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

TAUP 2007, Sendai, Sept. 12, 2007 1

Resutls of the search for inspiraling compact star binaries from TAMA300’s observation i

n 2000-2004

Hideyuki Tagoshi (Osaka Univ.)

on behalf of the TAMA collaboration

Ref. TAMA Collaboration, Phys. Rev. D74, 122002 (2006)

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117 people

TAMA Collaboration

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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

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558 hours(27 hours)

1.5x10-21 /Hz 1/26 weeksAutomatic operation

Nov. 2003 -Jan., 2004

DT9

1038 hours(22.0 hours)

5x10-21 /Hz 1/250 days1000 hours'

observation dataAug.-Sept.,

2001DT6


3x10-21 /Hz 1/22 months1000 hours

CoincidenceFeb.-April.,

2003DT8

25 hours2 daysFull operation with

Power recyclingAug.-Sept.,

2002DT7

111 hours 1.7x10-20 /Hz 1/2

(LF improvement) 1 week

(whole-day operation)100 hours' observation with high duty cycle

March, 2001DT5


1x10-20 /Hz 1/2

(typical)2 weeks

(night-time operation)100 hours'

observation dataAug.-Sept.,

2000DT4

13 hours1x10-20 /Hz 1/23 nightsObservation with

improved sensitivityApril, 2000DT3

31 hours3x10-20 /Hz 1/23 nightsFirst Observation runSeptember, 1999DT2

10 hours(7.7 hours)

3x10-19 /Hz 1/21 nightCalibration testAugust, 1999DT1

Total data(Longest lock)

Typical strain noise level

Observation time

ObjectiveData Taking

Data taking run (1)- Observation runs of TAMA300-

All data longer than 100 hours are analyzed

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MotivationPrevious 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DT4(unpublished)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.

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56

1

2

3

456

10

2

3

456

100

2

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Observable Distance with SNR=10 [kpc]

0.1 1 10 100mass of accompanying star [Msolar]

Distance of detecting inspirals with SNR=10

2003/11/04 (DT9) 2003/02/20 (DT8) 2002/08/31 (DT7) 2001/06 (DT6)

0.5Msolar-32.6kpc

1.4Msolar-72.5kpc

2.7Msolar-96.3kpc

10Msolar-21.9kpc

Observable distance for inspiraling binaries (SNR=10, optimal direction and polarization)

DT9

DT6

TAMA300 covers most part of our Galaxy

DT6: 33kpc (～ 18kpc for SNR=8, sky-averaged)



1.4 Msolar binary inspirals

DT8

Data taking run (2)- Observable range -

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Binary inspirals

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10

0

-10

18.0017.9817.9617.9417.92s

•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.

“chirp” (frequency and amplitude grow with time) neutron starblack hole

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Mass range

• Mass range : 1-3Msolar for each member stars

(1Msolar,1Msolar) (1.4Msolar,1.4Msolar) (3Msolar,3Msolar)

Max. freq. 2198Hz 1570Hz 732Hz

Orbital radius at 100Hz (total mass unit)

47M 37M 22M

Time from 100Hz to ISCO or maximum frequency

3.78 [sec] 2.15 [sec] 0.60 [sec]

Cycle of wave from 100Hz to ISCO or maximum frequency

605 [cycle] 345 [cycle] 97 [cycle]

Observable frequency of TAMA300 ： 100Hz 〜 2kHz

Basic physical value of binary inspirals

ISCO: inner most stable circular orbit (where the inspiral ends, and the final plunge and the coalescence begins)

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• 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

)()()( tntAhts +=

Matched filtering

a measure of the deviation of events from real signal.

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χ 2

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Sn ( f )

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ρ(tc,m1,m2 ,K ) = 2˜ s ( f )h*( f )

Sn ( f )∫ df

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Chi square cut- statistic -ζ

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.

)(/ 2 ζχρ ≡

*ζζ > *ζζ

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χ 2

triggers by test Galactic signals

DT9 triggers

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Comparison of detection efficiency

Results of the Galactic signal injection simulation

ζ threshold

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Data length

blue: analyzed data, but not used for upper limit evaluationred: analyzed data used for upper limit evaluation

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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.

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Decision of threshold

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log10 N(> z) = a0 + a1 log10(z + p −1)

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log10 (z + p −1) threshold

We assume the following functional form of the trigger distributionand 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.

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z ≡1

2ζ 2 =

1

2

ρ 2

χ 2

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(p =16)

Threshold = 2.24 for the false alarm rate = 1/yr

We determine the threshold of ζ for a given false alarm rate (1 event/yr)

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Upper limit to the event rate

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Ri =N i

Tiε i

, i = DT6,DT8,DT9

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Ti : length of data, ε i : Detection efficiency

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N i is the upper limit to the number of events derived by

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Nbg： estimated number of triggers which exceed the threshold： observed number of triggers which exceed the threshold

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Nobs

Upper limit to the event rate

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Ti

Data length [hours]

Nbg Threshold of ζ

(false alarm rate = 1 /yr)

Ni

(C.L.=90%)

Detection probability of Galactic signals

Upper limit to the Milky Way Galaxy events [events /yr] (C.L.=90%)

DT6 876.6 0.1000 21.8 2.3 0.18 130

DT8 1100 0.1255 13.7 2.3 0.60 30

DT9 486.1 0.0555 17.7 2.3 0.69 60

Upper limit (1)

€

+59

−29

€

+4.9

−4.6

€

+8.0

−4.6

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

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Systematic errors

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.

1. Error of the detector calibrationAlthough it is expected to be less than 5%, it is not know exactly. We take a conservative value (+-10%)

4. Uncertainty of threshold (for a given false alarm rate)

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Systematic errors (2)

DT6 DT8 DT9

Threshold+0.001-0.000

+0.031-0.024

+0.013-0.022

Monte Carlo injection +/- 0.093 +/- 0.014 +/- 0.080

Calibration+0.034-0.028

+0.045-0.041

+0.040-0.039

+0.035-0.029

+0.056-0.049

+0.042-0.045

Wave form -0.028 -0.041 -0.039

Binary distribution model +/- 0.028 +/- 0.032 +/- 0.031

+0.028-0.056

+0.032-0.073

+0.031-0.070

Summary of the effects of the systematic errors to the detection efficiency of Galactic signals

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Ti

Data length [hours]

Nbg Threshold of ζ


Ni

(C.L.=90%)



DT6 876.6 0.1000 21.8 2.3 0.18 130

DT8 1100 0.1255 13.7 2.3 0.60 30

DT9 486.1 0.0555 17.7 2.3 0.69 60

Upper limit (1)

€

+59

−29

€

+4.9

−4.6

€

+8.0

−4.6

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

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Upper limit (2)

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Rcombined =NUL

Tiε i

i

∑

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NUL： Upper limit to the number of events which exceed the threshold by all of the observation

We combine these upper limits from each observation run, and derivean upper limit by

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Rcombined =17−1.51+3.02 [yr -1] (C.L. = 90%)

To obtain conservative upper limit, we take larger value as a final upper limit

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R = 20 [yr -1]

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Summary and discussion

•We performed the the analysis of TAMA300 data to searchfor 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.

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End

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Upper limit to the Galactic events

DT8 gives the most stringent upper limit because 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.)

Ti

Data length [hours]

Nbg Threshold of ζ


Ni

(C.L.=90%)



DT6 876.6 0.1000 21.8 2.3 0.18 130

DT8 1100 0.1255 13.7 2.3 0.60 30

DT9 486.1 0.0555 17.7 2.3 0.69 60€

+59

−29

€

+4.9

−4.6

€

+8.0

−4.6

Documents

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