Observational Limit on
Gravitational Waves from Binary
Neutron Stars in the Galaxy
Bruce Allen
TAMA Meeting, Tokyo
October 21, 1999
Physical Review Letters 83 (1999)1498.
http://xxx.lanl.gov/abs/gr-qc/9903108
Allen, Blackburn,Brady, J. Creighton, T.
Creighton, Droz,Gillespie, Hughes,Kawamura, Lyons, Mason, Owen, Raab,Regehr, Sathyaprakash, Savage, Whitcomb,
Wiseman
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The LIGO 40-meter prototype inNovember 1994

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Optical Topology of 40-meter
prototype in November 1994

Similar to full scale LIGO except:• No power recycling• Recombination is electronic, notoptical.
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Interferometric Data is ugly!
lockring

normalrock

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Data is multichannel

Shown: earthquake rocking the mode cleaner
suspension at 2.7 Hz. This causes alignment
errors giving rise to spurious optical modes.

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Data is multichannel

Shown: power level fluctuations in the laser(possibly due to saturation in a stabilization
feedback loop).

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Major Challenge: “clean up” data stream

This shows the effect of removing
sinusoidal artifacts using multi-taper
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Major Challenge: “clean up” data stream

Interferometer output, before and after
removing correlated environmental noise

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Data non-Gaussian
Histogram of Raw Data

NonGaussian
tails!

ADC value (12 bit, signed)

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Key Question:
Can one do sensible analysis in the presenceof this poorly-understood corruption of thedata?
Proof of principle: Set upper limit on the rateof galactic NS inspiral using November 1994
40-meter data.

Quiet region @600 Hz
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Data Taking Periods & Sensitivity
boxes: data recorded, bars: data analyzed

effective distance to 50% or 90% of sources
effective distance for Signal-to-Noise ratio = 10
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Typical Inspiral Chirp Signal

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Filtering Method(optimal/matched/Wiener)
Calibration Data
(once per run)

Data Stream 9868.42 Hz(12 bit ADC)

Segments: 26.6 sOverlap: 15.7 s

Skip 3 min intolock

Glitch-freesegments
OptimalFilter 1
mass: 1,1...

OptimalFilter 687
mass: 3,3

Average
power
spectrum (8segments)

Event List

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Gridding of Filters•687 different mass pairs (1 to 3solar masses)•“Evenly” spaced in “overlap”
space•No more than 2% loss of SNR
due to parameter mismatch
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“Beowulf” Filtering Engine(U. Wisconsin - Milwaukee)
48 x 300
MHz DECα (linux)
29 Gflops
peak
6 Gflops
real (fftbound)
Filtering 25
hours ofdata takes
32 hours
Cost: $65K

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Time/Frequency Discriminator (χ2 test)

Spurious interferometer noise rings off
filters. To discriminate these large filter
outputs from inspiral signals:•Break frequency band into p=20
subintervals•Subintervals chosen to make equal SNR
contributions• χ2 = sum of squares of deviations frommean signal in band
•Statistic has 38 degrees of freedom

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Time/Frequency Discriminator (χ2 test)
How does it work? (p=4 band example)

χ2 = 1.26
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χ2 = 68.4
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Results of Filtering

Loudest event
SNR = 8.34

Upper limit on event rate can be
determined from SNR of loudest event
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Detection Efficiency
Step 1: simulate galactic distribution ofbinary inspirals sources:
4.8 kpc disk radius
8.5 kpc toGalacticcenter2 kpc disk
thickness

Step 2: inject thousands of simulated
signals into real output from instrument.
What fraction are detected above SNR ofloudest event?

At SNR of loudest event
efficiency is 0.33

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Simulating Inspiral Events provides Endto-End test of analysis & simulation code

Several thousand simulated events arecorrectly detected. Errors in distance measure
is consistent with expected SNR fluctuations.
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90% Confidence Limit on
Rate of Galactic Inspiral
Limit on Rate:R <3.89
ε T = 0.5/hourNumerator: determined by confidence (90%)ε = 0.33 = detection efficiency at loudest event
T = 25.0 hours = total length of analyzed data
An ideal detector would have ε = 1.0 so thelimit would be 0.16/hour.
More than half of the difference arises because
detector antenna pattern makes effective
distance to Galactic sources too large to detect

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What Next?
Next step: simulated coincidence analysis
with 40-m data
• Construct data base of events &instrumental monitors• Introduce artificial time/space shift to halfof the data stream, to simulate simultaneous
operation of two sites• Construct lists of correlated events• Carry out further analysis of raw dataaround interesting time windows• Use real not simulated data:• don’t know how to simulate glitches• hardest part is handling non-stationary
and non-Gaussian noise• Build methods into LDAS framework
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