LASER INTERFEROMETER GRAVITATIONAL WAVE OBSERVATORY
- LIGO CALIFORNIA INSTITUTE OF TECHNOLOGY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Document Type
2003/05/02
PSU proposal for contributing to S2 burst
analysis plan
Michael Ashley, Lee Samuel Finn, John McNabb, Eric Rotthoff, Kevin
Schlaufman, Amber Stuver, Tiffany Summerscales, Patrick Sutton,
Matthew Tibbits, Kristina Zaleski
Distribution of this draft:
LIGO I Collaboration
California Institute of Technology
LIGO Project - MS 51-33
Pasadena CA 91125
Phone (626) 395-2129
Fax (626) 304-9834
E-mail: [email protected]
Massachusetts Institute of Technology
LIGO Project - MS 20B-145
Cambridge, MA 01239
Phone (617) 253-4824
Fax (617) 253-7014
E-mail: [email protected]
WWW: http://www.ligo.caltech.edu/
Processed with LATEX on 2003/05/02
Abstract
Contents
1 Introduction
2
2 Pipeline Overview
2.1 Veto generation and application . . . . . . . . . . . . . . . . . . . .
2.2 Data preconditioning . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Event Trigger Generation . . . . . . . . . . . . . . . . . . . . . . .
2.4 Characterizing single IFO events from Block-Normal change-points
2.5 Coincidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 Astrophysical Interpretation of Candidate Events
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4 Issue for discussion: L1, H1, and H2 coincidence
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5 Simulations
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6 Personnel
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7 References
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1 Introduction
This document describes the work that the Penn State group proposes to contribute to the Burst
Group analysis of S2 data.
The object of the work proposed here is to provide answers to the following questions:
• What is the bound in rate for gravitational wave bursts detected by the LIGO detectors?
• Is the energy distribution of events seen at zero-delay consistent or inconsistent with the
distribution expected from background at confidence level p (TBD)?
• What is the bound in (energy, rate) space for model gravitational wave bursts incident on the
LIGO detectors?
• What is the energy spectrum (i.e., energy per frequency band) of all observed bursts events
expected less frequently than (say) once per year, based on background estimation?
• How do our sensitivity and event rates compare with those produced by the resonant acoustic
detector community (including, especially but not exclusively, the “Rome events”)?
The remainder of this document describes how we will achieve these goals and the personnel
assigned principal responsibility for leading the different components of the effort.
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Simulation
Single
Interferometer
Event
Trigger
Generator
Data
Conditioning
AS_Q
Diagnostics
Veto
Generator
Event
Triggers
Veto Triggers and Epoch Vetoes
Single
Interferometer
Event
Characterizaion
Single IFO Events
Coincidence
GW Candidates
Interpretation
Figure 1: Schematic of the Pipeline
2 Pipeline Overview
Figure 1 shows, in schematic form, the analysis pipeline we will use to produce the events that
will be used to address the questions set forth in the introduction above. At the most abstract level
the pipeline does not differ from that used in the S1 analysis. The details of veto generation, data
conditioning, event trigger generation, and especially coincidence will be different from that previous analysis, however. The analysis described here will be carried out using only science mode,
triple-coincidence data which has been “blessed” by the Detector and Detector Characterization
groups.
The Penn State group will concentrate its effort on the use of the Block-Normal Event Trigger
Generator in addressing the questions raised in the introduction. Where possible we will re-use
or adapt existing software and analysis infrastructure; however, an important ancillary goal of this
analysis is the development of an analysis infrastructure that scales, or can be scaled, to encompass
more than the LIGO detectors and analyses beyond S2. Consequently, we anticipate the need to
develop new software and analysis infrastructure in some key areas.
2.1 Veto generation and application
The Syracuse group is proposing to undertake the study and development of vetoes for the S2 data
set and analyses. We intend to rely heavily on their leadership in this regard and will contribute
one FTE to that effort (see section 6). The rest of this section describes briefly the different types
of vetoes we envision using in this analysis and draws attention to where particular attention to
veto validation is necessary.
