N.KandaMiyagi Univ. of Education

Data Analysis of TAMANobuyuki Kanda

the TAMA collaborationsMiyagi University of Education, National Astronomical Observatory, University of Tokyo, University ofElectro-Communications, High Energy Accelerator Research Organization, Osaka University, Kyoto

University, Max-Planck-Institut fur Quantenoptik, National Research Laboratory of Metrology, HirosakiUniversity, Kinki University,

Tokyo Denki University, Osaka City University, Tokai University,Tohoku University, Niigata University, Hiroshima University

TAMA symposium2/6/2002

Hongo, Tokyo

N.KandaMiyagi Univ. of Education

Data Taking History

Period actual data amount

Data Taking 1 (DT1) 8/6-7/1999 (one night) ~3 + ~7 hours continuous lock

DT2 first Phyics run 9/17-20/1999 31 hours

DT3 4/20 - 4/23/2000 13 hours

DT4 8/21 - 9/3/2000 167 hours

DT5 3/1 - 3/8/2001 111 hours

Test Run 1 6/4 - 6/6/2001Longest stretch of continuous lock is 24hours 50min.The interferometer can operate in daytime of weedkay.

DT6 8/1 - 9/20/2001 1038 hours with duty cycle 86%h ~ 5×10-21 [1/√Hz]

1999-12-2

5

Detector Schematics (DAQ)

AD

C(S

ON

Y te

ktro

nix

VX

4244

)

SCSI

2GB

2 GB * 4 Disks1st level spool disk

DLT tape system(5 tapes at once)

UNIX Workstation(SUN Enterprise 450, OS Solaris 2)

VXI crate

intranet

2GB 2GB 2GB

Main IF signal * 7chL- feedback,Calibration Referenceetc.

20 kHz trigger signal(generated from 10MHz GPS clock)

IRIG-B time coded signal

MIX BUS Interface

• Continuous Data Taking• IF Calibration Signal Record

On-line analysis (1)

— Data acquisition system —

11

HDAQ raw data

MDAQ raw data

EPICS raw data

Mirror of HDAQ

crhsun1

online analysis (MF, SNR)

online analysis (IF diag., mdaq)

signals

signals

fft

mdaq

crhsun2

signals

VME

DAQ front end

ADC-SCSI

VXI-MXI

DLTHardDisk

Acquisition ArchiveSpool & Transfer

cresun1

NFS server

NFS server

~daq/online_monitor/copyRecent

DAQ processes(tqStart)

DAQ processes

DAQ processes (tqEpics)

scp

EPICS print taskprint out

NFSNFS

NFS

/export/home*/R*F*.raw

/usr4/

~daq/hdaq_mirroring

/import/usr4/onlmon/spool/

/data/hdaq/

/data/mdaq/

/import/data/hdaq/

/import/data/hdaq//import/data/mdaq

~daq/src/tqEpics/copyEdata

~daq/online_monitor/startMon

~daq/epics_monitor/startEmon

Monitor: HdaqMon

Monitor: MdaqMon

Monitor: EpicsMon

display

Monitor: ArchiveMon

N.KandaMiyagi Univ. of Education

DAQ and pre-process

DAQ systemDAQCalibration

accuracy ∆h/h ~1%

Pre-ProcessCut-out observation data

remove unlock or tuning periods

h(f) : strain equivarent spectrum calculusv(t)-> v(f) T(f) -> h(f)

Analysis

N.KandaMiyagi Univ. of Education

Two issues of the data analysis

Detector evaluation

IF operation stability, gaussianity

Detection Feasibility

GW search

Stochastic

Binary Coalescence

Burst

Continuous

N.KandaMiyagi Univ. of Education

Sensitivity / Data amount,and possible issues

before DTSimulationMethod study

DT1 / DT2 : a few night runCalibrationOff-line data selectionStability, non-Gaussinanity checkMatched filter analysis

DT3 / DT4 : more than 100 hours, operation in nightVeto analysisIF diagnosisContinuous analysis

