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Coherent Analysis by using multiple interferometric detectorsPowerPoint Presentation

Coherent Analysis by using multiple interferometric detectors

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Coherent Analysis by using multiple interferometric detectors

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Coherent Analysis by using multiple interferometric detectors

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Coherent Analysis by usingmultiple 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

at Bankoku Shinryoukan, Okinawa, Japan

Motivation

- Many plan of GW detectors are on going in the world.

- Japanese future plan : LCGT

(Large-scale Cryogenic Gravitational Telescope)

Better sensitivity

Fake-reduction

Two interferometers

An analysis method of multiple data is needed !

Analysis method

- Coincident analysis

Make event list of each detector

Compare these lists

Fake reduction

- Coherent analysis

Analyze a data set from a network

of detectors simultaneously

Improve sensitivity

Estimate the improvement of detection efficiency

by using multiple detectors

- Comparison with coincidence and coherence
- Take account of correlation between detectors
- Semi-analytic estimate

: output of each detector

injection signal : chirp signal

2-detectors :

- same location, same orientation
- same noise spectrum
- stationary Gaussian noise

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)

- SNR of 2-detector network

From the assumption,

- Probability distribution of SNR

For data with signal :

For no signal data :

- false alarm rate

(alert a detection for data without signal)

number of independent

templates

false alarm probability for

a single template

We can calculate the threshold for a given false alarm rate:

- false dismissal probability

(alert no detection for data with signal)

The detection efficiency is given by:

- false alarm rate

no window case

Taking account of parameter window

increasing the number of template

(Here, we assume Nwin=10.)

- detection efficiency

: False dismissal rate for single detector

- considered parameter

mass of binary :

coalescence time :

- estimate of the number of template

number of data point

number of template in mass space

Owen (’95)

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)

1-yr observation

stationary Gaussian noise

no correlation between detectors

All templates are independent.

We assume Nwin = 10.

detection probability

For

For

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.

- correlation in time

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. )

- correlation in mass space

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.)

2detectors, coherent

If we take account of the cor-

relation between templates,

the number of independent

templates decreases.

The detection efficiency increases.

detection probability

false alarm rate

- correlation in same frequency (2detectors)

- diagonalization of noise matrix

We define a new set of data with a linear combination of bare data.

Here,

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.

detection efficiency

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

- Detection efficiency of coherent analysis is better than the
- one of coincident analysis in stationary Gaussian noise case.

- Correlation between detectors makes the efficiency get worse.
- However, if the detectors’ correlation is less than 10%, they
- can observe better efficiently than by a single one.

Future works

- Simulation to estimate the more accurate detection efficiency
- Analysis with more realistic noise
- (non-Gaussian, non-stationary, …)