2 Setting event trigger generator thresholds . . . . . . . . . . . . . . . . . . 153.3.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3.4 Multi-interferometer coincidence: Sam . . . . . . . . . . . . . . . . . . . 163.3.5 Efficiency estimation: Sam . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3.6 Background estimation: Sam . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4 Veto channel selections and tuning . . . . . . . . . . . . . . . . . . . . . . . . . . 183.5 Final veto and event trigger generator tuning . . . . . . . . . . . . . . . . . . . . 203.6 Diagnostic trigger generator filter tuning . . . . . . . . . . . . . . . . . . . . . . . 203.7 Veto trigger tuning for L1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.8 Veto trigger tuning for H1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.9 No Veto used for H2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.10 Event trigger generator threshold tuning: TFCLUSTER . . . . . . . . . . . . . . . 21

3.10.1 Tuning the threshold on the absolute power in a cluster of black pixels . . . 233.11 Event trigger generator threshold tuning: slope . . . . . . . . . . . . . . . . . . . 243.12 The playground results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4 Results: unknown source search 254.1 Epoch Veto results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 Sanity checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.3 Background estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.4 Event rate bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.5 Interpreted bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5 Discussion: Unknown source search results 35

6 Gravitational waves associated with GRBs 35

7 Discussion: Gravitational waves associated with GRBs 35

8 Conclusions 358.1 Search for gravitational wave bursts of unknown origin . . . . . . . . . . . . . . . 358.2 Search for gravitational wave bursts associated with gamma-ray bursts . . . . . . . 358.3 Integration of GEO and LIGO data in a single analysis . . . . . . . . . . . . . . . 35

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1 Introduction

1.1 Purpose

In September 2001, shortly following the end of the S1 data run, the Burst Analysis Group com-mitted to complete and document the following analyses by November 1 [1]:

� Scientific result from a search for gravitational wave bursts of unknown origin. The specificresult is a bound on the rate of detected gravitational wave bursts, viewed as originating fromfixed strength sources on a fixed distance sphere centered about Earth, expressed as a regionin a rate v. strength diagram.

� Search for gravitational wave bursts associated with gamma-ray bursts. The result of thissearch is a bound on the strength of gravitational waves associated with gamma-ray bursts.

� The integration of GEO and LIGO data in a single analysis. The specific result is the demon-strated ability to run GEO and LIGO data through equivalent data processing pipelines, upto and through the construction of temporal coincidences.

The scientific result from a search for gravitational wave bursts of unknown origin is not an astro-physical interpretation. The GEO/LIGO data integration demonstration does not include the jointsimulations and calibrations required to interpret the results, nor does it include having resolvedall of the issues relating to the interpretation of coincidence between non-aligned interferometers.

The purpose of this report is to describe the Burst Analysis Group’s preliminary (“November1”) analysis of the LIGO S1 data set.

In this work, we focus attention on gravitational wave bursts of

� limited duration. For this work, we consider bursts of less than 1 second duration, andincluding some as brief as 1 msec duration.

� unmodeled waveform, so that (templated) matched filtering techniques are not useful. In-stead, techniques are employed that make no assumptions and exhibit little bias as to theform of the wavefom, so long as it has significant strain amplitude in the LIGO sensitivityfrequency band.

� Coincident or near-coincident ( 10 msec light travel time) signals between LHO and LLO.

1.2 S1 run and data set

PETER DRAFTS; SZABI INFORMATION ON GRB PLAYGROUND

1.3 Interpretation

We search for short-duration bursts of excess power in some frequency band where the detectorshave high sensitivity. After due care to reject instrumental or environmental sources, and afterrequiring coincidences in time and in burst characteristics between different detectors, we assumethat any remaining bursts are due to gravitational waves of extra-terrestrial origin.

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There are a variety of astrophysical sources of gravitational waves that have been consideredin the literature. These include compact binary inspirals [REF], black hole mergers [REF], matterplunging into massive black holes [REF], and supernovas [REF]. Some of these sources result ingravitational wave waveforms that can be modeled with sufficient accuracy that matched-filteringtechniques can significantly improve the detection signal-to-noise ratio. Searches for such wave-forms are described in a separate document [REF].

In this document, we focus on gravitational wave signals whose waveforms are a priori un-known. The search techniques, described in section [REF], are designed to find short-durationbursts of excess power (above the noise level) in the sensitive frequency band, with good efficiency.The parameters and thresholds for these search algorithms are adjusted to minimize the false eventrate due to detector noise fluctuations, while maintaining high efficiency for gravitational wavebursts. The resulting observed rate, or rate upper limit, can only be interpreted in the context ofsome model waveform. For example, we can associate a rate, or rate upper limit, with an efficiencyfor detecting gravitational waves with a particular waveform and peak (or rms) amplitude, incidenton the network of earth-based detectors. We can evaluate this efficiency through simulation of thewaveforms through the calibrated response of the detectors and the search algorithms, followingthe standard data pipeline (described below) as closely as possible. The sensitivity of the networkof detectors to source direction and polarization, including time delays between detectors, must betaken into account.

Many different waveform morphologies can be conceived of. However, the response of ourburst search pipeline is a complex, potentially non-linear function of the waveform, which canonly be evaluated through simulations. Since it is practically impossible to formulate a result forany conceivable waveform, we are forced to restrict our attention to a small but representative setof waveforms morphologies. We have considered two different classes of waveforms in this study:

� Ad hoc, narrow-band bursts: Sine-Gaussians, with central frequencies between 100 Hz and2 kHz, and durations yielding Q of around 9. These are indexed by their central frequencyand their peak amplitude. See Figure 1.

� Ad hoc, broad-band bursts: simple Gaussians, with durations varying from several ms toseveral 100 ms. These are indexed by their duration and their peak amplitude. See Figure 2.

For each waveform, we can evaluate the efficiency for coincident detection by a network ofdetectors, averaged over (assumed isotropically distributed) source direction and polarization, asa function of peak amplitude (or, in the case of ZM waveforms, source distance). The observedevent rates (or rate upper limits) must be interpreted in the context of this efficiency.

In the remainder of this subsection, we describe briefly three separate styles of analysis that wehave undertaken with the S1 data.

1.3.1 Excess events

The raw results from our analysis pipeline events that are each consistent with a single gravi-tational wave burst incident on the three LIGO detectors. Coincidence, in this regard, includestime-of-arrival, strain amplitude and possibly signal frequency and bandwidth. At the same time,we have an estimate of the expected number of coincident events arising from non-gravitationalwave backgrounds, which comes from evaluating coincidences between the three interferometers

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after having introduced a unique time-offset into each data stream. From these two figures (and as-suming Poisson statistics for the background) we can bound the number of actual coincident eventsin excess of our expected background. Divided by the detector live time this is a bound on the rateof excess events, which is in turn a bound on the rate of detected excess events of gravitationalwave origin.

1.3.2 The Babylonian sky

Suppose that the Earth is awash in gravitational wave bursts that arrive isotropically and take theform of a Gaussian pulse in a single polarization state and with a single amplitude. Bursts like thesewill result in an expected distribution of events in the detector with amplitudes that vary owing tothe different relative orientations of the detector with the bursts incident direction and polarization.From simulations we determine the expected observed distribution of event amplitudes for incidentwaves of this character.

Now assume that the observed event distribution (in amplitude) is the weighted sum of twodistributions: the background distribution and the gravitational wave event distribution. Takingthis as the likelihood function we determine the bounds on the fraction of observed events that areattributed to the gravitational wave distribution associated with incident waves of this character.The bound on the fraction of events, divided by the live-time and the detection efficiency forincident waves of this character and amplitude, is a bound on the event rate at the given wavestrength. We repeat this procedure for bursts of different amplitude to produce a bound in therate-strength plane.

