Status of TAMA data analysis Hideyuki Tagoshi Osaka

Status of TAMA data analysis Hideyuki Tagoshi (Osaka Univ. ) on behalf of the TAMA collaboration The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 1

Outline • TAMA 300 data taking history • TAMA data analysis 1. Inspiral analysis 2. Burst analysis 3. Ringdown analysis • Summary The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 2

Data taking run (1) - Observation runs • TAMA observation runs Data Taking Objective Observation time Typical strain noise level Total data (Longest lock) DT 1 August, 1999 Calibration test 1 night 3 x 10 -19 /Hz 1/2 10 hours (7. 7 hours) DT 2 September, 1999 First Observation run 3 nights 3 x 10 -20 /Hz 1/2 31 hours DT 3 April, 2000 Observation with improved sensitivity 3 nights 1 x 10 -20 /Hz 1/2 13 hours DT 4 Aug. -Sept. , 2000 100 hours' observation data 2 weeks (night-time operation) 1 x 10 -20 /Hz 1/2 (typical) 167 hours (12. 8 hours) DT 5 March, 2001 100 hours' observation with high duty cycle 1 week (whole-day operation) 1. 7 x 10 -20 /Hz 1/2 (LF improvement) DT 6 Aug. -Sept. , 2001 1000 hours' observation data 50 days DT 7 Aug. -Sept. , 2002 Full operation with Power recycling 2 days DT 8 Feb. -April. , 2003 1000 hours Coincidence 2 months DT 9 Nov. 2003 Jan. , 2004 Automatic operation 6 weeks 5 x 10 -21 /Hz 1/2 111 hours 1038 hours (22. 0 hours) 25 hours 3 x 10 -21 /Hz 1/2 1157 hours (20. 5 hours) 1. 5 x 10 -21 /Hz 1/2 558 hours (27 hours) Today’s talk The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 3

Data taking run (2) - Obervable range - Observable range 1. 4 Mo binary inspirals Detectable distance for binary inspirals (SNR=10, optimal direction and polarization) DT 6: 33 kpc DT 8: 42 kpc DT 9: 72 kpc (～ 30 kpc on average) Now, TAMA 300 covers most part of our Galaxy DT 6 DT 9 DT 8 The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 4

TAMA data analysis - overview Inspiral of compact binaries waveforms are well-known (chirp) Bursts from stellar-core collapses, etc wavefoms are not known precisely Black holes quasi-normal mode damped sinusoidal waves (ringdown) Pulsars continuous periodic waves Others veto analysis, etc. The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 5

Inspiral analysis (1) amplitude Inspiral phase of coalescing compact binaries are promising target because expected event rate of NS-NS merger for LCGT and adv. LIGO is a few within 200 Mpc / year, and because waveforms are well-known, etc. chirp signal neutron stars black holes Gravitational Waves time The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 6

Inspiral analysis (2) - Matched filtering - • Detector outputs: h(t) ：　known gravitational waveform (template) n(t) ： noise • Matched filter : Sn(f) : noise power spectrum We need to introduce fake event reduction method because of non-Gaussian noise • Fake event reduction by χ2 selection a measure of the deviation of events from real signal. Parameters (mass, coalescence time, …) are not known a priori. We must search the parameter space. The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 7

Inspiral analysis (3) -ρ- χ2 relation - TAMA trigge rs TAMA triggers vs Galactic signals s l a n g ic si ct a l a G ρ • We found that the ρ- χ2 relation is different between the non-Gaussian triggers and the simulated Galactic signals. Thus, we can distinguish them and reduce the fake event rate produced by non-Gaussian noise. The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 8

Inspiral analysis (4) - DT 8 result mass region: 1 -3 Msolar Log 10[Number of events] Mass region : 1‐ 3 Msol Threshold Set False alarm rate to 0. 8 event/yr The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 9

Inspiral analysis (5) -Upper limit to the Galactic event rate - • Threshold=12. 5 (～S/N = 9) (fake event rate = 0. 8 / year) • Detection efficiency from Galactic event simulation: • We obtain upper limit to the average number of events which exceed the threshold by standard Poisson statistics analysis NUL = 2. 3　(C. L. = 90%) • Observation time T ＝ 1163 hours Upper limit to the event rate events/hour = 29 event/yr (C. L. = 90 %) (1 -3 Msolar) The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 10