DT5 : preparation of 1000 hoursDT6 : 1000 hours

Fast IF diagnosisExpected SNR monitor

= Real time monitor, feedback to the detector operation

02.2.6

7

Calibration

1.0

1.2

1.4

1.6

1.8

2.0

Sep 1920:00

Sep 1922:00

Sep 2000:00

Sep 2002:00

Sep 2004:00

Sep 2006:00

Gai

n

Time

Drift of openloop TF at 625 Hz

40

30

20

10

0

yield

-4 -2 0 2 4

delta G between 16 frames/mean at time [%]

'measured'

'gauss fit (result: 1sigma

Gain drift for night ~ 30%

Calibration accuracy ∆h/h ~ 1% @625Hz

run12 (DAQ 2)

02.2.6

6

DAQ 2 & DAQ 3: Noise Instability

noise average around 1kHz

run12 (DAQ 2)

run34 (DAQ 3)

run35 (DAQ 3)

9 hours

1e-21

1e-20

1e-19

1e-18

08/01 08/02 08/03 08/04 08/05 08/06 08/07 08/08

SN

R

1e-21

1e-20

1e-19

1e-18

08/08 08/09 08/10 08/11 08/12 08/13 08/14 08/15

SN

R

1e-21

1e-20

1e-19

1e-18

08/15 08/16 08/17 08/18 08/19 08/20 08/21 08/22

SN

R

1e-21

1e-20

1e-19

1e-18

08/22 08/23 08/24 08/25 08/26 08/27 08/28 08/29

SN

R

1e-21

1e-20

1e-19

1e-18

08/29 08/30 08/31 09/01 09/02 09/03 09/04 09/05

SN

R

1e-21

1e-20

1e-19

1e-18

09/05 09/06 09/07 09/08 09/09 09/10 09/11 09/12

SN

R

1e-21

1e-20

1e-19

1e-18

09/12 09/13 09/14 09/15 09/16 09/17 09/18 09/19

SN

R

1e-21

1e-20

1e-19

1e-18

09/19 09/20 09/21 09/22 09/23 09/24 09/25 09/26

SN

R

tuning or unlock stateh at 1 kHz

h at 100 Hz

Sensitivity History of Data Taking 6

0 10 20 30 40 50 60 70 80 90 100N/O

Obs

HDAQ Data Analysis and Monitor (ver 2.10), Run : 107, File : 1200 Start : 52155 MJD, Sep 02, 2001, Sun, 09:35:21 JST, Current : 52155 MJD, Sep 02, 2001, Sun, 11:23:29 JST

Ob

serv

atio

n

S

tatu

s

Obs.

0 10 20 30 40 50 60 70 80 90 1000

0.10.20.30.40.5

Dar

k P

ort

P

ow

er 0.07192 [V]0.0117 [V

rms]

0 10 20 30 40 50 60 70 80 90 100

100

Op

en−L

oo

p

Gai

n

1.676432.3 [deg]

0 10 20 30 40 50 60 70 80 90 10010

−21

10−20

10−19

10−18

No

ise

Lev

el (

935H

z)

9.762e−21 [1/Hz1/2]

0 10 20 30 40 50 60 70 80 90 100

0

1

2

Exc

ess

(G

auss

ian

ity)

Time (min.)

0.2223

On-line analysis (2)

— On-line monitor —

• One of the monitor screens for HDAQ

· Obs. status, power, servo gain, averaged noise level, excess.

12

0 5 10 15 20100

102

104

Co

un

ts

Excess

c2=1(F.A. <10ppm)

DT6 total

Theoritical distribution(Simulated Gaussian noise)

0 1 2 3100

101

102C

ou

nts

Excess

c2=1(F.A. <10ppm)

DT6 total

Theoretical distribution(Simulated Gaussian noise)

Quiet period

(nornalized)

c2=0.19(F.A. 3%)

(10hours, Aug. 06 night )

Interferometer diagnosis (6)

— Gaussianity evaluation —

• Excess (Gaussianity)

— evaluated in every 1 min.

· Gaussianity parameter

c2 : 1 (F.A < 10ppm)

— 14.0%.

· Quiet hours

· Threshold F.A.: 3%

— 11.3%.

→ Slightly larger

Consistent distribution.

⇓· Investigation with

the other signals.

