Coherent Analysis by using multiple interferometric detectors. Norichika Sago (Osaka) with Hideyuki Tagoshi (Osaka) Hirotaka Takahashi (Osaka City) Nobuyuki Kanda (Osaka City) S. Dhurandhar (IUCAA). 6th Edoardo Amaldi Conference, June 20-24, 2005
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Coherent Analysis by usingmultiple interferometric detectors
Norichika Sago (Osaka)
Hideyuki Tagoshi (Osaka)
Hirotaka Takahashi (Osaka City)
Nobuyuki Kanda (Osaka City)
S. Dhurandhar (IUCAA)
6th Edoardo Amaldi Conference, June 20-24, 2005
at Bankoku Shinryoukan, Okinawa, Japan
(Large-scale Cryogenic Gravitational Telescope)
An analysis method of multiple data is needed !
Make event list of each detector
Compare these lists
Analyze a data set from a network
of detectors simultaneously
Estimate the improvement of detection efficiency
by using multiple detectors
: output of each detector
injection signal : chirp signal
Output from a network of detectors
From the assumption (same location, same orientation),
: modifided Bessel function
Finn, PRD 63, 102001 (2001)
Pai, Dhurandhar and Bose, PRD 64, 042004 (2001)
From the assumption,
For data with signal :
For no signal data :
(alert a detection for data without signal)
number of independent
false alarm probability for
a single template
We can calculate the threshold for a given false alarm rate:
(alert no detection for data with signal)
The detection efficiency is given by:
no window case
Taking account of parameter window
increasing the number of template
(Here, we assume Nwin=10.)
: False dismissal rate for single detector
mass of binary :
coalescence time :
number of data point
number of template in mass space
for LCGT case
MM : minimal match (=0.97)
f0 : frequency at minimal noise spectrum
mmin : minimal mass for search
maximum mass for search :
2 detector (LCGT)
stationary Gaussian noise
no correlation between detectors
All templates are independent.
We assume Nwin = 10.
false alarm rate
Actually, templates correlate each other.
: parameter set
Overestimate of false alarm rate
If events A and B are dependent,
We can estimate the more accurate false alarm rate
by considering the independent portion of all templates.
We regard that two templates are independent if the difference
of the coalescence time between them is larger than 8 msec.
( Match of them is sufficiently small. )
Here we consider the cases that 1%, 10% and 50% of all templates
are independent, respectively.
(A estimate by simulations is needed for a more realistic evaluation.)
If we take account of the cor-
relation between templates,
the number of independent
The detection efficiency increases.
false alarm rate
We define a new set of data with a linear combination of bare data.
The psuedo-detector 1 contains no signal.
We can regard the case that a signal with amplitude,
is injected into a detector with
correlation factor between
two detectors, e
Here we assume the phase of
signal is known in advance.
solid line : coherence
dashed line : coincidence
(Nwin = 10)
The blue, green and red lines
show the cases of
black solid : single detector
false alarm rate