1.3.3 Gravitational waves from GRBs

1.4 Outline of the remainder of the report

2 Analysis pipeline overview

2.1 Event triggers and their generation

The search for possible gravitational wave signals starts by feeding the interferometer differentialarm-length error signal (called AS Q) into filtering software that we call the Event Trigger Gener-ator (or ETG.) Technically, these are Dynamical Shared Objects in LDAS. XX better terminology.

During S1, we used two different Event Trigger Generators: one called slope, and anothercalled TFCLUSTER. In succeeding sections, we will describe how each of these operates, andlater in the paper will present upper limits derived from each one. We will also describe two otherEvent Trigger Generators: Power, and BlockNormal. Excess Power is almost as well characterizedas the first two ETGs, so we will show some results, although not a final upper limit on gravitywave flux. BlockNormal is still in early development.

2.1.1 Slope

The slope algorithm (implemented by Ed Daw) is an example of a pure time-domain search tech-nique. [2] The fundamental step is to perform a linear least-squares fit to the slope of a sample of nsamples of a pre-filtered version of the AS Q time series (in our case n = 10 samples, for a sample

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duration of 0.6 msec.) An event is written to the database when the value of the slope exceeds athreshold. Not every threshold crossing is recorded, though; all crossings within W samples (in ourcase, W = 49 samples, for a window of 3 msec) are recorded as a single event, whose amplitude isthe largest value of the slope within that window. The search output consists of an event list. Foreach event, the start time and maximum measured gradient is recorded.

2.1.2 TFClusters

The TFCLUSTER algorithm is an adaptive time-frequency method, developed by Julien Sylvestre.XXref It begins by cutting a pre-filtered version of the AS Q time series into intervals 1/8 sec induration, each of which is Fourier transformed to produce an estimate of the power spectrum duringthat interval. The set of those power spectra can be pictured as being displayed as a spectrogram,whose elementary time-frequency pixels have dimensions 1/8 sec by 8 Hz. TFCLUSTER thenperforms the following steps:

� Each pixel is compared with its mean value (as calculated over XX what interval?XX.) If itexceeds that mean value by a large enough multiple of that pixels standard deviation (XX isthis it?), then it is called a black pixel. All other pixels are called white pixels.

� The black-and-white version of the spectrogram is searched for clusters of contiguous blackpixels. In addition to recognizing such clusters, the algorithm also computes the size ofso-called generalized clusters, consisting of individual clusters that are close compared withtheir size. XX check, also pointer to Juliens paper XX

� For all clusters and generalized clusters that are larger than a certain number of black pixels,TFCLUSTER reports to the database the integrated power in the corresponding pixels of theoriginal spectrogram.

Each event is characterized by the power in the cluster, the frequency range spanned by thecluster, and the start time and duration occupied by the cluster.

2.1.3 Power

The Event Trigger Generator called Power is based on the Excess Power Statistic method of Flana-gan, Anderson, and Brady. (XX right authors?) Like TFCLUSTER, it is a time-frequency method.However, instead of examining each spectrogram for clusters of strong pixels, Power measuresthe spectral power in a set of pre-defined tilings of the time-frequency plane. These span a rangefrom short-duration coarse-resolution tiles to long-duration fine-resolution tiles. (XX numbers?)(XX Normalizing or other prefiltering steps?) Power reports an event to the database whenever thepower in a t-f tile exceeds a given level of significance. XX awk, correct?

2.1.4 BlockNormal

The BlockNormal event trigger generator surveys the data for adjacent intervals whose mean andvariance are approximately constant. It identifies those moments of time when these statisticschange; thus, it can be characterized as a change-point analysis.

This event trigger generator is currently under development and was not available for the S1analysis report here.

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2.2 Vetos and their generation

A second data analysis path operates in parallel with the Event Trigger Generation described above.The function of this second path is to test the state of the interferometer and its physical environ-ment, in order to distinguish between times when gravitational wave data should be consideredvalid (for purposes of the burst search) and when any putative burst candidates should be discarded.

In the remainder of this section, we discuss two kinds of vetoes, those that rule out substantialchunks of data (we call them epoch vetoes), and those that veto only brief intervals (of orderseconds or less.) The latter we call veto triggers.

2.2.1 Veto triggers

Veto triggers may be generated by detailed examination of any of the many interferometer controland diagnostic signals recorded along with AS Q, or of any of the many environmental signalsfrom instruments such as seismometers, accelerometers, microphones, tiltmeters, magnetometers,power line monitors, etc. To date, only signals from other interferometer control signals and lasercontrol signals have shown a strong match with any frequent transient phenomena in AS Q. Wehave also measured couplings between the physical environment and AS Q, but (by successfuldesign) those couplings are weak enough that interferometer transients due to those channels arerare.

Our examination of the diagnostic channels was performed by a monitor (i.e., a program) calledglitchMon (written my Masahiro Ito), running in the LIGO environment XX correct term?XXcalled the Data Monitor Tool, or DMT. GlitchMon examines each (pre-filtered) channel for ex-cursions above a fixed threshold. When one is found, it defines an event by finding the durationuntil that signal returns to stay below the threshold for 0.25 seconds. The event is described by itsstart time and duration, and by an amplitude given as the largest instantaneous excursion duringthe events duration.

Our success at sometimes finding interferometer diagnostic channels that explain certain tran-sients in AS Q is due to the lack of complete orthogonality between the ostensible gravity wavechannel and other channels. Looked at from the opposite point of view, we need to ensure that anyuse of other interferometer channels to define vetoes would not veto a true gravitational wave sig-nal. We have studied each such proposed veto by examining the instruments response to injectedmirror motions, and constructed a signal strength ratio test to guarantee that any events that arevetoed did not enter the interferometer as genuine gravitational waves.

2.2.2 Epoch vetos

It is important that the search for transient gravitational waves be carried out only on data thatcomes from sufficiently stationary interferometers. At the most basic level, we only analyze datathat comes from segments of time during which the interferometer is locked in its full configura-tion, and during which no alignments or other adjustments have taken place. The interferometeroperator certifies that the instrument has entered this state (called Science Mode) by pressing abutton on the control screen, and an automatic system detects when the state has changed. Theintervals of Science Mode data were recorded in the database.

For the burst search, we performed an additional cut on the data. We measured the rms noisein the AS Q channel in several broad frequency bands, and rejected lock segments during which

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the broad-band noise was extraordinarily large. The details of this test are listed in Table XX (XXbands used, mean value in each band, where cut was placed, what fraction of time was vetoed byuse of epoch veto.)

XX New proposed epoch veto: XX During the S1 run, the calibration between gravitationalwave strain and counts in the AS Q channel drifted, by more than a factor of two. In order tobe able to interpret our upper limits on event rates in terms of gravitational wave strain, we haverejected all data where the strain calibration was poorer than a factor of XX than the nominalsensitivity. (See the section on calibration/efficiency/interpretation XX? for an explanation of howwe account for the time-varying calibration in establishing our final upper limits.)

2.3 Coincidence

A primary feature which distinguishes gravitational-wave signals from noise fluctuations is thatgravitational-wave signals should appear simultaneously and with similar characteristics in all co-aligned interferometers of comparable sensitivity. The next step in the analysis pipeline is thereforeto check that the event triggers from each interferometer show similar values for start time, fre-quency range, and amplitude or power.

2.3.1 Temporal Coincidence

We first impose the criterion of temporal coincidence. That is, in order for a given event trigger tobe considered as a candidate gravitational wave we require that there be event triggers in the othertwo interferometers with (almost) the same start time.