Prior to bringing the data from the several interferometers together we identify in each interferometer’s data stream a set of events that that we have reason to believe may contain gravitational
wave signals. Only some fraction of these events will be of gravitational wave origin. The goal
of veto generation and application is to select-out from a preliminary set of events those that have
a strong likelihood of being due to non-gravitational wave instrumental or environmental effects.
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We distinguish two different veto classes:
Diagnostic vetoes (represented by veto triggers) mark transient behavior (e.g., “glitches”) in channels other than AS Q which are measured to correlate with event triggers in AS Q. These
triggers are of durations comparable to those of the gravitational-wave signals being looked
for. They are subdivided by their origin into two sets:
IFO vetoes are derived from interferometer length-sensing and control and optics channels.
Since these channels may have a coupling to AS Q, IFO vetoes need to be carefully
considered to insure we are not selecting against gravitational wave events.
PEM vetoes are derived from physical environment monitors such as the seismometers,
magnetometers and temperature sensors around the interferometer. Vetoes derived
from these channels are effectively insensitive to gravitational waves or AS Q events.
Epoch vetoes are based on the AS Q channel. They mark relatively long periods of time (minutes
or more) when the interferometer is performing anomalously in some way that makes events
generated during the period of anomalous behavior suspect.
2.2 Data preconditioning
Data preconditioning in this analysis serves two purposes:
• it places the data into the form expected by the event trigger generator; and
• it separates the data by frequency band, enabling the identification of event energy spectra
and more sophisticated downstream coincidence analysis.
The analysis described here will be based on the Block-Normal Event Trigger Generator.
Block-Normal operates best on data that is white: i.e., has constant power spectral density. The
data preconditioning we will undertake separates data into sub-bands and whitens the data in each
sub-band.
The process of data conditioning can be broken down into three basic steps: prefiltering, basebanding and bandlimiting, and final whitening. These three steps are described in detail below
along with the ordering needed to simplify successive steps.
2.2.1 Prefiltering
The object of prefiltering is to remove the most outstanding features of the data. Prefiltering is
done before the data is broken into different frequency bands. This includes line removal and a
coarse flattening of the power spectrum. We will use Kalman filtering to remove violin modes [1].
We will investigate Kalman filtering and regression for power lines.
2.2.2 Base-banding and bandlimiting
The base-banding [2] and bandlimiting operation is performed for each identified frequency band.
Focus attention on the frequency band (fc − ∆f /2, fc + ∆f /2), where 0 < ∆f ≤ 2fc . By
the following steps we identify a timeseries yk with sample rate 2/∆f from a higher bandwidth
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timeseries xk with sample rate fs > 2(fc + ∆f /2), that captures just the power in the band
(fc − ∆f /2, fc + ∆f /2) of xk :
1. Mix the timeseries x down by frequency fc : i.e., construct zk equal to xk e2πikfc /fs . The band
of interest is centered at zero frequency in the timeseries zk .
2. Resample (with anti-aliasing) z to bandwidth 2∆f : i.e., frequencies (−∆f, ∆f ).
3. Lowpass filter the (resampled) timeseries z with a halfband filter: i.e., with a lowpass filter
whose band-edge is at half the Nyquist frequency. Note that the only power that remains in
z is the power in the band of interest.
4. Mix the timeseries z up by frequency ∆f /2: i.e., construct y k equal to zk e−2πik∆f /2fs . The
contribution to x in the band (fc − ∆f /2, fc + ∆f /2) is equal to the contribution to y in the
band (0, ∆f ) and there is no power in y outside this band.
5. Finally, take the real part of y to create a real time series.
2.2.3 Final Whitening
Final whitening is performed separately on each bandlimited timeseries produced in the basebanding step described above. We will whiten the data in each base-banded timeseries using
autoregressive (AR) parametric filter, trained on the nearest science mode playground segment,
to remove any remaining spectral features. If xk is the time series representation of a particular
frequency band, then the AR model filter satisfies
xj +
Na
ak xj−k = ej
(1)
k=1
where ej is a white noise process: i.e., the result of filtering the timeseries x according to the
transfer function
Na
A(z) = 1 +
ak z −k
(2)
k=1
is a white process.
