Transcript Coherent and Coincidence Network analysis for coalescing

Testing coherent code for
coalescing binaries network
analysis
Simona Birindelli
INFN Pisa, Università di Pisa
Leone B. Bosi
INFN Perugia, Università di Perugia
Andrea Viceré
INFN Firenze, Università di Urbino
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Determination of the source position
With a network of three detectors we can determine the
source position (modulo a reflection with respect to the
three interferometers plane), using the coincident and
coherent analysis methods.
We have tested a combination of the two methods, which
starts from a coincidence and tries to improve the
determination using the coherent analysis, first using a
“classic” maximization and successively with a fit of the
network statistic.
We have considered the usual network composed by Virgo
and the two 4 Km LIGOs.
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Coherent analysis method
The basic idea is to “construct” an ideal detector equivalent to
the network, to which each real detector coherently
contributes with its sensitivity, position, orientation..
The most useful network statistic (see Phys.Rev D 64,
042004(2001) by Pai, Dhurandhar and Bose) is the
Logarithm of the Likelyhood Ratio, and can be written as:
 I t   ,   J t   ,    I t   ,   J t   ,  




t


,


C0  J
C 2  I
C 2  J
L pIJ
C 0  I

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where p is a matrix with as many rows as the number of
detectors in the network, depending on the interferometers
locations, their relative sensitivities and source position
C is the usual Wiener correlator computed (for the two
quadratures) by each experiment, and depends on stellar
masses and location
 I is the time delay of the I-th detector with respect to the
network frame.
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IJ
I
The work
L.Bosi produced with Merlino coalescing binaries events
using the LIGO-Virgo project 1b simulated data.
The exact masses of the injections were used for the Wiener
filter.
The SNR threshold was set at SNR 4, thus resulting in a rate
of several events per second.
In order to make it possible to compute the logarithm of the
likelyhood ratio for different directions in the sky(and
therefore different shifts within the correlators) for each
detector and for each events, the correlators were saved
around the maxima.
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First simple test: crude maximization of the LLR
Choosing a pair of interferometers we have searched for
double coincidences (events with both SNR > 6), then we
have searched over the events of the third detector to find
the one which maximizes the LLR (with masses and time
delays compatible).
More in details, for each double coincidence we have
computed the LLR, and we have maximized it over the
correlators (the two quadratures) of the third detector.
So we have extrapolated the best guess for the signal arrival
time at the third interferometer, and determined the source
position with the same geometric method used for the
coincident search.
We have repeated the procedure with the other two possible
combinations of interferometers (a couple, and the third),
and chosen the reconstructions with maximum LLRs.
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First test: accuracy of the reconstruction
For each event we have
computed the source
position also with the
triple coincidence
method, using the time
of the maximum of the
correlator at each
detector.
The crude maximization of
LLR did not seem to
systematically improve
the determination,
probably because the
maximization over one
correlator only is not
sufficient to optimize
the position
reconstruction
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Second test: global maximization and
parabolic fit to the LLR
• Perform a global
maximization over all the
correlators
simultaneously:
Starting from a triple
coincidence, we have
maximized the LLR
around each maximum
over the three correlators
in order to refine the
reconstruction.
(Coherent maximization)
• Make a fit of the LLR
behavior instead of simply
take its maximum value:
From its behavior near the
maxima, we have
supposed that the LLR
could be fitted with a
parabolic function of the
three correlator indexes.
(Coherent fit)
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Comparison between the methods
The reconstructed
position is improved
fitting the likelyhood
respect to the
coincidence one, and
also respect to the
LLR total
maximization
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NGC6744 reconstructed position - real position
M87 reconstructed position - real position
•Coincident
meana= 0°46’ •Coincident
The accuracydec
during
day is quite uniform
dec standard deviation = 6°40’
for all the three
methods RA mean = -7°43’
•Coherent fit
dec mean = 3°45’
dec standard deviation = 8°59’
RA mean = -3°31’
RA std. dev = 52°35’
RA std. dev = 14°49’
dec mean = 0°04’ •Coherent fit
dec mean = 0°38’
dec standard deviation = 2°45’
dec standard deviation = 3°37’
RA mean = 1°08’
RA mean = -0°02’
RA std. dev = 4°20’
RA std. dev = 1°58’
•Coherent max dec mean = 0°48’ •Coherent max dec mean = 0°09’
dec standard deviation = 8°55’
dec standard deviation = 7°20’
RA mean = 1°10’
RA mean = 1°40’
RA std. dev = 14°34’
RA std. dev = 9°21’
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Conclusions and future work
In this work we have done a comparison of coincident and
coherent methods in the reconstruction of the source
position, using a network of three interferometers.
We have focused on signal emitted by binary newtron stars.
The results obtained using LIGO-Virgo simulated data appear
to be promising.
The maximization of the network LLR followed by a fit of
the LLR allowed to improve the source position
The next step is to fully characterize the method, assessing its
performance at different SNR levels, for a wider range of
sky locations.
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