Of course, one does not expect exact coincidence between events. Several factors limit theprecision to which the start time of events from different interferometers can be expected to agree.Among these are the difference in arrival times between the interferometer sites (up to 10ms), theinherent timing resolution of the ETGs producing the event triggers (125ms for TFCLUSTERS,3ms for SLOPE), the ringing time of the filters applied to the data, the noise, and the characteristicsof the signal itself. We have determined empirically that at least 99% of simulated Gaussiansignals, when added simultaneously to the data from each interferometer, would be detected withstart times equal to within 50ms by SLOPE and equal to within 500ms by TFCLUSTERS (thisincludes an allowance for the light travel time between the sites). We therefore have adopted thesetimes as the ‘windows’ for considering events to be simultaneous between interferometers.

Coincidence is then imposed as follows: we compare the start times of the event triggers fromeach interferometer, and declare one triple-coincidence event for each triplet of single-interferometerevents for which the maximum difference in start times is less than the window duration (50ms forSLOPE or 500ms for TFCLUSTERS).

Note that a given event from one interferometer may be a member of several triple-coincidencesets; this is accounted for in the ‘clustering’ step which follows.

2.3.2 Clustering

The next step in the multiple-interferometer coincidence analysis is to ‘cluster’ the events fromeach interferometer.

It has been determined through simulations that a single signal will typically produce severalclosely spaced event triggers. Reconstructing the characteristics of the original signal, such as the

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total power, therefore requires combining events which are closely spaced in time. We accomplishthis by grouping together all events from one interferometer separated by less than 0.5sec into asingle ‘cluster’. A frequency range, duration, etc. is assigned to the cluster by combining thecorresponding quantities for the component events in a straightforward manner. This is done forboth SLOPE and TFCLUSTERS event triggers.

2.3.3 Frequency Cut

The next step in the multiple-interferometer coincidence analysis is to require that the individualevents in a triple coincidence share a common frequency range. Since SLOPE does not providea frequency range for the event triggers it produces, this cut is applied to TFCLUSTERS clustersonly. It is required that the intersection of the frequency ranges of the cluster from each interfer-ometer be nonzero. Failing that, they must not be separated by more than 80Hz (ten times thefrequency resolution of TFCLUSTERS).

2.3.4 Amplitude Cut

Another requirement for multiple-interferometer coincidence is that each interferometer measurethe same amplitude or power in the purported gravitational-wave signal. A check based on thisprinciple has yet to be implemented.

2.4 Determination of detection efficiency

The efficacy of our burst search algorithms is established by evaluating the efficiency for findingburst waveforms in the data (as a function of the large parameter space such burst waveformsoccupy), for search algorithm thresholds that yield a tolerable trigger rate in the absence of GWbursts in the data. One important goal of these simulations is to test and compare these searchalgorithms against each other. It is likely that while some algorithms may perform better forsome waveform morphologies, no one algorithm will perform best for all possible (simulated)morphologies. Therefore, we will continue to pursue the analysis using multiple algorithms.

2.4.1 Fidelity of simulation pipeline to data pipeline

Effort was made to ensure that the entire analysis pipeline was the same, in these simulations, as itis with real data. In particular, simulated bursts were injected into the data stream as close to thebeginning of the pipeline as was practical.

2.4.2 Detector response

The detector response to gravitational waves is evaluated by applying small sinusoidal forces tothe end test masses of the interferometers, and observing the response in the gravitational-wavechannel at those applied frequencies. The changes in position of the test masses in response to thesesmall forces is determined through a separate procedure. Before and after the data taking, swept-sine calibrations were performed over the sensitive frequency band of the detector (20 Hz to 4kHz). During data taking, variations in the detector response (due, for example, to gradual changesin the mirror alignments) were monitored by continuous application and monitoring of calibration

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lines, typically at 51.3 Hz and 972.8 Hz. All these elements of the calibration procedure result ina response function which can be parameterized with a simple zero-pole-gain model. Simulatedwaveforms are passed through a linear filter that implements the strain-to-counts response functionas determined by this calibration procedure.

2.4.3 Efficiency of multiple interferometer coincidence

The efficiency of an Event Trigger Generator (ETG) to a particular waveform with peak amplitudeh can be determined by simulation within LDAS. The waveform is added to the raw ( noisy AS Q)data such that it corresponds to optimal response with respect to source direction and polarization.The result is that the efficiency is 0 for very small h, 1 for very large h, and smoothly rising from0 to 1 in between. (This is the efficiency for detection during unvetoed live-time). This turn-on inefficiency is well modeled by a sigmoid in log(h); call it eff(h). It is specific to a given waveform,ETG algorithm, and data epoch. Some examples are shown in XX, as dashed lines for four differentdetectors (one specific waveform and data epoch). (XX get figure)

However, our true detection efficiency depends on the source direction and polarization. Wecan assume that the sources are distributed isotropically, with only one polarization component(we’ll return to this assumption later), which is oriented randomly. In that case, we can easilycalculate the resultant detection efficiency averaged over source directions (q,f) and polarization ythrough the well-known detector antenna function R(q,f,y), as follows: XX insert equation here.

The average efficiency versus h obtained in this way is shown in solid curves for four detectorsin XX. The average value for R(q,f,y) is 0.37.

It is straightforward to generalize this to multiple detector coincidences, by evaluating XXinsert equation here

where a, b, ... label different detectors in coincidence. The ... means that we can add ef-ficiencies for 2, 3, 4, or more detectors in coincidence. We can use Earth-centered co-rotatingcoordinates for the locations and orientations of the different detectors, and for the source direc-tion and polarization. For example, efficiency curves for triple and quadruple coincidences of 4detectors running during S1 are shown in Figure XX.

It must be remembered that these curves must be re-drawn for different waveform morpholo-gies, different ETG algorithms and thresholds, and different data epochs / calibrations.

Note that detailed simulations in LDAS are only required for single detectors, with optimalsource orientation and polarization; the remainder of the averaging over source directions andpolarizations, and coincidence efficiencies, are handled through simple numerical integrations.

However, we have made some crucial assumptions:

� There is no loss of coincidence efficiency due to the time delay between bursts in differ-ent detectors; the coincident time window must be kept large compared with the source-direction-dependent delay times.

� There is no loss of coincidence efficiency due to any post-coincidence cuts, such as requir-ing coherence between the burst waveforms, or their amplitudes or frequency bands, in thedifferent detectors.

� We assume that the burst waveforms come in only one polarization (or, more generally, bothpolarizations have the same waveform, with fixed amplitude ratio). If, contrary-wise, bursts

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have two polarizations with different waveforms, then the resultant excitation of the IFO dif-ferential mode will be some source-direction-dependent combination of the two waveforms.This can only be dealt with by going back to the LDAS simulations; and the parameter spacethat must be explored via those simulations becomes much larger.

2.5 Interpretation

2.5.1 Events from multiple ETGs

The events we interpret here are generated by two different ETGs: SLOPE and TFCluster. Even-tually we hope to establish the relationship between events generated by different ETGs, in whichcase we may find that one ETG may do the job of several, or that different ETGs are senstive toevents of different character, and use that information as part of our analysis to characterize events.We have not done that characterization, however, and for now we treat the events generated byeach ETG separately and report separate limits based on the events generated by each individuallyand without respect to the events generated by the other.

2.5.2 Excess events

This straightforward interpretation asks only whether the number of observed events is consistentwith the number of events expected owing to background. Estimation of the expected number ofbackground events is described in section 3.3.6.

2.5.3 Distribution analysis

The background estimation analysis described in section 2.5.2 also yields the amplitude distribu-tion of the background events. If there are a sufficient number of events at zero time-delay thenwe can ask whether the distribution at zero time-delay is the same or different than the backgrounddistribution. This question can be addressed by a �2 test or by a Kolmogorov-Smirnov test [?].

