GWDAW10, UTB, Dec. 14 - 17, 2005 1

Search for inspiraling neutron star binaries using TAMA300 data

Hideyuki Tagoshi

on behalf of the TAMA collaboration

GWDAW10, UTB, Dec. 14 - 17, 2005 2

Outline

I will describe the revised analysis of the binary neutron star search using TAMA300 data.

The data we use is TAMA DT6, DT8, and DT9 data.

Mass range: 1-3M_solar (for each member star)

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Data Taking ObjectiveObservation

timeTypical strain noise level

Total data(Longest lock)

DT1 August, 1999 Calibration test 1 night 3x10-19 /Hz 1/210 hours

(7.7 hours)

DT2 September, 1999 First Observation run 3 nights 3x10-20 /Hz 1/2 31 hours

DT3 April, 2000Observation with

improved sensitivity3 nights 1x10-20 /Hz 1/2 13 hours

DT4Aug.-Sept.,

2000100 hours'

observation data2 weeks

(night-time operation)1x10-20 /Hz 1/2

(typical)167 hours

(12.8 hours)

DT5 March, 2001100 hours' observation with high duty cycle

1 week(whole-day operation)

1.7x10-20 /Hz 1/2

(LF improvement)111 hours

DT6Aug.-Sept.,

20011000 hours'

observation data 50 days 5x10-21 /Hz 1/21038 hours(22.0 hours)

DT7Aug.-Sept.,

2002Full operation with

Power recycling2 days 25 hours

DT8Feb.-April.,

20031000 hours

Coincidence2 months 3x10-21 /Hz 1/2

1157 hours(20.5 hours)

DT9Nov. 2003 -Jan., 2004

Automatic operation

6 weeks 1.5x10-21 /Hz 1/2 558 hours(27 hours)

Data taking run (1)- Observation runs -

• TAMA observation runs

This presentation

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56

1

2

3

456

10

2

3

456

100

2

3

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

Now, TAMA300 covers most part of our Galaxy

DT6: 33kpc

DT8: 42kpc

DT9: 72kpc

(～ 30kpc on average)

1.4 Mo binary inspirals

DT8

Data taking run (2)- Observable range -

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Revised analysis

Difference from the analysis so far

• DT6: mass range 1-2M_solar (PRD70,042003(‘04))

=> 1-3M_solar

• DT8: In the previous analysis, calibration data was not taken into account properly, due to the error of file format. We have redone the analysis.

(This was applied to LIGO-TAMA S2-DT8 inspiral analysis too.)

• DT9: new results (initial results were reported at Amaldi6)

• Systematic error is estimated.

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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.

We search the parameter space.

We need to 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.

B. Allen, PRD 71, 062001 (2005)

€

χ 2

€

Sn ( f )

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We use as the 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.

Chi square cut- statistic -ζ

)(/ 2 ζχρ ≡

*ζζ >*ζ

ζ

€

χ 2

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Comparison of DT6, DT8 and DT9 efficiency

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DT6, DT8, DT9 trigger lists

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In the case of Gaussian noise, the square of , or ,

obeys the F distribution with the degree of freedom (2,2p-2).

Decision of threshold

€

z =1

2ζ 2 =

1

2

ρ 2

χ 2

(p: the number of division of a template in the definition of chi^2. In our case, p=15. )

The probability density function g(z) of z is given by

€

g(z) = ( p −1)p (z + p −1)− p

€

N(z) ≡ d ′ z z

∞

∫ g( ′ z ) = (p −1)p−1(z + p −1)− p +1

Thus, in Gaussian case, if we make a log(N(z))-log(z+p-1) plot of the triggers, it becomes linear with slope=-p+1.This suggest that z+p-1 is a more natural variable for the estimation of the false alarm rate than .

€

ζ

€

ζ

and

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DT9 threshold (1)

€

log(1

2ζ 2 +15)

Looks like linear,although the slope is Different from Gaussiancase

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DT9 threshold (2)

€

log(1

2ζ +15)

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

€

log(1

2ζ 2 +15)

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DT8 threshold

€

log(1

2ζ +15)

Threshold = 2.04 for the false alarm rate = 1/yr

€

log(1

2ζ 2 +15)

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DT6 threshold

Threshold = 2.40 for the false alarm rate = 1/yr

€

log(1

2ζ 2 +15)

Unfortunately, the DT6 distribution does not look like linear even in this log-log plot.

It is not easy to have accurate estimate of the false alarm rate.

Thus, we take a very large value of the threshold to have a conservative upper limit.

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Systematic errors (1)

1. Uncertainty of Galactic simulation Uncertainty of mass distribution Uncertainty of the position of solar system in our Galaxy Error due to finite number of simulation

2. Uncertainty of ρ due to uncertainty of theoretical wave form -10% at most.

3. Calibration errorIt is not know exactly (although it is expected to be less than 5%).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

Uncertainty of the binary distribution model

+0.03

-0.04

+0.03

-0.05

+0.03

-0.05

Error of Monte Carlo injection

+0.01

-0.01

+0.01

-0.01

+0.01

-0.01

Uncertainty of wave form -0.03 -0.04 -0.04

Calibration error+0.03

-0.03

+0.05

-0.04

+0.04

-0.04

Uncertainty of threshold+0.00

-0.00

+0.03

-0.02

+0.01

-0.02

Total error of efficiency+0.05

-0.05

+0.07

-0.08

+0.05

-0.07

preliminarysummary

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Upper limit to the Galactic events

Data length [hours]

Mass range of a member star

[Msolar]

Detection probability of Galactic signals

Threshold of ζ

(false alarm rate = 1 /yr)

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

DT6 876 1-3 0.18 21.8 130

DT8 1100 1-3 0.60 13.7 30

DT9 486 1-3 0.69 17.7 60

€

+0.05

−0.07

€

+0.07

−0.08

€

+0.05

−0.05

€

+7

−4

€

+5

−3€

+50

−30

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.)

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Summary

Reanalysis of DT6 and DT8, and the analysis of DT9 to searchfor the neutron star binaries were done.

•the low mass binary black hole•higher mass bh-bh and/or bh-ns binaries with spin

We will perform the search for

in the near future

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DT8 threshold (1)

€

log(1

2ζ 2 +15)

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DT6 threshold (1)

€

log(1

2ζ 2 +15)

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DT6, DT8, DT9 trigger lists

€

ζ −logN(> ζ ) plot