9

N.KandaMiyagi Univ. of Education

Detector evaluation: Veto Analysis

HDAQ signals (DT4)

Y`i\c4 L-��

Y`i\c6 ��]gRK w���

Y`i\c9 d%V%�¦��

Y`i\c: ¢¶�¨��

Y`i\c; L+��

Y`i\c= X%T^%[K �����

<���K��Q¬D��>

FFT

,G(f)

<h(f)300Hz>

¦�

300Hz

¦�

<h(f)700Hz>

700Hz

<h(f)1kHz>

¦�

1kHz

vetovetovetoveto

<h(f)300Hz>

¦�

300Hz

¦�

<h(f)700Hz>

700Hz

<h(f)1kHz>

¦�

1kHz

Pass

«~  $ ­y

��

(5.7#5.8��)

V(f)

V(t)V(t) V(t) V(t)

¹¡K�£(5.4��)&���B®p£F "?M'GDM·u(CK·uJ§EMZ*WQ��DM)"

���K��K©j(5.3��)

S1frame = Σ{V(t) } K¦�²¯   2

V(t)

h(f) ´��J <h(f)300Hz>#<h(f)700Hz># <h(f)1kHz>Q��(5.5��)

10HzªqF³�DM

h(f) KUb]

log

log1/2Hz

Hz

300Hz 700Hz 1kHz

1]d*_µJS1frame = Σ{V(t) } K ��

1]d%_=3.2768s

V(t)

s

V(t)

s

|�±K2�¡K ¸QGM

}�

¦�

S1frame

��²¯J�A

¦�

S1frame

Nσ Nσ

¦�

S1frame

ln

¦�

S1frame

ln

����¤�M°@

xth

{�JL®¥{�JL®¥{�JL®¥{�JL®¥

¦�

S1frame

��²¯J�OI@

V(t)

2

図5.18:

veto解析の流れ

47

26x10-6

24

22

20

18

16

S1frame[V2]

500040003000200010000

N

図 5.5: ADCチャンネル 4·地面振動信号の振幅 2乗和 S1frame 　縦軸は振幅 2 乗和 S1frame[V

2]、横軸は計算したフレーム数 (×3.2768 秒)を表している。

図 5.6: ADCチャンネル 4·地面振動信号の振幅 2乗和 S1frameの度数分布 　縦軸は度数、横軸は振幅 2乗和 S1frame[V

2]を表している。赤実線はガウスでフィッティングしている。この分布は正規分布に従うと見なす。

37

80

60

40

20

0

[%]

5654525048464442

run

AND

ch2

ch3

ch4

ch6

図 5.26: 干渉計の状態を表す信号別に表した 1kHz付近の < h̃(f) >1kHz 分布の µh1k±5σh1kの範囲外での雑音除去率 　縦軸は信号の取り除かれた割合、横軸は run番号である。ch2は実験フロアの音響、ch3はレーザー強度、ch4は地面振動、ch6はダークポートの干渉光強度信号、ANDは干渉計の状態を表す信号の条件すべてを合わせた場合を表す。取り除く前の < h̃(f) >1kHz

分布の µh1k±5σh1k 以外の度数を 100[%]とした。

図 5.27: veto前後での < h̃(f) >700Hz の度数分布の変化白抜きのグラフがデータを veto前、網掛けのグラフが veto後の度数分布。縦軸は logスケールで、赤実線はガウスにフィッテイングしてある。平均値より離れたデータほど雑音が取り除かれていることがわかる。

53

60

50

40

30

20

10

0

SN

R

10-12 3 4 5 6 7 8

1002 3 4 5 6 7 8

1012

Expected SNR to binary mergers at 10kpc

[Msolar]