2.5.4 Model-dependent analyses

For the remainder of section 2.5 we will focus on interpretations in terms of a model. In this sub-section we set-out the methodology for interpreting our data in terms of a model; in the subsectionsthat follow we describe different models that we have used or are planning to use to characterizeour observations.

Let PB(h) be the probability (relative frequency) of observing a background event with ampli-tude h. This distribution is one we estimate from analysis of time-delay analysis of our data.

Let PF (hjh0; �; I) be the distribution of observed events that arise from gravitational waveevents generated by a source model characterized by, e.g., a space density of sources �(r;) anda source amplitude scale parameter h0, and perhaps other assumptions I . For a concrete example,� may reflect a galactic source distribution model, the radiation pattern (i.e., the fraction of theradiated power into a given solid angle) may follow some fixed model, and the overall sourceluminosity follow a luminosity function known up to a scale determined by h0.

Background events, regardless of amplitude, events occur at some rate _NB; foreground (grav-itational wave events) occur at some rate _NF . The probability of observing a particular event of

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amplitude h is thus

P (hjh0; �; _NB; _NF ; I) = aPB(h) + (1� a)PF (hjh0; �; I) (1)

where

a :=_NB

_NB + _NF

: (2)

Without loss of generality write P (hjh0; a; I) for P (hjh0; �; _NB; _NF ; I), where we understand I

to represent all those aspects of the model and data (e.g., the background rate _NB) that are knownor fixed. From P (hjh0; a; I) we can write the likelihood function �(Hjh0; a) for a data set Hconsisting of N events hk

H := fhkjk = 1 : : : Ng (3)

�(Hjh0; a) =NYk=1

P (hkjh0; a; I): (4)

We desire to determine, from the observations, point estimates, confidence intervals or upperlimits on _NF (or, alternatively, a), and h0. We can determine any or all of these from the likelihoodfunction:

� The point estimate for (h0; a) is the (h0; a) pair that maximizes the likelihood function;

� A confidence interval or upper limit on a and h0 can be found by the usual Neyman-Pearsonconstruction.

The rate we determine in this way, (1 � a) _NB , is the rate of observed gravitational waveevents. To translate this into a statement about the intrinsic event rate we will need to divide bythe efficiency with which we detect sources from the model. This efficiency is determined throughsimulation.

[[WHAT MORE IS NEEDED HERE? A DISCUSSION OF GOODNESS OF FIT: I.E., WEMAY DETERMINE PARAMETERS THAT BEST FIT THE MODEL TO THE DATA, BUTTHAT DOESN’T MEAN THAT THE FIT IS CREDIBLE.]]

2.5.5 Babylonian analysis

In the Babyonian analysis we assume that all sources are distributed uniformly on a sphere at aconstant distance from Earth. Each source is linearly polarized and the distribution of polarizationangles associated with the ensemble of bursts incident from any direction is uniform in angle.Lastly we assume that each burst has an identical “waveform” that we take to be a Gaussian pulse:

hij = h0e�(t�t0)2=2�2ep (5)

where ep is the polarization tensor associated with the waveform and � is the timescale of thepulse.1

1None of our ETGs depend on or presuppose a particular waveform: two of our ETGs depend only on the powerin a band or tile in the time-frequency plane, a third identifies as events epochs with large trends in the level of thegravitational wave channel over short (i.e., ms scale) time periods in a particular band, and a fourth ETG searches forevents by looking for changes in the mean amplitude or variance in a particular band. Eventually we hope to be ableto characterize these events in terms more appropriate to what they measure (e.g., rms signal amplitude in a band).This type of characterization would be more faithful to the broadband nature of interferometric detectors. For now,however, we adopt the simpler, if overly coarse, characterization of events in terms of a specific waveform model.

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2.5.6 Astrophysical analysis

This section is a place-holder for post-November 1 analysis work.

3 Methods

3.1 Overview

3.1.1 Playground vs. production

3.1.2 Iterative nature of the process

3.2 Preliminary studies: veto channel candidates

During S1, we made various estimates of the rate of large transients in the AS Q channel. A glitch-finding DMT monitor, Zglitch, reported each Xxminute? the number of transients exceeding 4sigma. The rate of such excursions was gratifyingly low, not much different than expected bychance. We also looked at histograms of the AS Q channel, which showed a few transients, butnot so many as to be very worrisome.

Also during the run, the AS Q channel from each interferometer was examined for cross-correlation (in the wavelet domain) with a list of diagnostic channels, using a DMT monitor calledWaveMon (written by Sergey Klimenko.) In each interferometer, there were channels exhibitedcorrelations with AS Q at levels substantially greater than chance.

[XX Table here from Sergeys report?]These channels, and others, were examined by hand in a second investigation. Spectrograms

were constructed for segments of data selected from the S1 playground. In a few of these spectro-grams, strong glitches were easily recognizable as brief broad-band features. We then examinedspectrograms (for the same intervals of time) of a list of other interferometer signals. For L1, spec-trograms of AS I showed an excellent match with those of AS Q. (XX also, channels with poorermatch?) For H2, REFL Is pattern of glitches was a good match to those from AS Q.

Note that there is not very good agreement between the candidate veto signals suggested bythese two methods. This may not be all that surprising, since the spectrogram method was appliedonly to very large glitches, while WaveMon reports correlations that are dominated by small fluc-tuations. We took both kinds of suggestions as input into the construction of our actual vetoes,which were based on diagnostic triggers generated by glitchMon.

In order to convert an upper limit on event rates into an interpreted upper limit on the rate ofarrival of gravitational waves, we need to determine the efficiency of our entire interferometer-plus-analysis-chain to signals of various strengths. We do this separately for each waveform forwhich we want to quote an upper limit. In this report, we give results for pure Gaussian impulses ofvarious time constants (XX give list) and for Gaussian-modulated sinusoids of various frequencies(with a fixed Q = 9.)

The first part of this process makes use of the calibration of each interferometers response func-tion, as measured by the Calibration Group. (XX name?) The response function is used as a filter,to produce a digital time series (in ADC counts) to represent the response of the interferometer toan incident gravitational wave of a given waveform and strength arriving from the zenith.

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Once this model input signal has been generated, we add copies of it to (playground) data fromeach interferometer, and determine what fraction of each of the sets of signals (as a function ofsignal amplitude) are detected at the end of the analysis chain, all the way through to recognitionof a coincidence. XX awk The efficiency versus strength curve will have the form of a sigmoid.(See the example in Figure XX.)

Only waves arriving from the zenith will produce the nominal response from the interferom-eter; waves that arrive from other angles cause smaller responses. Since our upper limit will beexpressed in terms of waves of a given strain amplitude arriving from all over the sky, we needto convolve the nominal efficiency curve with a function representing effect of the interferometersantenna pattern. Carrying out that convolution (XX display the integral?) yields an efficiency thatlooks like the example shown in Figure XX.

One imperfection of the S1 data causes an additional complication in establishing the efficiency.The interferometer calibration was not steady, but varied by more than a factor of two, over a widerange of time scales. We have not developed a method to remove this effect from the data. Rather,we calibrate our search conservatively, and quote our result as if the sensitivity were always at thepoorest end of the data that we use.

3.3 Preliminary studies: event trigger generators

3.3.1 Overview

The initial investigations of the event trigger generators began with the establishment of runningparameters for each generator that lead to a single interferometer event rate of approximately 1 Hzover the playground data set.

Once these event rates are determined, coincidences between events generated in differentinterferometers are determined, using a simple coincidence criteria.

3.3.2 Setting event trigger generator thresholds

We set the thresholds for our ETGs empirically, by searching for the level that allowed us to set thebest upper limit. Too high a threshold needlessly decreases efficiency; too low a threshold leads totoo high a false-alarm rate, without a compensating increase in efficiency.

