Search for Gravitational Waves from Inspiraling Compact Binaries - - PowerPoint PPT Presentation

Search for Gravitational Waves from Inspiraling Compact Binaries using TAMA300 data

Hideyuki TagoshiA,Nobuyuki KandaB, Daisuke TatsumiC, Yoshiki TsunesadaC,and The TAMA Collaboration A,B,C,D,E,F…

Osaka University A,Osaka City University B,National Astronomical Observatory C,…

Hirotaka Takahashi

(Osaka University / Niigata University / YITP)

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

• mpact

binaries using TAMA300 data. binaries using TAMA300 data.

Coalescing compact binaries

Gravitational Waves Neutron stars Black holes 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.

Possibility of MACHO black hole

chirp signal

amplitude time

1

m

2

m

,

c c

t φ

A

3/5

M η

= M

: total mass : reduced mass

M

η

1 2

1.0 , 3.0 ≤ ≤

solar solar

M m m M

In this search, mass region:

1 2

1.0 , 2.0 ≤ ≤

solar solar

M m m M

for DT6 for DT8

History of TAMA300 Sensitivity for inspiraling for inspiraling compact binaries

• mpact binaries

DT6:Range (SNR=10) : 33kpc DT8:Range (SNR=10) : 42kpc

Matched filter

• Detector outputs:

： known gravitational waveform (template) ： noise.

• Outputs of matched filter:
• noise power spectrum density
• Signal to noise ratio is
• Find the parameter which realize the maximum of

for each certain interval of

s t Ah t n t ( ) ( ) ( ) = + h t ( ) n t ( )

* 1 2

( ) ( ) ( , , ,...) 2 ( )

c n

s f h f t m m df S f ρ = ∫

• 1

2

1 2 , , ,...

max ( , , ,...)

c

c t m m

t m m ρ

SNR = / ρ 2

2.5 Post-Newtonian approximation

( )

n

S f

ρ

c

t

∆

• (

25 )

c

t ms

• Divide each template into n mutually independent bins in

frequency domain.

• Test whether the contribution to from each bins agree with

that expected from chirp signal

fmin f1 f2 f3 f4 f5 fmax

• ρ1

ρ2 ρ3 ρ4 ρ5

• ρ

ρ ≡

F H G I K J

=

z

( , )

~( )~ ( ) ( )

*

s h

s f h f S f df

n

2

2 2

( ) ,

i i i i

n χ ρ ρ ρ ρ ≡ − =

∑

• The real data contained large amount of non-stationary and

non-Gaussian noise.

• In order to remove the influence of such noise, we also

introduce

2

χ

2 2/

( 2 2 ) ˆ n χ χ = −

(In this analysis n=16)

m a x m in

1 / 2 7 / 3

4 ( )

f f n

f d f S f

− −

     

∫

min max

100Hz, f 2500Hz f = =

DT8:2/14-4/14/2003 Variation of Noise power (1 minute average)

[1.09minutes]

DT6:8/1-9/20/2001

• Before the matched filter analysis, we examine

the fluctuation of noise power.

• The vale of noise power is evaluated for each data with length 1.1min.

Mean: Std.:

19

10− ×

19

10 − ×

DT6 DT8

19

3. 2 10− ×

19

1. 5 10− ×

19

1. 9 10− ×

20

7. 5 10− ×

Variation of Noise power (histogram) (2)

Mean: Std.:

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.

Noise power Number of occurrence Number of occurrence Noise power

Distribution of template number

DT6 DT8

• The variation of number of templates is not due to the variation of absolute amplitude
• f 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.

• 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.

• A discrete mass parameter space is determined so that the maximum loss of SNR

become less than 3%

Mass region :1‐2Msol Mass region :1‐3Msol

ρ ρ

2

ˆ χ

2

ˆ χ

DT6 DT8

Mass region :1‐2Msol Mass region :1‐2Msol

• We find from the distribution of that the DT8 result has longer tail than DT6 data.

Such events with large must be due to the non-Gaussian noise since the value of

• f them are also very large.
• The distribution of is also more spread in DT8 case than in DT6 case.
• Thus, in terms of the distribution of and , the stability of DT8 does not seem to

be better than DT6.

• However, most of events with large in DT8 have larger than that of DT6.

ρ ρ

2

ˆ χ

2

ˆ χ

2

ˆ χ

2

ˆ χ

ρ ρ

Log10[Number of events]

Log10[Number of events]

• We found that the value of becomes larger, when the

amplitude of signal becomes larger even if the events are real. In such situation, if we reject events simply by the value of , we may lose real events with large amplitude.

• We thus introduce a statistic , to distinguish between

candidate events and noise events

2

/ ρ χ

• 2

ˆ χ

2

ˆ χ

2

/ ρ χ statistics

Test signals

2

/ 12.5 ρ χ =

TAMA events

2

ˆ 1.5 χ =

TAMA events vs Galactic event

Compare DT6 results to DT8 results DT6 DT8

Log10[Number of events] Log10[Number of events]

2

/ ρ χ

• Mass region :1‐2Msol

Mass region :1‐2Msol

If GW events really happened, the value of would become much larger than tail of distribution.

2

/ ρ χ

• 2

/ 16.0 ρ χ =

• 2

/ 12.0 ρ χ =

• Threshold

Threshold

Fitting Set False alarm rate to 0.8 event/yr

Preliminary

Upper limit to the Galactic event rate

N T ε

• Ｎ ：Upper limit to the average number of events
• ver certain threshold
• Ｔ：Length of data [hours]
• :Detection efficiency

ε

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.

To estimate detection efficiency, we perform Galactic event simulation Threshold efficiency DT6 16 0.23 DT8 12

0.58

1 2

1.0 , 2.0 ≤ ≤

solar solar

M m m M

search mass region: (False alarm rate = 0.8 / year )

Galactic event detection efficiency

Efficiency of DT8 becomes three times better than that of DT6

Upper limit to the event rate: Poisson statistics

• Threshold
• Expected number of fake events over threshold：Nbg= 0.1 , 0.1
• Observed number of events over threshold: Nobs= 0 , 1

Assuming Poisson distribution for the number of real/fake events

• ver the threshold,

we obtain upper limit to the expected number of real events from

( )

( ) ! 1 ( ) !

= − + = = − =

+ = −

∑ ∑

• b s

b g

• b s

b g

n n N N N b g n n n N N b g n

N N e n C L N e n

N = 2.3 , 3.8 (C.L.=90%)

We evaluated upper limit to the average number of events

• ver certain threshold.

2

/ 12 ρ χ =

2

/ 16 ρ χ =

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 2

1.0 , 2.0 ≤ ≤

solar solar

M m m M

(False alarm rate = 0.8 / year )

Preliminary search results search results for inspiraling for inspiraling compact binaries compact binaries

We can obtain that upper limit of DT8 becomes about two times more stringent than that of DT6.

2

/ ρ χ

• Log10[Number of events]

Mass region :1‐3Msol

Uusing the DT8 search results (mass region:1-3Msol ), we estimate the upper limit to the galactic event rate.

2

/ 12.5 ρ χ =

• Threshold

Set False alarm rate 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)

• detection efficiency from Galactic event simulation:
• We also obtain upper limit to the average number of events
• ver threshold by standard Poisson statistics analysis

N = 2.3 (C.L. = 90%)

• Observation time T ＝ 1163 hours

0.61 ε =

0.0033 / hour ε = N event T

1 2

1.0 , 3.0 ≤ ≤

solar solar

M m m M

= 29 event/yr (C.L. 90 %)

Preliminary

Summary

We performed a event search for inspiraling a event search for inspiraling compact

• mpact

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)