Inspiral analysis (6) - summary • DT 6(2001) (1038 hours) Range: ～ 33 kpc 83 events/yr (1 -2 Msolar) • DT 8(2003) (1163 hours) Range: ～ 42 kpc 29 events/yr (1 -3 Msolar) • DT 9(2003 -4) (558 hours) Range: ～ 72 kpc analysis is not finished Initial results of DT 8 analysis: Takahashi et al. Class. Quant. Grav. 21 (2004) S 697 The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 11

Inspirla analysis (7) - Coincident analysis (20 m IFO, Kamioka) Coincident analysis of DT 6 data of TAMA and LISM was done. orientation latitude longitude TAMA 225°　 35. 68°N 139. 54°E 　 LISM　　 165°　　 36. 25°N 137. 18°E　 Kamioka (LCGT, CLIO site) 220 km west from Tokyo • Distance between TAMA and LISM ～ 220 km • Maximum delay of signal arrival time～ 0. 73 msec • Relation between TAMA and LISM arms direction Kamioka 220 km Tokyo (NAOJ) IIAS The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 12

Inspiral analysis (8) - Coincident analysis Data length: 275 hours TAMA triggers H. Takahashi et al. PRD 70, 042003 (2004) compare LISM triggers require consistency DT 6 results 99. 96% triggers are removed by coincident analysis The number of remained triggers are consistent with the accidental coincidence (no detection) The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 13

Inspiral analysis (9) - Coincident analysis - • We demonstrated the power of coincident analysis by real data. • Many technical issue were tackled. Now, LIGO-TAMA coincident analysis which targets the inspiral signals is now underway by LIGO-TAMA joint working group (S. Fairhurst, H. Takahashi, et al. ) Please see the poster by Takahashi. The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 14

Burst analysis (1) - overview - • Excess-power filter analysis (Ando et al. gr-qc/0411027) Target: Unmodelled: Stellar-core collapse, etc Ref. waveforms by numerical sim. Schemes: Excess-power filter Fake reduction: Veto with auxiliary channel Time-scale selection Galactic simulation detection efficiency Upper limit for event rate Detectable range : ~ 300 pc (optimal direction, polarization) The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 15

Burst analysis (2) - Excess power filter - • Burst filter : Excess power filter Raw Data (time series) Evaluate signal power in given time-freqency regions Spectrogram Total power in given T-F region Signal !! Time- Frequency plane (spectrogram) Freq. sum Assumptions for signal … time scale, frequency band Robust for waveform uncertainties The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 16

Burst analysis (3) - Target waveforms - • Burst waves by stellar core collapse. Reference waveforms general relativistic, conformal flat, axisymmetric simulation by Dimmelmeier et al. (DFM) H. Dimmelmeier et al, Astron. Astrophys. 393 (2002) 523. 26 waveforms Amplitude : h rss : 4 x 10 -22 /Hz 1/2 (at Galactic center: 8. 5 kpc) Energy : E tot : 9 x 10 -8 Moc 2 Common characteristics Short burst waves Spike wave ~1 msec Duration time <30 msec • Determine time-frequency band • Fake reduction The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 17

Burst analysis (4) - Fake reduction - • Fake reduction, Injection test　　 Two veto methods 1. Time-scale selection Burst signal < 100 msec Confirm that false Most detector noises > a few seconds dismissal rate is small remove long-duration triggers by injection tests 2. Veto with monitor channels Correlated bursts in intensity monitor channel Effective to short spikes Hardware and software injections Safety check : not to reject real signals Confirm that monitor channel bursts were not caused by real GW signal False-dismissal rate estimation Less than 2% Calibration : SNR (filter output) hrss Event threshold DT 8 analysis results (before veto) veto threshold Hardware injection results The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 18

Burst analysis (5) - Analysis results - • Analysis results Trigger rate with vetoes Improvement in rates with veto analyses Better in DT 9 than DT 8 Fake rate : 30 – 100 times Sensitivity : 3 -6 times Much larger than results with Gaussian noise DT 8 DT 9 (before veto) DT 9 DT 6 Still many fake events The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 19