First, consider the case of the slope ETG. Figures XX – XX (from http://emvogil-3.mit.edu/ cado-nati/S1/slopeThreshold/slopeThreshold.html) illustrates the optimization. The threshold tuningwas carried out on software-injected signals near the optimum sensitivity of the slope ETG: sine-Gaussians (with Q 9) with central frequency near 550 Hz. The range of injected amplitudes thatwas studied were chosen to span the range over which the efficiency (for three-interferometer co-incidences) makes its steep transition from low to high values. Holding the threshold at H2 fixed(XX Laura, why?), we varied first the L1 threshold and then the H1 threshold. A clear, if broad,optimum is apparent for each threshold.

The case of TFCLUSTER is a bit more complicated, because it has several thresholds. The firstone is the so-called black-pixel probability, which determines whether a pixel in the time-frequencyplane has enough power to qualify for membership in a cluster. Our initial investigations showedthat the efficiency to weak signals could be improved by lowering the black pixel probability belowits original value. The second threshold in the TFCLUSTER ETG is set on the total power in a clus-ter. Figures XX XX (from http://emvogil-3.mit.edu/ cadonati/S1/thresholds/tfclusterThreshold.html)

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Table 1:

Universal attributest0 Start timeÆt DurationA Amplitude

TFCluster specific attributesf0 Cluster central frequencyÆf Cluster bandwidth

SLOPE specific attributes

POWER specific attributes

BlockNormal specific attributes�

show the upper limits that can be set on several model signals, as a function of this latter threshold.As in the case of the slope threshold, a optimum is easy to recognize.

3.3.3 Calibration

The detector response to gravitational waves is evaluated by applying small sinusoidal forces tothe end test masses of the interferometers, and observing the response in the gravitational-wavechannel at those applied frequencies. The changes in position of the test masses in response to thesesmall forces is determined through a separate procedure. Before and after the data taking, swept-sine calibrations were performed over the sensitive frequency band of the detector (20 Hz to 4kHz). During data taking, variations in the detector response (due, for example, to gradual changesin the mirror alignments) were monitored by continuous application and monitoring of calibrationlines, typically at 51.3 Hz and 972.8 Hz. All these elements of the calibration procedure result ina response function which can be parameterized with a simple zero-pole-gain model. Simulatedwaveforms are passed through a linear filter that implements the strain-to-counts response functionas determined by this calibration procedure.

3.3.4 Multi-interferometer coincidence: Sam

Each event trigger is associated with certain attributes. At a minimum these include a start time,a duration, and an amplitude. An ETG may endow events with other attributes as well. (Table 1describes the nomenclature we use to refer to event attributes.) The coincidence step in the dataprocessing pipeline the attributes of events in different interferometers and identifies sets of events,one from each interferometer, whose attributes are identical to within a given tolerance.

Start time.

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Duration.

Amplitude. Before being compared in vent amplitudes are calibrated to an absolute strain. Thestrain amplitudes are compared among the different interferometers and are required to be equal,to within a given tolerance, for coincident events.

Since ETG events are very low-dimensional representations of the complex timeseries associ-ated with a real gravitational wave signal, this calibration is model dependent. The strain ampli-tude calibration is carried out by simulating, in software, events from a particular model of a givenstrain amplitude in interferometer k and determining the distribution Pk(Ajh0) of event amplitudesas identified by the ETGs.

From the distribution we choose an amplitude window �A and require that the differencesbetween the Ak

As implemented to date the event amplitude coincidence cut : : :The distribution of event amplitudes is expected to narrow as the strain h0 of the simulated event

increases. In a more subtle analysis this would be taken into account by making the amplitude morestringent for stronger events. This we have not yet done.

3.3.5 Efficiency estimation: Sam

The time-history of the instrument noise level and instrument calibration are critical elements inany analysis seeking to bound the intrinsic rate of gravitational wave events. As either varies therate of background events varies will also vary with time and, similarly, the efficiency of the de-tector system to gravitational wave events will also vary, independently. These variations haveimportant repercussions in the analysis; fortunately, however, for the analyses we undertake herethe proper treatment does not lead to insurmountable difficulties, but requires only care in simula-tions and background estimation. We describe that care here.

The expected rate of gravitational wave bursts of amplitude h depends on the source rate den-sity, intrinsic luminosity and its variability, polarization, and the incident angle of the radiationon the detector. Write the number density of sources at a distance r in the direction as �(r;)and the expected distribution of event amplitudes h (measured in the detector) corresponding to aburst arriving from a distance r in the direction as P (hjr;). (This quantity is a convolutionof the intrinsic luminosity and variability, polarization, and incident angle of the radiation on thedetector.) The expected distribution of gravitational wave events with amplitude h is then

P (hj�; �) =1

N

dN

dh(6)

N =

Zdh

dN

dh(7)

dN

dh= �(h)

Z1

0

dr

ZS2

d2 �(r;)

Z1

0

dhP (hjr;) (8)

If the detector noise level and/or calibration are changing with time, then � is also a function oftime and

dN

dh=

�1

T

Z T

0

dt �(h; t)

�Z1

0

dr

ZS2

d2 �(r;)

Z1

0

dhP (hjr;) ; (9)

page 17 of 36

The efficiency that appears in determining the total event rate or its distribution in amplitude is thetime-averaged efficiency. The time averaged efficiency is readily calculated by software injectionof events into the data stream, using either the entire data stream or a subset whose noise level andcalibration distribution is in proportion to the whole. While it is computationally more intense thatdealing with a stationary detector this is not an insurmountable challenge for the analysis.

3.3.6 Background estimation: Sam

Given an ETG and a detector whose noise statistics and/or calibration varies with time there will bean instantaneous rate of background events _�(t). Over an observation of duration T the expectednumber of background events is

� =

Z T

0

dt _�(t): (10)

Given an ensemble of identical detectors (i.e., identical noise levels and calibrations as a functionof time), the ensemble of observations of the actual number of background events will be Poissondistributed with Poisson parameter �. (Note that this is Poisson in the ensemble sense and doesnot refer to the distribution of events in time.) Following [3] we then determine whether theactual number of observed events is consistent with the expected number owing to background.Performing this analysis reduces to determining the background rate �.

To determine � we introduce a time-delay into the coincidence step of the analysis: i.e., wesearch for sets of events that meet all of the coincidence criteria set-out in section 3.3.4 except thatthe start-time of the events are required to be so separated in time that they could not have arisenfrom a gravitational wave burst. This bounds the time-delay from below. The time delays arebounded from above by the requirement that they are short compared to the timescale over whichthe calibrations or noise levels change. If we repeat this time-delay coincidence for many differenttime-delays then the mean number of time-delay coincident events will be equal to the �: i.e., wecalculate � directly and without the need to calculate _�(t).

[[NEED TO DISCUSS ERRORS IN BACKGROUND DETERMINATION. QUESTION: TOWHAT EXTENT ARE TIME SHIFTS INDEPENDENT EXPERIMENTS FOR THE PURPOSEOF ESTIMATING ERRORS IN BACKGROUND RATE]]

3.4 Veto channel selections and tuning

The basic method of veto channel selection was to look for channels that produced glitchMontriggers that were often in coincidence with event triggers from the AS Q channel. A useful vetois one that explains many AS Q triggers (in the sense of justifying their removal from the list ofgravity wave candidates), while causing only a small loss of livetime from accidental overlaps.Veto selection was performed on data in the playground set only.

The channels that were examined are those listed in Table 1 XX. GlitchMon filtered each witha 30 Hz high pass filter. Glitches that were found in the filtered time series were recorded withamplitude, start time, and duration, for later comparison with a list of event triggers generated byTFCLUSTER.