2.3 Event Trigger Generation
The Block-Normal event trigger generator identifies places in time where the mean or variance
of the data changes. Since gravitational waves are uncorrelated with detector noise, an incident
gravitational wave burst must change one or both of these quantities during the period of the burst.
Block-Normal operates in the time domain. The errors in its statistical determination of where
or when the statistics change are minimized when it operates on data that is white. Block-Normal
reports the location, by either sample or GPS time, of each change-point in the statistics of the
input timeseries, probability measures (odds) associated with the identification of a change point,
and the mean and variance of the data to either side of the putative change point.
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Identifying change points is not quite the same as identifying gravitational wave events. The
events we want to identify are epochs during which the signal mean or variance are away from
their nominal values. Correspondingly, we must construct events from change-points. This step is
described in the next subsection.
2.4 Characterizing single IFO events from Block-Normal change-points
Block-Normal identifies change-points in the statistics of its input. We will identify events as the
largest set of consecutive intervals in any single band, bounded by change-points, where the mean
or variance or both are different than their nominal values in that band.
Each single interferometer event will have the following attributes:
• IFO
• Frequency Band
• Start Time
• End Time or duration
• Calibrated Energy
In addition there may be uncertainties associated with the start time, end time, and calibrated
energy. This conversion from an event trigger to an “event” will require input not only from the
trigger, but also from calibrations and simulations.
2.5 Coincidence
The coincidence step of the data processing pipeline takes as input single interferometer events
from each detector and produces as output a list of candidate gravitational wave bursts. The coincidence step also requires knowledge of the uncertainties in the determination of start time, end
time or duration, and calibrated energy. These will be determined by simulation.
The coincidence methodology creates the output from the input through the following steps:
1. For each frequency band in turn create clusters of events with start/end times consistent with
the incidence of a plane gravitational wave on the detectors. Discard single IFO events that
do not have corresponding events in the same frequency band in the other interferometers.
2. Focus on the clusters identified in the previous step. Still within each frequency band, select
clusters with calibrated energy consistent with the incidence of a plane gravitational wave
on the detectors. Discard all other clusters.
3. Form a global estimate of the calibrated energy in the band for each cluster.
4. Focus on clusters selected in previous step. Cluster all clusters, regardless of frequency band,
that are within a time window of short (e.g., 1s) duration.
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5. Perform time-series cross-correlation, using the Cadonati r-statistic. This test produces for
each detector pair a cross correlation statistic and the time difference that maximizes that
statistic. Select only those clusters whose cross-correlation statistic is sufficiently large and
for which the returned time differences between detectors are consistent with real gravitational waves, discarding all others.
6. Form, for each of the clusters identified above, a map of the energy spectrum over time for
the cluster.
The result is a set of candidate gravitational wave events characterized by the following attributes:
• Start time;
• End time or duration;
• Total calibrated energy;
• Energy spectrum as function of time;
• Outputs of the cross correlation routine for each pair of detectors.
3 Astrophysical Interpretation of Candidate Events
Here we describe, question by question, how we will address the science goals set forth in the
introduction:
• What is the bound in rate for gravitational wave bursts detected by the LIGO detectors?
We will address this question by estimating, using time-delays, the expected background
event number and comparing, using standard classical confidence interval techniques, with
the zero-delay event number.
• Is the energy distribution of events seen at zero-delay consistent or inconsistent with the
distribution expected from background at confidence level p (TBD)?
It is our intent to set a relatively low threshold so that we have a significant number of events
passing our coincidence cut. Using time-delay methods we will establish a background event
population in total event energy. We will compare this background population with the zerodelay population using the Mann-Whitney test, which is non-parametric and distribution
independent.
• What is the bound in (energy, rate) space for model gravitational wave bursts incident on the
LIGO detectors?
