Search for Gravitational Waves from Inspiraling Compact Binaries using TAMA300 data Hirotaka Takahashi (Osaka University / Niigata University / YITP) Hideyuki Tagoshi A ,Nobuyuki Kanda B , Daisuke Tatsumi C , Yoshiki Tsunesada C ,and The TAMA Collaboration A,B,C,D,E,F… Osaka University A ,Osaka City University B ,National Astronomical Observatory C ,… GWDAW-8 @ Milwaukee, Wisconsin, USA.
Introduction • TAMA300 observed during August 1 and September 20, 2001. (Data Taking 6) Total length of data amounted to 1039 hours. • TAMA300 also observed during February 14 and April 14, 2003. (Data Taking 8) Total length of data amounted to 1163 hours. • We have tried a event search for inspiraling We have tried a event search for inspiraling compact ompact binaries using TAMA300 data. binaries using TAMA300 data.
Coalescing compact binaries Inspiral phase of coalescing compact binaries are main target because expected event rate of NS-NS merger :a few within 200Mpc / year , well known waveform etc. t φ , Possibility of MACHO black hole Neutron stars c c Black holes chirp signal m m amplitude 2 1 Gravitational Waves A : total mass M = M η 3/5 M η : reduced mass time ≤ ≤ In this search, mass region: for DT6 1.0 M m m , 2.0 M solar 1 2 solar ≤ ≤ for DT8 1.0 M m m , 3.0 M solar 1 2 solar
History of TAMA300 Sensitivity for inspiraling for inspiraling compact binaries ompact binaries DT6:Range (SNR=10) : 33kpc DT8:Range (SNR=10) : 42kpc
Matched filter = + s t ( ) Ah t ( ) n t ( ) • Detector outputs: h t ( ) ： known gravitational waveform (template) ： n t ( ) 2.5 Post-Newtonian noise. approximation • Outputs of matched filter: � � = ∫ * s ( f h ) ( f ) ρ ( t , m , m ,...) 2 df c 1 2 S ( f ) n ( ) S f • noise power spectrum density n ρ • Signal to noise ratio is SNR = / 2 ρ • Find the parameter which realize the maximum of t for each certain interval of c ρ ∆ max ( , t m m , ,...) � ( 25 ) t ms c 1 2 c t m m , , ,... c 1 2
• The real data contained large amount of non-stationary and non-Gaussian noise. • In order to remove the influence of such noise, we also χ 2 introduce • Divide each template into n mutually independent bins in frequency domain. ρ • Test whether the contribution to from each bins agree with that expected from chirp signal ~( )~ ( ) * F I s f h f ρ ≡ ( , ) s h = 2 df z G J S ( ) f H K ρ 1 ρ 2 ρ 3 ρ 4 ρ 5 n � � f min f 1 f 2 f 3 f 4 f 5 f max ∑ χ ≡ ρ − ρ 2 2 n ( ) i i ρ = ρ , i i χ = χ − 2 2 / ( 2 n 2 ) ˆ (In this analysis n=16)
Variation of Noise power (1 minute average) − 1 / 2 − 7 / 3 f f ∫ m a x 4 d f S ( f ) f m in n • Before the matched filter analysis, we examine = = 100Hz, f 2500Hz f the fluctuation of noise power. min max • The vale of noise power is evaluated for each data with length 1.1min. DT6:8/1-9/20/2001 DT8:2/14-4/14/2003 [1.09minutes]
Variation of Noise power (histogram) (2) DT6 DT8 × 10 − 19 1. 9 × 10 − 19 Number of occurrence Mean: 3. 2 Mean: Number of occurrence 10 − 5 10 − × × 19 20 1. 7. 5 Std.: Std.: Noise power × 10 − Noise power × 10 − 19 19 The fluctuation of noise power in DT8 is small. It is found that the stability of DT8 data is better than that of DT6 data with respect to amplitude of noise power spectrum.
Distribution of template number • A discrete mass parameter space is determined so that the maximum loss of SNR become less than 3% • The mass parameter space depend on power spectrum of noise. This parameter space is not changed within the continuously locked segment. However, in order to take into account the variation of the noise power spectrum with time , we use a different mass parameter space for different locked segment. DT6 DT8 Mass region :1 ‐ 2Msol Mass region :1 ‐ 3Msol • The variation of number of templates is not due to the variation of absolute amplitude of power spectrum, but due to the variation of the shape of noise power spectrum. It is found that DT8 data are more stable than DT6 data with respect to the number of templates, which probably means the stability of DT8 data whit respect to the shape of the power spectrum.