To evaluate the success of a candidate veto, we made a plot of the efficiency of the veto (frac-tion of event triggers in coincidence) versus the deadtime produced by application of the veto, asparametrized by a threshold on the glitchMon amplitude. Figure XX shows one such graph. A

page 18 of 36

Table 2: The following channels (same for all 3 interferometers) were included in the first surveyof Veto channels. The ones marked with + made it into the final selection. The ones with * werefinally selected as best ones. (No veto was used for H2.)

Channel L1 H1 H2

LSC-AS I +LSC-REFL Q + +LSC-REFL I * +LSC-POB QLSC-POB I + +LSC-MICH CTRLLSC-PRC CTRL + +LSC-MC LLSC-AS DC *LSC-REFL DCIOO-MC FIOO-MC LPSL-FSS RCTRANSPD FPSL-PMC TRANSPD F

candidate veto with no utility will only overlap event triggers by chance, and so its points will lieon or near the y = x line in such a graph. A successful veto is one that more nearly hugs the y axis.

For a channel that shows promise on such a graph (such as AS DC at L1), the remaining stepis to choose a threshold. The method we used was to examine, for a variety of thresholds, the ratiobetween the efficiency of the veto to the background efficiency, as determined from a “lag plot”in which coincidences between the veto and AS Q are made at many different artificial time lagsbetween veto time and event trigger time. The method is illustrated in Figures XX and XX. Athreshold of 21 is favored for L1:LSC-AS DC, and of 11.6 for H1:LSC-REFL I; these have thebest ratio of true efficiency to background efficiency.

Not surprisingly, the efficacy of a veto depends also on the threshold used to produce the listof event triggers. (If the event trigger threshold is set low enough, the list contains mostly eventsdue to the statistical variation of AS Q itself.) The S1 data had a low enough density of glitchesthat, in order to recognize a useful veto, we had to use an event trigger list that consisted only ofthe largest events. (XX Add a sentence to more specifically describe the choice.)

Figures XX through XX show the results of this process for the three LIGO interferometers inS1. For L1, we chose AS DC, and for .XX For HXX, we found no channel that gave a useful veto.

How do we decide if we need vetoes at all? If vetoable events were rare enough, the one couldimagine trusting that the coincidence step would reduce the number of accidental gravity wavecandidates to an acceptable level all by itself. In the S1 case, though, we clearly gain by the vetoon HXX, which reduces the singles rate by about a factor of two, with only a negligible (XX%)reduction in livetime.

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Deadtime fraction0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Vet

o E

ffic

ien

cy

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

L1:LSC-AS_DC playground without segment 10

L1:LSC-AS_I playground without segment 10

L1:LSC-AS_DC whole playground

L1:LSC-AS_I whole playground

L1:LSC-AS_DC playground only segment 10

L1:LSC-AS_I playground only segment 10































Figure 1: Efficiency vs deadtime curves for L1:LSC-AS DC and L1:LSC-AS I. The veto ismost effective on the loud segment 10, but also does a reasonable job on the whole playground.Also L1:LSC-AS DC does a better job that L1:LSC-AS I.

3.5 Final veto and event trigger generator tuning

3.6 Diagnostic trigger generator filter tuning

Based on earlier experience we by default used a 30Hz, 4th order butterworth high pass filter forthe pre-filtering in glitchMon. To check whether this filter is adequate we also ran a 100Hz and a300Hz high pass filter, both 4th order butterworth, over the playground segments. The differencebetween 30Hz and 100Hz was neglectable. The 500Hz is performing significantly worse.

3.7 Veto trigger tuning for L1

A preliminary study of all 14 channels listed in table 2 did not show strong correlations. Follow-ing hints from hand-scanning spectrograms we then focused on the loudest playground segment(No.10, GPS 715087222, 649sec) for the further tuning.

Based on figure 1 we chose L1:LSC-AS DC as our prime veto channel. To be able to pick agood threshold we plotted the veto efficiency as a function of an artificial time shift (figure 2). Wepicked threshold 21 for which we get the clearest peak (biggest difference between peak and tail)at shift 0. This is a very conservative choice since we only get a deadtime on the order of 1%, butwe still get rid of roughly 40% of the event triggers (see figure 1).

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lag (s)-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

frac

tio

n o

f ve

toed

eve

nts

10-1

1

Threshold6.308.4012.6014.7016.8021.00

Veto Lag Plot at L1:LSC-AS_DC 30HzHP

Figure 2: L1:LSC-AS DC Veto Efficiency vs. time-shift. The peak in the veto efficiency at 0shift is clearest for threshold 21. Also note the 2nd bump around roughly 0.7 sec suggesting aperiodicity of the triggers. This has already been observed in E7.

3.8 Veto trigger tuning for H1

The main feature of H1 was a huge glitch roughly every 20min. We tried to find a veto channel thatefficiently gets rid of those big transients. H1:LSC-REFL I turned out to be the best choice. Figure3 is a veto efficiency vs. deadtime plot for H1:LSC-REFL I, comparing against TFCLUSTERtriggers after a power cut. Clearly the veto is most effective in getting rid of the bigest glitches.

Figure 4 shows 2 plots of the H1:LSC-REFL I veto efficiency for different artificial time shiftsbetween the 2 trigger streams. (a) uses a TFCLUSTER POWER > 15 cut. The peak at 0 is hiddenin the background. (We emphasize an increased detection efficiency - see paragraph 3.10). (b)however shows that the peak repears for higher TFCLUSTER POWER cuts.

The decision for the final threshold of 11.6 ADC counts was mostly guided by figure 3. It al-lows rejection 98% of the glitches bigger than POWER=500 while only loosing 4% of the livetime.Also this threshold gives the biggest difference between Veto Efficiency and accidental rate (peak- tail) in figure 4(a).

3.9 No Veto used for H2

We tried to find a veto for H2 following much the same scheme as for H1. However, H2 didn’tshow any particularly bad typical glitches (at least not in the 13 playground segments). Thereforethe veto efficiency vs. deadtime plots for all potential channels (see table 2) all were consistentwith random coincidence with AS Q. We ended up using no veto for H2.

3.10 Event trigger generator threshold tuning: TFCLUSTER

There are two kinds of threshold we can tune for tfcluster:

� the black pixel probability p,that is the probability that a pixel is black in absence of a signal. This number affects therate of events produced by tfcluster and in general we want it to be small. It is specified inthe LDAS job filterparams, thus it needs to be decided before processing the data. We can

page 21 of 36

Deadtime fraction0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Vet

o E

ffic

ien

cy

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

H1: No TFCLUSTER thresholdH1: TFCLUSTER POWER > 10H1: TFCLUSTER POWER > 50H1: TFCLUSTER POWER > 100H1: TFCLUSTER POWER > 500





Figure 3: Effect of a H1:LSC-REFL I veto of TFCLUSTER triggers with different POWER cuts.It clearly takes out the loudest glitches. The threshold finally chosen (11.6) corresponds to thesecond dots from the left (� 4% deadtime).

lag (s)-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

frac

tio

n o

f ve

toed

eve

nts

10-1

1

Threshold4.355.808.7010.1511.6014.50

Veto Lag Plot at H1:LSC-REFL_I 30HzHP

lag (s)-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

frac

tio

n o

f ve

toed

eve

nts

10-1

1

Threshold4.355.808.7010.1511.6014.50

Veto Lag Plot at H1:LSC-REFL_I 30HzHP

(a) (b)

Figure 4: H1:LSC-REFL I Veto Efficiency vs. time-shift(a) Veto Efficiency vs. time-shift for a TFCLUSTER POWER >15 cut. The peak at 0 lag is hiddenin the high background.(b) Veto Efficiency vs. time-shift for a TFCLUSTER POWER >500 cut.

page 22 of 36

(a) (b)

Figure 5: Dependency of the upper limit on the power threshold.Estimated upper limit vs. tfcluster power threshold(a): 1ms gaussians; (b): 554 Hz sine gaussiansA tfcluster power threshold of 15 is recommended.

think of p as a relative threshold, a measure of how much the power in a pixel needs to stickout of the background in order for it to be black. We used the following values:

L1 H1 H2p rate p rate p rate comment

0.022 0.94Hz 0.050 1.01Hz 0.026 1.01Hz values chosen to set thefake rate at 1 Hzover the playground

� threshold on the absolute power in a cluster of pixels:this is a post-processing cut for single event triggers. Ideally one would make this a frequency-dependent cut, but we will, in this context, use a frequency-independent cut and tune it withthe help of signal additions (software injections).

