The Probability Event Horizon Search Technique

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ACIGA
The Probability Event Horizon Search
Technique Eric Howell
University of Western Australia
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Probability Event Horizon (PEH) The
PEH is a tool to search for the signature of
astrophysical GW populations.
Explain the concept of the PEH
Observe a horizon of approaching events
Show how the PEH maps the approach of the
closest events as a function of observation time
Apply the PEH concept to 2 cases
a) Astrophysical GW background signals
b) Gaussian noise
Future Work
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Accumulated z data for core-collapse SNe
PDF
Accumulated z values

• Tobs estimated from mean event rate of sources

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Extract running minimum z from accumulated data
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• Running minima of z (Tobs) define a horizon
  approaching the detector

• The horizons initial approach is rapid for
  around the first 100 events

• The horizon slows down as a function of Tobs

Low probability tail
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Running minimum z (Tobs) for Tobs 2 years
Horizon
PDF

running min z (Tobs)
Adv LIGO 100 Mpc potential detectability
horizon
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Using Poisson statistics and knowledge of the
event rate we can define a PEH
The min z ( Tobs ) for at least 1 event to
occur at a 95 confidence level
( see D.M.Coward R.R.Burman, accepted MNRAS,
astro-ph0505181)
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null PEH - the 95 confidence threshold below
which we expect no events
2 years of simulated running minimum data using
2 different SFR evolutions
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.
O
Simulated GW amplitude
Running maximum amplitude
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SUMMARY
We demonstrate a new method for detecting a
cosmological background of GWs.
One can fit a PEH model to different
astrophysical populations using the local rate
density of events as a variable.
There may be a regime where the signature of an
astrophysical population can be identified before
a single local event occurs above the noise
threshold.
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Future Work
We plan to extend the PEH concept to a signal
detection algorithm using real interferometer
data.
Inject simulated signals in real data to test
algorithm performance.
Utilize the PEH algorithm in the frequency
domain.
Determine a fitting function for dominant
astrophysical signals and noise to apply at
around SNR 1.
Iterative search through data for dominant
trends.
Correlate frequency and amplitude search data.
CRAY XT3 Supercomputer.
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THE END
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PEH
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Poisson process - probability distribution of
the number of occurrences of an an event that
happens rarely but has many opportunities to
happen
M mean number of events R(z) rate of events
throughout the Universe T observation time
p(r) Mr e-M
, where M R(z) T
r!

P(at least 1 event) 1 e -M
If we set a 95 confidence level
0.95 1 e R(z)T
-R(z)T ln(0.05)
R(z)T 3
additionally P(0) e M
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null PEH - the 95 confidence threshold below
which we expect no events
2 years of simulated running minimum data using
2 different SFR evolutions
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SFR
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• Probability density function P(z)
• SFR model
• cosmology flat-? with Om 0.3, O? 0.7
• local source rate density 5 X 10-12 s-1 Mpc-3

Cumulative distribution function P(z)
Uniform distribution
Z value
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The dimensionless SFR density evolution factors
e(z) normalized to unity in our intergalactic
neighborhood.
Heavens.A Panter.B (2004) Nature 428
Hernquist.L Springle.V (2003) MNRAS 339,312
Constant (non-evolving) SFR density model
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References Coward D.M., Burman R.R., Blair
D.G., 2001, MNRAS, 324, 1015 (CBB) Coward D.M.,
Burman R.R., Blair D.G., 2002, Class Quantum
Grav, 19, 1303 Coward D.M., Burman R.R., Blair
D.G., 2002, MNRAS, 329, 411 Howell E., Coward
D., Burman R., Blair D., Gilmore J., 2004, Class
Quantum Grav, 21, S551 Howell E., Coward D.,
Burman R., Blair D., Gilmore J., 2004, MNRAS,
351, 1237
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Ind Slides
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null PEH - the 95 confidence threshold below
which we expect no events
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2 years of simulated running minimum data using
2 different SFR evolutions
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Old Slides
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Improved test of PEH fitting
For i 1T
e.g. for data set of 106 using increments of 104
We get 100 iterations
Extract running maximum amplitudes from data set N
Reposition first N/T to end of data set
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Running maximum amplitudes extracted iteratively
using intervals of 104 on a simulated data set of
106 events
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Difficulties etc Gaussian distribution fast fall
off with amplitude noise bursts no larger than
few sds Non- Gaussian noise - large transients
eg noise from sudden strain releases in wires
holding test masses
Algorithm repeatedly summing over from each max
to accumulate more data
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If we make the assumption that our detector noise
is Gaussian Use a standard model for NS merger (
Shibata et al 2005) Determine detectors rms
noise from noise curve at fc of the source model,
giving a mean and sd Determine PEHs for both the
noise and source distributions
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PEH Algorithm
Using local rate densities utilize PEH
evolution for different populations
Determine a fitting function for dominant
astrophysical signals and noise and apply at
around SNR 1
Iterative search through data for dominant
trends
Correlate search data obtained from the
frequency and amplitude domains
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PEH Algorithm
Using local rate densities utilize PEH
evolution for different populations
Determine a fitting function for dominant
astrophysical signals and noise and apply at
around SNR 1
Iterative search through data for dominant
trends
Correlate search data obtained from the
frequency and amplitude domains
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null PEH - the 95 confidence threshold below
which we expect no events