DT6 DT8 Mass region :1 ‐ 2Msol Mass region :1 ‐ 2Msol Log10[Number of events] Log10[Number of events] ρ ρ χ 2 χ 2 ˆ ˆ ρ • We find from the distribution of that the DT8 result has longer tail than DT6 data. ρ χ 2 Such events with large must be due to the non-Gaussian noise since the value of ˆ of them are also very large. χ 2 • The distribution of is also more spread in DT8 case than in DT6 case. ˆ ρ • Thus, in terms of the distribution of and , the stability of DT8 does not seem to χ 2 ˆ be better than DT6. ρ χ • However, most of events with large in DT8 have larger than that of DT6. 2 ˆ
� statistics ρ χ 2 / TAMA events vs Galactic event TAMA events ρ χ = 2 / 12.5 Test signals χ = 2 ˆ 1.5 χ 2 ˆ • We found that the value of becomes larger, when the amplitude of signal becomes larger even if the events are real. χ 2 ˆ In such situation, if we reject events simply by the value of , we may lose real events with large amplitude. � ρ χ 2 / • We thus introduce a statistic , to distinguish between candidate events and noise events
Preliminary Compare DT6 results to DT8 results DT8 DT6 Log10[Number of events] Log10[Number of events] Mass region :1 ‐ 2Msol Mass region :1 ‐ 2Msol Fitting Threshold Threshold � � ρ χ = ρ χ = 2 2 / 16.0 / 12.0 � ρ χ Set False alarm rate 2 / to 0.8 event/yr � ρ χ 2 If GW events really happened, the value of would become / much larger than tail of distribution.
In matched filtering analysis, we do not see events which exceed the tail of the distribution of events significantly. Even in this case, we can estimate the upper limit to the event rate. Upper limit to the Galactic event rate N T ε • Ｎ ： Upper limit to the average number of events over certain threshold • Ｔ： Length of data [hours] ε • :Detection efficiency
Galactic event detection efficiency To estimate detection efficiency, we perform Galactic event simulation Threshold efficiency DT6 16 0.23 0.58 DT8 12 (False alarm rate = 0.8 / year ) search mass region: ≤ ≤ 1.0 M m m , 2.0 M solar 1 2 solar Efficiency of DT8 becomes three times better than that of DT6
Upper limit to the event rate: Poisson statistics We evaluated upper limit to the average number of events over certain threshold. ρ χ = 2 ρ χ = • Threshold / 12 2 / 16 • Expected number of fake events over threshold ： N bg = 0.1 , 0.1 • Observed number of events over threshold: N obs = 0 , 1 Assuming Poisson distribution for the number of real/fake events over the threshold, we obtain upper limit to the expected number of real events from + = n n N ( N N ) ∑ o b s − + ( N N ) b g e b g n ! = − = n 0 1 C L = n n N ( ) N ∑ o b s − N b g b g e n ! = 0 n N = 2.3 , 3.8 (C.L.=90%)
Preliminary search results search results for inspiraling for inspiraling compact binaries compact binaries threshold number of evtnts(CL90) obs. time detection effici. Galactic event rate (CL90) DT6 16 0obs,0.1bg ,2.3 1039 0.23 0.0095 event/h = 83 event/yr DT8 12 1obs,0.1bg,3.8 1163 0.58 0.0056 event/h = 49 event/yr ≤ ≤ (search mass region: ) 1.0 , 2.0 M m m M solar 1 2 solar (False alarm rate = 0.8 / year ) We can obtain that upper limit of DT8 becomes about two times more stringent than that of DT6.
Uusing the DT8 search results (mass region:1-3Msol ) , we estimate the upper limit to the galactic event rate. Preliminary Mass region :1 ‐ 3Msol Log10[Number of events] Threshold � ρ χ = 2 / 12.5 � Set False alarm rate ρ χ 2 / to 0.8 event/yr
Preliminary Upper limit to the Galactic event rate • threshold=12.5 ( ～ S/N = 9) (fake event rate = 0.8 / year) ε = 0.61 • detection efficiency from Galactic event simulation: • We also obtain upper limit to the average number of events over threshold by standard Poisson statistics analysis N = 2.3 (C.L. = 90%) • Observation time T ＝ 1163 hours N ε = 0.0033 event / hour T = 29 event/yr (C.L. 90 %) ≤ ≤ 1.0 M m m , 3.0 M solar 1 2 solar
Summary We performed a event search for inspiraling a event search for inspiraling compact ompact binaries using TAMA300 data. binaries using TAMA300 data. DT6 (2001) Range (SNR=10) : 33kpc Mass range : 1-2Msol Upper limit : 0.0095 event/hour (= 83 event/yr) DT8 (2003) Range (SNR=10) : 42kpc Mass range : 1-2Msol Upper limit : 0.0056 event/hour (= 49 event/yr) Mass range : 1-3Msol Upper limit : 0.0033 event/hour (= 29 event/yr)
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