3.10.1 Tuning the threshold on the absolute power in a cluster of black pixels

For two of the typical waveforms (1 ms gaussians, 554 Hz sine gaussians) we plotted the upperlimit vs. the power threshold (see figure 5). The upper limit is estimated as

ULestim =2:44 +

pb

LiveT ime� efficiency(11)

where b is the number of events (in absence of simulations) detected in triple coincidence atthe end of the pipeline. 2.44 is, in the Feldman-Cousins approach, the 90% upper limit that can beset for b=0, n=0.

Form figure 5 we concluded that a power threshold of 15 should give the best final results.

page 23 of 36

(a) (b)

Figure 6: Dependency of the upper limit on the amplitude threshold.(a) Varying the L1 threshold for fixed H1 and H2 threshold.(b) Varying the H1 threshold for fixed L1 and H2 threshold.

3.11 Event trigger generator threshold tuning: slope

Again the main hint on how to tune the slope threshold came form simulations.The slope filterparams were chosen in order to have maximum sensitivity at around 400 Hz

(slope calculated over 10 sampling points = 0.6 ms). For this reason the performance on 1 msgaussians is not as good as for tfcluster. The sine gaussians allow to analyze different frequenciesseparately, so we chose to perform this study over the 554 Hz sine gaussians.

Following the procedure used for tfcluster we now calculated the remaining numer of eventsafter triple coincidence and the detection efficiency sigmoid for different choises of thresholds.

First we noticed that once the L1 and H1 thresholds are tuned, there is nothing to gain byincreasing the H2 threshold (no changes in the background, only reduced efficiency). This isconsistent with a very broad amplitude spectrogram for H2. We therefore left H2 on the lowthreshold of 12800 initially chosen to get managable trigger rates.

The plots in figure 6 show a dependence of the upper limit for each signal intensity as a functionof the threshold at one site, with the other two fixed. The upper limit is estimated as

ULestim =2:44 +

pb

T ime� efficiency(12)

where b is the number of events (in absence of simulations) detected in triple coincidence atthe end of the pipeline. 2.44 is, in the Feldman-Cousin approach, the 90% upper limit that can beset for b=0, n=0.

Based on figure 6 we chose the following amplitude thresholds:

L1: 6000 (3.6 �)H1: 10000 (3.4 �)H2: 12800 (3.0 �)

page 24 of 36

3.12 The playground results

TFCLUSTER L1 H1 H2

Singles produced by tfcluster 28882 27019 29274reject events with Fmin>3000Hz 14606 18690 12080reject events with Fmax<100Hz 12901 11297 7746reject events with Power<15 4824 5521 6197Apply veto 3006 3994 5364

SLOPE L1 H1 H2

Singles produced by slope 1208 12690 51654Apply veto 416 12005 50946

triple coincidences TFCLUSTER TFCLUSTER w/ veto SLOPE SLOPE w/ veto

Live Time (seconds) 30240 29128 30240 29128Triple coincidences 91 38 0 0(no clustering)clustered 41 27 0 0frequency match cut 0 0 0 0background 1.64 +/- 0.01 0.61 +/- 0.01 0.18 +/- 0.004 0.03 +/- 0.00190% upper limit(Feldman Cousins) 1.31 1.87 2.26 2.41on # events90% upper limit(Feldman Cousins) 0.043 0.064 0.075 0.083on the rate (mHz)

4 Results: unknown source search

4.1 Epoch Veto results

Table 3: Epoch veto cuts used in the analysis so far performed. Starting point are the band limitedRMS in figure 7 (360 sec averages). The cuts are proportional to �, the 68-percentile in thedistribution of BLRMS for each band and each interferometer.

Band cut criterion L1 H1 H2320 - 400 Hz 10� 0.0050 0.0350 0.0050400 - 600 Hz 3� 0.0075 0.0345 0.022560 - 1600 Hz 3� 0.0135 0.0675 0.1065

1600 - 3000 Hz 3� 0.0075 0.0885 0.0825

The epoch veto used in this analysis was described in section XXXX2. Figure 7 shows the band

2section 2.2.2 of the initial draft refers to a table with the parameters - I am including here table 3 with the detailsof the cut - the table could be placed here OR in section 2.2.2, but needs cross referencing

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limited RMS (averaged over 360 seconds) at the three interferometers in the triple coincidencesegments, during S1. The vertical lines mark playground segments, the horizontal lines (two oneach figure) mark the cut used for the two higher frequency bands: 600-1600 Hz and 1600-3000Hz.

The epoch veto affects two playground segments: number 1 and 8. Playground segment 1 wassingled out earlier on as a single-occurrence outlier in the 320-400 Hz band and thus excludedfrom the tuning studies. Playground segment 8 was included in the playground tuning, however,the 600-1600Hz BLRMS at H2 was barely above threshold in a 360 sec period out of 3240 sec, soit was not deemed necessary to repeat the playground tuning without segment 8.

Table 4: Effect of epoch veto and single interferometer veto on the single rate from TFCLSUTERand SLOPE. For each ETG, the first column gives total time and event numbers, the second columnreports the same quantities after the epoch veto is applied and the third column lists the vetoefficiency.

TFCLUSTER SLOPEall data epoch veto effect all data epoch veto effect

Total time (s) 322200.0 223560.0 30.6% 322200.0 223560.0 30.6%Live time (s) 320706.8 222705.1 30.6% 320706.8 222705.1 30.6%Dead time frac. 0.46% 0.38% 0.46% 0.38%L1 no veto 46058 28474 38.2% 23406 3916 83.2%L1 AS DC veto 33883 24417 27.9% 7399 2854 61.4%L1 veto efficiency 26.3% 14.2% 68.4% 27.1%H1 no veto 63582 42612 33.0% 2427980 134628 94.5%H1 REFL I veto 56447 38046 32.6% 2418357 133561 94.5%H1 veto efficiency 11.2% 10.7% 0.4% 0.8%H2 no veto 88026 50577 42.5% 1051035 149746 85.7%

Table 4 reports the number of events detected by TFCLUSTER and SLOPE at each site, withand without application of the epoch veto. The epoch veto causes a 30% live time loss.

The number of TFCLUSTER triggers is reduced by about the same fraction; the shape changeof the single interferometer power histogram can be seen in figure 8-a, while figures 9, 10 and 11show the combined effect of epoch and single-IFO veto on the TFCLUSTER power versus timeand rate versus time distributions. The epoch veto singles out segments with large rate, while thesingle interferometer is effective at eliminating the larger power events, especially at H1.

The epoch veto has a remarkable effect on the SLOPE event rate: being an absolute thresholdsearch algorithm, SLOPE is particularly sensitive to the high frequency RMS fluctuations at H1and H2. The epoch veto rules out the loudest segments, thus reducing the singles rate by 95% atH1 and 86% at H2.

4.2 Sanity checks

The histograms of power (TFCLUSTER) and amplitude (SLOPE) at the different stages of theveto procedure are shown in figure 8, where we also show the corresponding histogram in the

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Figure 7: Band limited RMS at L1, H1 and H2 in the S1 triple coincidence segments. Each datapoint is an average over 360 seconds. The vertical lines (magenta) mark the playground segments.The horizontal lines mark the cut used for the 600-1600 Hz band (green) and for the 1600-3000Hz band (blue).