Burst analysis (6) - Results • Results of Galactic injection test Event-selection threshold : SNR>2. 9 Detection efficiency : 1. 5 x 10 -5 Observation result : 7. 5 x 10 -2 events/sec Upper limit DT 9, 2 nd half : 200 hours (Christmas, new-year holidays) Better noise level Stable environment Assume a Poisson distribution for the observed event number N obs N ul Galactic event rate 5 x 103 events/sec GW energy rate 4 x 10– 4 Moc 2/sec (90% C. L. ) The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 20

Burst analysis (7) - Summary – Burst-wave analysis with TAMA 300 data TAMA 300 DT 9, 200 hours of data Excess Power filter, Fake reduction Galactic event simulation Galactic event rate 5 x 103 events/sec Galactic GW energy rate 4 x 10– 4 Moc 2/sec Too large for real events Originate in residual fake triggers (90% C. L. ) Details can be found in Ando et al. , gr-qc/0411027 Other activities of burst analysis in TAMA • Akutsu et al. (Poster): DT 9 analysis by an ALF filter • Hayama (Poster): Development of a wavelet-based filter • LIGO-TAMA coincidence analysis The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 21

Ringdown analysis (1) Binary, SN expl. inspiral-merger BH formation core collapse Waveform: Damped sinusoid Ringdown QNMs perturbed BH Kerr BH (Quasi-normal modes) h(t)=exp(－πfct/Q)sin(2πfct) central frequency Quality factor Fitting formula for the least damped QNM by Echeverria (1989) M: mass a: angular momentum (non-dimension) * Probe for BH direct observation * BH physics in inspiral-merger, core collapses, . . . * Good SNR expected, ~ 100@10 kpc (TAMA sensitivity) The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 22

Ringdown analysis (2) - template space s(f): signal + noise h(f): template Sn(f): noise power spectrum Template space (parameter space) construction in (fc, Q) plane which is slightly more efficient than previously proposed methods. (Nakano et al. , PRD 68, 102003 (2003), PTP 111, 781 (2004) ) Q fc = 100 ~ 2500 [Hz] (a = 0 ~ 0. 998) Q = 2 ~ 33. 3 682 templates (SNR loss < 2%) This template space is effectively independent to Sn(f) because of its narrow band nature. fc The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 23

Ringdown analysis (3) - Event selection True signal : * exponential tail * symmetric around the local maximum Fake triggers : * exp rising, no tail Time t Time Domain Cuts: -cut filter output expected tail Time t -cut True signal B F ---> smaller Time t The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 24

Ringdown analysis (4) - Detection probability Larger Mass for Galactic events Lower Mass 100% 50% Assumption: E～ 0. 03 MBHis radiated by QNM gravitational wave 10% The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 25

Ringdown analysis (5) - Galactic event rate - Integrated over Q axis Preliminary Tobs [Hours] DT 6: 959 DT 8: 1086 DT 9: 430 fc > 1500 Hz: (M < 20 Msolar) DT 6: DT 8: DT 9: (SNR > 20) The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 26

Ringdown analysis (6) - Summary - * BH ringdown is promising GW source * Matched filtering code developed * TAMA has good sensitivity to detect Galactic events, detection probability > 10% * DT 6, DT 8, DT 9 analysis is almost done See Tsunesada et al. gr-qc/0410037 : Initial results which include detection probability, pamameter estimation errors, etc. and poster by Tsunesada for more discussion of the results The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 27

Summary • Inspiral analysis, burst analysis, ringdown analysis have been developed and the results for DT 6 -9 are now being obtained. • The tasks needed to be done; inspiral : lower and higher mass search, spin, etc. burst: other filters, more effective fake reduction method, ringdown: more effective fake reduction method. All of these are now under investigation. • Coincidence analysis LIGO-TAMA joint analysis for inspiral and burst is in progress. ROG-TAMA (bar-interferometer) • Other activity Continuous wave search (target: 1987 A remnant) K. Soida et al. , Class. Quantum Grav. 20 (2003) S 645 ALF filter analysis, Wavelet method, Veto analysis, …… The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 28

End The 4 th TAMA Symposium and the Winter School of GW @ Osaka City University, 2005. 2. 17 29