2001/8/3DT6

2001/6/2

2000/9/4DT4

mass of a member star

05

10152025303540

08/01 08/02 08/03 08/04 08/05 08/06 08/07 08/08

SN

R

05

10152025303540

08/08 08/09 08/10 08/11 08/12 08/13 08/14 08/15

SN

R

05

10152025303540

08/15 08/16 08/17 08/18 08/19 08/20 08/21 08/22

SN

R

05

10152025303540

08/22 08/23 08/24 08/25 08/26 08/27 08/28 08/29

SN

R

05

10152025303540

08/29 08/30 08/31 09/01 09/02 09/03 09/04 09/05

SN

R

05

10152025303540

09/05 09/06 09/07 09/08 09/09 09/10 09/11 09/12

SN

R

05

10152025303540

09/12 09/13 09/14 09/15 09/16 09/17 09/18 09/19

SN

R

05

10152025303540

09/19 09/20 09/21 09/22 09/23 09/24 09/25 09/26

SN

R

tuning or unlock state10-10 Msolar

1.4-1.4 Msolar0.5-0.5 Msolar

Expected SNR history for typical GW event at 10kpc away

Histogram of Expected SNR for DT6

0.5Msolar-0.5Msolar

10Msolar-10Msolar

1.4Msolar-1.4Msolar

Total Timetime expected SNR > mean - 1s

expect. SNR expect. SNR

expect. SNR

entr

y by

bin

(cal

cula

ted

for

1 m

in.)

entr

y by

bin

(cal

cula

ted

for

1 m

in.)

80.51%82.37%83.32%

for 0.5-0.5Msolarfor 1.4-1.4Msolarfor 10-10Msolar

-> Efficent operation status is more than 80%

N.KandaMiyagi Univ. of Education

GW search: Binary inspiral

Matched filterOne step search

Hierarchical search

Wavelet

Resampling

講演者: 神田展行 (宮城教育大 ) 日時: 12/8/2001 シート12

連連連連星星星星のののの出出出出すすすす重重重重力力力力波波波波 (2)

-15

-10

-5

0

5

10

15時

空の

歪み

（相

当）

15s1050[sec]

20

10

0

-10

x10-1

8

18.0017.9817.9617.9417.92s

拡大

講演者: 神田展行 (宮城教育大 ) 日時: 12/8/2001 シート18

ママママッッッッチチチチドドドドフフフフィィィィルルルルタタタターーーー法法法法 (2)

20

10

0

-10

-20

x10-1

5

18.0017.9517.9017.85

20

10

0

-10

-20

x10-1

5

18.0017.9517.9017.85

20

10

0

-10

-20

x10-1

5

18.0017.9517.9017.85

20

10

0

-10

-20

x10-1

5

18.0017.9517.9017.85

信号

ベストマッチ (黒線が予想波形)

Matched filter• Detector outputs:

：　known gravitational waveform (template)： noise.

• Outputs of matched filter:

• noise spectrum density

• signal to noise ratio • Matched filtering is the process to find optimal

parameters which realize

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

ρ ( , , , . . . )~ ( )

~( )

( )

*

m m ts f h f

S fd fc

n1 2 2= z

max ( , , ,...), , ,...m m t c

c

m m t1 2

1 2ρFH IK

SNR = /ρ 2

Post-Newtonian approximation

( )nS f

Matched filtering analysis

tRead data

FFT of dataApply transfer function

Conversion to stain equivalent data

overlaps

Evaluate noise spectrum near the data( )nS f

　　　　　　　　1 2( , , )ct m mρ

max ( , , , .. . ), , ,...m m t

cc

m m t1 2

1 2ρFH IK

Event list

2 2c ct t

c c ct t t∆ ∆− ≤ ≤ +∆ ; 25ct ms

52 sec

00.7.1

10

DAQ2: Preliminary Result of Binary SearchPreliminary Result of Binary Search

with SNRthreshold = 7.2 (which corresponds to 6.2 kpc for 1.4-1.4Msolar event, 2.9 kpc for 0.5-0.5Msolar event, optimal incident direction and polarization),

2 events survived / 2.5 expected background-> 0.59 events/hour in C.L.90%

1

10

100

Number of events/bin

80604020

SNR2

background expect NBG = 2.5

χ2 < 2.5 χ2 < 1.5 χ2 < 1.0 fitting to χ2 < 1.5

prelim

inary

2/ρ χ)

Log

10[N

umbe

r of e

vent

s]

12.7

Discussion•Coalescing compact binary search of TAMA300, 1000 hours data and LISM data, are progressing.

•We have not observed events, which significantly exceed the threshold in both TAMA and LISM’s independent analysis.

•Even in the case if there are no significant events, we can still obtain upper limit to the event rate in the data using e.g. Poisson statistics.

