Hideyuki Tagoshi (Osaka Univ.) on behalf of the TAMA collaboration

1. Resutls of the search for inspiraling compact star binaries from TAMA300’s observation in 2000-2004 Hideyuki Tagoshi (Osaka Univ.) on behalf of the TAMA collaboration Ref. TAMA Collaboration, Phys. Rev. D74, 122002 (2006) TAUP 2007, Sendai, Sept. 12, 2007

2. TAMA Collaboration 117 people

3. Outline • I will describe the results of the search for the gravitational wave from (non-spinning) inspiraling compact star binaries (composed by neutron stars and/or black holes) using TAMA300 data in 2000-2004 • Significant candidate of the gravitational wave events are not found • Upper limit to the event rate are derived

4. Data taking run (1)- Observation runs of TAMA300- Data Taking Objective Observation time Typical strain noise level Total data (Longest lock) DT1 August, 1999 Calibration test 1 night 3x10-19 /Hz 1/2 10 hours (7.7 hours) DT2 September, 1999 First Observation run 3 nights 3x10-20 /Hz 1/2 31 hours DT3 April, 2000 Observation with improved sensitivity 3 nights 1x10-20 /Hz 1/2 13 hours DT4 Aug.-Sept., 2000 100 hours' observation data 2 weeks (night-time operation) 1x10-20 /Hz 1/2 (typical) 167 hours (12.8 hours) DT5 March, 2001 100 hours' observation with high duty cycle 1 week (whole-day operation) 1.7x10-20 /Hz 1/2 (LF improvement) 111 hours DT6 Aug.-Sept., 2001 1000 hours' observation data 50 days 5x10-21 /Hz 1/2 1038 hours (22.0 hours) DT7 Aug.-Sept., 2002 Full operation with Power recycling 2 days 25 hours DT8 Feb.-April., 2003 1000 hours Coincidence 2 months 3x10-21 /Hz 1/2 1157 hours (20.5 hours) DT9 Nov. 2003 - Jan., 2004 Automatic operation 6 weeks 1.5x10-21 /Hz 1/2 558 hours (27 hours) All data longer than 100 hours are analyzed

5. Motivation • Previous work (inspiral analysis) • DT4(unpublished) • Results of a part of data from DT6 and DT8 were published. • DT6: TAMA-LISM coincidence analysis (Phys. Rev. D70, 042003 (2004)) • DT8: LIGO-TAMA coincidence analysis (Phys. Rev. D73, 102002 (2006)) • DT5, DT9 : new analysis • ・Until DT6, TAMA300 was the only large scale interferometer in the world. • At DT6 period, TAMA had the world best sensitivity. • Thus, it is important to search for possible signals in the data. • ・Before the current ongoing, LIGO S5 observation, TAMA data are • the world longest data. In order to take advantage of long length of data, • we analyze all of above data in a unified way.

6. Data taking run (2)- Observable range - Observable distance for inspiraling binaries (SNR=10, optimal direction and polarization) 1.4 Msolar binary inspirals DT6: 33kpc(～18kpc for SNR=8, sky-averaged) DT8: 42kpc (～23kpc for SNR=8, sky-averaged) DT9: 72kpc(～40kpc for SNR=8, sky-averaged) DT6 DT9 DT8 TAMA300 covers most part of our Galaxy

7. Binary inspirals neutron star black hole “chirp” (frequency and amplitude grow with time) • Binary inspirals・・・two compact stars, before merger, orbiting each other emitting gravitational waves. • The orbital radius decreases due to the energy and angular momentum loss by gravitational wave emission. • Most promising sources for ground based detectors • Their waveforms (i.e.,“chirp” wave form) can be computed accurately by the post-Newtonian approximation of GR.