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Figure 8: Histogram of single event power (TFCLUSTER) or amplitude (SLOPE) at each interfer-ometer after application of the epoch veto and the diagnostic veto. The playground histogram isshown in green.

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playground. These histograms, combined with the observations on the epoch veto in the previousparagraph, suggest the playground was representative of the post-epoch veto set. It included oneanomaly (playground segment 1) but not the very loud segments at H1, which were unveiled onlyin the extension to the full data set. Other than this, the playground tuning proved valid for thewhole set.

The distribution of TFCLUSTER power and rate of events versus time is shown in figure 9 forL1, 10 for H1 and 11 for H2. In all cases, we show in black the complete S1 triple coincidence dataset, in red the data that is actually used, after the epoch veto and the single interferometer veto. Therate versus time plots show how effective the epoch veto actually is at removing loud segments.

Figures 12-a,b are distribution of the delay between consecutive events, at each interferometerand for the two ETGs. These distributions present a structure at about 3 sec for L1 and 4 sec forH1, a pathology that was brought to the attention of the commissioning team.

Figure 13 shows distributions of central frequency and duration for the final (post veto) sets oftfcluster data at each interferometer. The frequency histograms are particularly interesting, withstructures below 500 Hz at L1 and H1 and a set of 3 peaks up to 700 Hz at H2. These plots suggestwe can do a better job in pre-conditioning the data before applying the ETGs: this study is alreadyin progress and is targeted for a post “Nov. 1” analysis.

4.3 Background estimates

We followed the procedure outlined in Section 3.3.5, above. The background is calculated byshifting the L1 and H2 time series respect to the H1 time series, then applying all post-coincidencecuts in the same manner as if we were looking at the actual (zero time-shift) search. The shifts usedwere: -5, -4, -3, -2, 2, 3, 4, and 5 sec, with the additional requirement: abs(L1shift - H2shift)¿=2sec. In all, we used 44 points in the background calculation. (XX number of points is beingaugmented now.)

Figure XX shows the histogram of background estimates from this set of time-shift trials, forboth TFCLUSTER and slope. The mean background for TFCLUSTER was 14.25 events, while for

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Figure 13: TFCLUSTER: Central frequency and duration histograms, before and after applicationof the single-IFO veto (L1:LSC-AS DC, H1:LSC-REFL I)

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slope it was 1.30 events. (XX Figures are: http://emvogil-3.mit.edu/ cadonati/S1/final/figures/tfcluster10V-backgroundHisto-FrequencyCut.gif, and the equivalent one for slope when it is produced.)

There is some reason to worry that our background estimates are biased because we use thesame data set (the full S1 data) to estimate both the background and the foreground. One mightalso worry that the variance among the different background trials would not be the same as ifthose trials were done on independent data sets. We have carried out numerical experiments tocheck these worries, and find that these effects, while real, are small. For the properties of the S1analysis, we expect that we have made a truly negligible mistake in the background level, but thatour estimate variance is too large by a factor of XX. (XX Julien to supply this number or fix thisparagraph.)

4.4 Event rate bound

As described in Section 2.4.2 above, we set an upper limit on the coincident event rate using themethod of Feldman and Cousins [XX ref]. (XX At this stage of the draft, 2.4.2 doesn’t yet describethe F-C technique.) The necessary inputs are the background estimates (from Section 4.3) and theactual observed (”zero-lag”) number of coincidences. With our chosen epoch veto, individualinterferometer veto, and coincidence tests, we found 9 coincidences in the TFCLUSTER analysis,and 2 coincidences using slope.

Using the Feldman-Cousins technique, we set a 95% confidence upper limit on the expectednumber of coincidences of XX for TFCLUSTER, and XX for slope.

More interesting is the upper limit we can set on the rate of events. This is obtained by dividingthe coincidence number upper limit by the live time of our observation. Our S1 analysis had alive time of XX seconds. (XX Note that this time is shorter than the 222705 sec given in Laura’stable at http://emvogil-3.mit.edu/ cadonati/S1/final/S1results.html, since that accounts only for theepoch veto, but not for the deadtime from the individual vetoes. XX? Also, when we add in theindividual veto effect, how careful do we need to be about accounting for total ”footprint” of veto,as opposed to the simple sum of the duration of the veto intervals?) Thus, we set a 95% confidenceupper limit on event rate of XX using TFCLUSTER, and XX using slope.

4.5 Interpreted bound

To go from an event rate upper limit to a limit on the rate of arrival of gravitational wave bursts,we need efficiencies to gravitational waves of various waveforms, as a function of strength. Themethod for determining the efficiency is described in Section 3.3.2 and 3.3.4 above. (XX We’vegot Sam’s treatment in 3.3.4, and a blend of Peter and Alan discussing procedures in 3.3.2.)

For the results listed here, efficiency was estimated by adding signals into the playground dataonly. (Before we submit a paper, we intend to replace those estimates by ones made over the wholeS1 data set.) We give results for two classes of waveforms. The first are pure Gaussian bursts ofthe form h(t) = h0 � exp(�(t�0:5)

2=�2), with � = 0.001 and 0.0025 sec. The second class weresine-Gaussian bursts of the form h(t) = h0 � sin(2�f0t)e�(t�t0)2=�2 , with f0 � � = 2, correspondingto a Q 9. Figure XX shows examples of each of these two waveforms.

As outlined in Section 3.3.2, the first step in the efficiency estimation was the determinationof efficiency of each interferometer to each waveform, injected as if arriving from the zenith withoptimal polarization. For this step, we adopted the nominal calibration factors determined by

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the Calibration Group, without correction for the variation of calibration between lock segments.(Before submitting a paper, we intend to replace these results with ones that make use of segment-by-segment calibration.) Figures XX-XX show these curves.

Each of these curves is then converted to an efficiency for detection of signals averaged over anisotropic distribution on the sky and averaged over all (linear) polarization angles. Those curvesare shown in Figure XX - XX. (XX How many of these do we want to show?) Finally, we computethe coincidence efficiency for the set of 3 LIGO interferometers. The results for each waveformare shown in Figures XX - XX.

XX next, need paragraph(s) describing conversion of efficiency graphs into rate-strength upperlimits.

5 Discussion: Unknown source search results

6 Gravitational waves associated with GRBs

7 Discussion: Gravitational waves associated with GRBs

8 Conclusions

In this section we summarize our progress to date in reaching the goals set-out immediately fol-lowing the end of the S1 data taking [1].

8.1 Search for gravitational wave bursts of unknown origin

The specific result is a bound on the rate of detected gravitational wave bursts, viewed as origi-nating from fixed strength sources on a fixed distance sphere centered about Earth, expressed as aregion in a rate v. strength diagram.

8.2 Search for gravitational wave bursts associated with gamma-ray bursts

The result of this search is a bound on the strength of gravitational waves associated with gamma-ray bursts.

8.3 Integration of GEO and LIGO data in a single analysis

The specific result is the demonstrated ability to run GEO and LIGO data through equivalent dataprocessing pipelines, up to and through the construction of temporal coincidences.

References

[1] Lee Samuel Finn. S1 analysis goals: Burst analysis working group. Laser InterferometerGravitational Wave Observatory Document Control Center LIGO-G020419-Z, 2002. Internalworking note of the LIGO Laboratory.

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[2] N. Arnaud et al.. XX. Phys. Rev. D, 59, 082002, (1999).

[3] Gary J. Feldman and Robert D. Cousins. Unified approach to the classical statistical analysisof small signals. Phys. Rev. D, 57(7):3873–3889, 1 April 1998.

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