Using simulations we will determine the efficiency for the detection of prototypical gravitational wave bursts taken from a galactic population. Several models will be considered,
drawn from a set including but not limited to
– Black hole ringdowns;
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– Gravitational wave bursts from broadband axisymmetric sources;
– Gravitational wave bursts from broadband non-axisymmetric sources.
Each model implies an energy spectrum. When calculating the number of events in background and at zero delay an additional cut, on the energy spectrum, will be applied to the
events that pass coincidence.
An overall bound in (rate, energy) space will also be investigated. Such a bound is more
subtle than in the S1 analysis since our events will also be characterized by a total calibrated
strain energy deposited in the detector.
• What is the energy spectrum (i.e., energy per frequency band) of all observed bursts events
expected less frequently than (say) once per year, based on background estimation?
Background estimation, based on a large number of timeshifts, can be used to estimate the
expected event rate for rates much lower than once per livetime. For any zero-delay event
whose occurrence in the data is found, through background estimation, to be very unlikely
(e.g., less likely than once per year livetime) we will examine the event energy spectrum and
attempt to understand the event origin.
• How do our sensitivity and event rates compare with those produced by the resonant acoustic
detector community (including, especially but not exclusively, the “Rome events”)?
We will select a particular narrow band, from approximately 900 to 930 Hz, for analysis.
Events identified in this band, regardless of their character in other bands, are similar to
those that would be identified in the ALLEGRO, AURIGA, EXPLORER and NAUTILUS
resonant acoustic detectors. Answers to the first three questions described above for just
these events, and focused on just this band, can be unambiguously compared to the same
questions asked of these other detectors.
4 Issue for discussion: L1, H1, and H2 coincidence
As described above we operate only on triple coincidence science mode data “blessed” by the
detector and detector characterization groups and require that all events be identified independently
in all three interferometers. Correspondingly our sensitivity is controlled by the detector with the
worst combination of sensitivity, data quality and livetime. There are several variations we can
consider that would mitigate this limitation on our sensitivity; two are described below:
• Require L1, H1 coincidence, and a minimum H1, H2 and L1, H2 r statistic.
This option would reduce our dependence on H2, our least sensitive detector. It would still
be the case that we require evidence of a signal in H2 (through the r statistic), but we would
not require that the event be identified independently there.
• Require L1, H1 coincidence only when consistent with thresholds and L1 event energy, but
always require a minimum L1/H1, L1/H2 and H1/H2 r statistic.
This option would maximize our “reach”, based on L1’s great sensitivity. As above, however,
we still require confirmation of an event through correlation between the timeseries of all
three detectors.
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These or other variations would increase our sensitivity at some cost in confidence that an event
is present. Our current favor is to require triple coincidence as described in the main body of
the proposal; however, we are cognizant that this represents one extreme of the balance between
safety and risk, which should be settled through broader discussion within the burst group and the
collaboration.
5 Simulations
Simulations will be required to determine uncertainties in various parameters, including but not
limited to,
• uncertainties in event start and end times, and energies in each band;
• efficiencies for detection of different model events and r-statistic false rates as a function of
thresholds;
• background estimation.
We will contribute to the work of the Caltech group on simulations.
6 Personnel
Penn State personnel and primary areas of responsibility are described below. Leaders of the Penn
State component of the effort in these areas are designated by italics.
• Vetoes: Ashley, Zaleski, Schlaufman
• Data preconditioning: Summerscales, Rotthoff
• Block-Normal ETG and single IFO event generation: Finn, Stuver, Tibbits
• Coincidence: McNabb, TBD
• Statistics and interpretation: Finn, Sutton
• Simulations: McNabb, TBD
7 References
[1] Lee Samuel Finn and Soma Mukherjee. Data conditioning for gravitational wave detectors:
A Kalman filter for regressing suspension violin modes. Phys. Rev. D, 63:062004, 2001. grqc/0009012.
[2] Lee Samuel Finn. Basebanding vs. high-pass filtering for burst searches. Technical Report
T030027, Laser Interferometer Gravitational Wave Observatory and The VIRGO Experiment,
LIGO Document Control Center, California Institute of Technology, 2003.
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