8. Mass range • Mass range : 1-3Msolar for each member stars Basic physical value of binary inspirals Observable frequency of TAMA300：100Hz 〜2kHz ISCO: inner most stable circular orbit (where the inspiral ends, and the final plunge and the coalescence begins)

9. Matched filtering • Detector outputs: h(t) ：　known gravitational waveform (template) n(t) ： noise • Matched filter : : one sided noise power spectrum density Parameters (mass, coalescence time, …) are not known a priori. They are searched in the parameter space. Mateched filter is equivalent to the maximum likelihood detection strategy in the case of stationary Gaussian noise. However, the detector’s noise are not stationary Gaussian, we need additional methods. We introduce fake event reduction method because of non-Gaussian noise • Fake event reduction by a measure of the deviation of events from real signal.

10. Chi square cut- statistic - We define as the new detection statistic to discriminate fake events from true signals. We set a threshold of as where is determined by the false alarm rate. The chi square cut is automatically introduced by these procedures. This statistic can accommodate large signals which could occur due to mismatch between signals and templates. DT9 triggers triggers by test Galactic signals

11. Comparison of detection efficiency Results of the Galactic signal injection simulation ζ threshold

12. Data length blue: analyzed data, but not used for upper limit evaluation red: analyzed data used for upper limit evaluation

13. Trigger lists In these plots, there are no triggers which deviate from the tail of the distribution significantly. From this, we conclude that there is no candidate signal which can be interpreted as a real gravitational wave signal.

14. Decision of threshold We determine the threshold of ζ for a given false alarm rate (1 event/yr) We assume the following functional form of the trigger distribution and fit the data This functional form is motivated from the F-distribution which z obeys in the case of Gaussian noise. In this functional form, the trigger distribution becomes much like linear, and it becomes easy to extrapolate the distribution. Threshold = 2.24 for the false alarm rate = 1/yr

15. Upper limit to the event rate Upper limit to the event rate is the upper limit to the number of events derived by ：estimated number of triggers which exceed the threshold ：observed number of triggers which exceed the threshold

16. Upper limit (1) DT9 was the most sensitive observation. However, since DT8 was twice longer than DT9, contribution of DT8 to the upper limit is the largest.

17. Systematic errors 1. Error of the detector calibration Although it is expected to be less than 5%, it is not know exactly. We take a conservative value (+-10%) 2. Uncertainty of Galactic simulation Uncertainty of mass distribution Uncertainty of the position of solar system in our Galaxy Uncertainty of the Monte Carlo injection simulation 3. Uncertainty of theoretical wave form -10% at most. 4. Uncertainty of threshold (for a given false alarm rate)

18. Systematic errors (2) Summary of the effects of the systematic errors to the detection efficiency of Galactic signals

19. Upper limit (1) DT9 was the most sensitive observation. However, since DT8 was twice longer than DT9, contribution of DT8 to the upper limit is the largest.

20. Upper limit (2) We combine these upper limits from each observation run, and derive an upper limit by ：Upper limit to the number of events which exceed the threshold by all of the observation To obtain conservative upper limit, we take larger value as a final upper limit

21. Summary and discussion • We performed the the analysis of TAMA300 data to search • for the inspiraling compact star binaries in the mass range 1-3Msolar. • Candidate gravitational wave events were not found. • We obtained the upper limit to the Galactic events, 20 [yr-1] c.f. LIGO S2 : 47 [yr-1] LIGO-TAMA S2-DT8 : 49 [yr-1] Recently, LIGO reported 2 [yr-1 MWEG-1] for BNS from LIGO S3/S4 data (arXiv:0704.3368) • However, these value are much larger than the estimate from the • observation of binary radio pulsars ：8.3 × 10-5 [yr-1] (Kalogera et al., Ap.J.601, L179(2004)) • To obtain more astronomically relevant upper limit, • or to detect them, we need advanced detectors, • such like LCGT (Japan) , advanced LIGO (USA), etc.

22. End

23. Upper limit to the Galactic events • DT8 gives the most stringent upper limitbecause of • Largest length of data • Rather high sensitivity to the Galactic events • Very stable operation (low threshold) • (DT9’s detection probability would have been much larger. However, the first half of DT9 was not very stable. Fake events with large ζ were produced during that period. They degrade the detection probability of DT9.)