•With 1000 hours data, we will be able to set an upper limit ～0.004 events /hours

c.f.: Caltech 40m : 0.17/hours (90% C.L.)

TAMA DT2 : 0.59/hours

TAMA DT4 : 0.020/hours

01.12.10

20

Wavelet

testing code (discrete)

expected SNR evaluation

(H.Yakura, N.Kanda)

11/9/97 3

TAMA group / Department of Physics, Miyagi University of Education Nobuyuki Kanda

A principle of the Resampling method

for GW from binary starts

To recognize GW as a sinusoidal wave, distort time axis according to the GW frequency changing.

-> “Re-sample” ADC sampling data

dt = omega(t) / omega_cutoff

resampling interval : dt

omega(t) : frequency prediction of GW at t

(-> template of GW)

omega_cutoff : cutoff frequency of resampling

• must be chosen less than coalescence frequency

• in current study, we choose cutoff as500 Hz in Keplar Motion in this analysis ( near by 1000 Hz in GW )

"resampling" points

constant sampling interval

distort along the chirp freq.

11/9/97 13

TAMA group / Department of Physics, Miyagi University of Education Nobuyuki Kanda

Check3. How many templates we need?

6x10-21

5

4

3

2

1

exc

ess

heig

ht

in F

FT

-20x10-3

-10 0 10

template arrival time parameter [sec]

4

6

81

2

4

6

810

2

4

6

8100

2

S/N threshold

arrival time interval

Typical interval: ∆t0 ±5msec (or =itaration interval/5msec)

01.12.10

18

Continuous GW from1987A remnant

(K. Soida)

01.12.10

19

(K. Soida)

N.KandaMiyagi Univ. of Education

New issue : Coincidence

Coincidence between two or more detectors !Event candidates list comparison

coherence of ρρρρ(t) = (signal | GWtemplates)

constraint of arrival time, mass

assumption of waveform

correlation of full time series data h(t)

01.12.10

21

TAMA-LISM coincidence

Coincidence between LISM (20mIF in Kamioka mine) and TAMA300

Distance: 220 km (maximum delay for arrival time : 0.73msec)

LISM:

h ~ 8 × 10-20 [1/√Hz]

8/1 - 8/23/ 2001

9/3 - 9/17/2001 total 777 hours

　

TAMA　　　　　　　　　　　　　　　　　　　LISM　　　　　　　　　 data reading data reading

　　　　　　　　　　　　　　　　　　　　　　 　　　　　　　　　　 　　Matched filter 　　 Matched filter 　　　　

　　　

　　　　　　　　　　　　　TAMA event list LISM event list　　　　　　　　　　　　　　　　　　　　　　　　　　　 　　　　　　　　　　

　　　　　　　　　　　　　　　　　 keep the events in the common lock parts

　　　　　TAMA event list　 LISM event list 　　　　　　　　　　

　　　　　　for common lock parts　　　　　　　　　　　 for common lock parts

　　　　 coincident event search

TAMA－LISM Analysis Algorithm

2,, ,c lism lism lism lismlismt M η ρ χ2, , , ,η ρ χctama tama tama tama tamat M

• Data length analyzed～ 121 hours

)),,((max 21,2,1

…… ctmm

tmmc

ρ

2 2c ct t

c c ct t t∆ ∆− ≤ ≤ + 3.27ct s∆

)),,((max 21,2,1

…… ctmm

tmmc

ρ

2 2c ct t

c c ct t t∆ ∆− ≤ ≤ + 3.27ct s∆

Results of coincident event search

TAMA LISM 65672 events 56725 events

After -veto31 events

After -veto3 events

After -veto0 event

ct

, ,ct ηM

, , ,ct η ρM

Results of onestep search for common lock parts

N.KandaMiyagi Univ. of Education

LIGO-TAMA

International cooperation

How about combined performance ?stability

fake rate estimation

Where is promising search ?mass region

kind of sources

N.KandaMiyagi Univ. of Education

Summary

We prepared, and developed IFGW detector

analysis issues: IF evaluation from the view of event detector,

Event search (observational limit, experience of

real data)

We proceed to realistic event detection:Coincidence