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Coherent Analysis by using multiple interferometric detectors

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 using multiple interferometric detectors

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  1. 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

  2. Introduction 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

  3. Purpose of this work Estimate the improvement of detection efficiency by using multiple detectors • Comparison with coincidence and coherence • Take account of correlation between detectors • Semi-analytic estimate

  4. : output of each detector assumption 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),

  5. : modifided Bessel function Coherent analysis with two detectors(no correlation between detectors) 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 :

  6. 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:

  7. Coincident analysis case • 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

  8. Number of template • 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 :

  9. Lower limit of detection efficiency 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

  10. More accurate 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.

  11. Number of independent 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.)

  12. More accurate detection efficiency 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

  13. Two detectors with correlation • 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

  14. Detection efficiency (correlated detectors) 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

  15. Summary and Future works • 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, …)

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