bounding the strength of a stochastic gw background in ligo’s s3 data

GWDAW-9, Annecy - 12/16/04

LSC/SB 1

Bounding the strength of a Stochastic GW Background

in LIGO’s S3 Data

Sukanta Bose (Washington State University, Pullman)

for the LIGO Scientific Collaboration

LIGO DCC No. LIGO-G050536-00-D


LSC/SB 2

SGWB: Properties

Individual detector

strain: Zero mean

Covariance:

SGWB power

spectrum:

What are we bounding?

0~

fhA

'2

1'

~~* ffffSfhfh ABgwBA

fd

fdf gw

gw ln

1

critical

32

20

10

3

f

fHfS gw

gw

[Christensen, PRD46 (1992)]


LSC/SB 3

The Search Statistic

Cross-correlation

(CC) statistic:

Theoretical mean

of CC statistic:

Theoretical variance:

Optimal filter:

fQffSdfT

ABgw

~

2

2

2 ~

4fQfPfPdf

TBA

)()()()(

~3 fPfPf

ff

fPfP

ffSfQ

BA

ABgw

BA

ABgw

QhhKttQththdtdtY BA

T

T

BA ,,''2/

2/

[Allen-Romano, PRD59, 102001 (1999)]


LSC/SB 4

The Search Statistic (contd.)

The optimal cross-correlation(CC) estimator is:

And the (inverse of the)optimal theoretical variance is: The measured Omega is:

i = 1 2 3 …

t

60sec

ii

iii Y

Y2

2

opt

i

i22

opt TYh opt2

1000


LSC/SB 5

S3: Reference sensitivities The figure shows the

typical equivalent-strain noise-densities of the 3 LIGO detectors during S3. Also shown is the strain density corresponding to a stochastic background with

40 10

2410

50 100 500 Frequency (Hz)

1810


LSC/SB 6

Optimallycombine Y

i ,

i2

Compute CC statistic Yi

Downsample, HP filter, Freq-mask & calibrate

Compute optimal filter Qi

and theoretical variance i2

Estimate PSDs (using prev & next segs)

Window & FFT

Detector 2 -60 sec data segments

Detector 1 -60 sec data segments

Downsample, HP filter,Freq-mask & calibrate

Estimate PSDs (using prev & next segs)

Window & FFT

Post-processing

Softwareinjections

Analysis pipeline

2 21 1 2 2{ , , , ,... } Y Y ˆ 1.28gw gw


LSC/SB 7

Choice of frequency cut-offs

Frequency bandwidth chosen from 70 - 220 Hz (H1-H2)

Overlap reduction functionsSensitivity vs Max cut-off for H1-H2 (S3)

0 50 100 150 200 250 300

Frequency (Hz)

50 100 150 200 250 300 350 400 450 500 Max. cut-off frequency (Hz)

[Flanagan, PRD48, 2389 (1993)]

0

1


LSC/SB 8

S3: H1-H2 Frequency mask

60 80 100 120 140 160 180 200 220

Frequency (Hz)

110 112 114 116 118 120 122 124 126 128 13010

-6

10-5

10-4

10-3

10-2

10-1

100

Co

her

ence

Frequency (Hz)


LSC/SB 9

Sigma-cut of data intervals Sigma-integrand is proportional to

1/(P1*P2) P1, P2 estimated using data outside

of 60s interval being analyzed, to avoid bias in cross-correlation

Not good PSD estimators when the noise is non-stationary over this time period

Compare this PSD to that computed with data in the interval; reject interval if they don’t agree

PI

t

60s


LSC/SB 10

Sigma-cut of data intervals Sigma-integrand is proportional to

1/(P1*P2) P1, P2 estimated using data outside

of 60s interval being analyzed, to avoid bias in cross-correlation

Not good PSD estimators when the noise is non-stationary over this time period

Compare this PSD to that computed with data in the interval; reject interval if they don’t agree

PI

t

60s

60 0

5

00

(S2) cutsoutlier with H1L1 of Histogram 00


LSC/SB 11

S2 H1-L1 analysis: Distribution of the

theoretical

Distribution of the theoretical S2

/


LSC/SB 12

S3 H1-H2 analysis: Distribution of the

theoretical

Distribution of the theoretical S3

Abs

S3 data was more non-stationary.


LSC/SB 13

H1-L1 analysis: Long-duration features in CC-statistics (S2)

Time (in days)

CC

-sta

tis

tic

5 15 25 35 45

S2 data was treated as “playground” for S3, esp., to check for long-duration trends.


LSC/SB 14

H1-L1 analysis: Lombe-Scargle Power Spectrum of CC statistics (S2)

Injected line at 1/f = 1 hour

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Frequency (in mHz)

Po

wer

1 day 10 min


LSC/SB 15

H1-L1 analysis: Distribution of the Power of the CC-statistics (S2)

0 2 4 6 8 10 12

Power

N

1

1000


LSC/SB 16

H1-L1 analysis: CC statistic trend (S2)

PRELIMINARY


LSC/SB 17

H1-L1 analysis(S2): Kolmogorov-Smirnov test

The K-S value of 0.483 implies that the distribution is close to normal. i

i Relative freq.

Relativefrequency

0.483 test

Smirnov-Kolmogorov

2/exp Curve 2

x

011.0

23249

2

yx

xy

N

0 9 10-5

0

-5


LSC/SB 18

S3 results: H1-H2Error-estimate (+3 plotted for the H1-H2 pair as a function of run time.

410


LSC/SB 19

S3 results: H1-L1Error-estimate (+3 plotted for the H1-L1 pair as a function of run time.

310


LSC/SB 20

LIGO results history on gw

h100

2

LIGO run H-L H1-H2 Freq range Observation Time

S1*

< 23 +/- 4.6

(H2-L1)

Cross-correlated instr. noise

found40-314 Hz

64 hours

(08/23/02 – 09/09/02)

S2< 0.018

+0.007- 0.003

(H1-L1)

Cross-correlated instr. noise

found 50-300 Hz

387 hours

(02/14/03 – 04/14/03)

S3 ??

Can account for instrument noise

in bounding 50-250 Hz (H1-L1)

70-220 Hz (H1-H2)

~350 hrs (H1-L1)

~550 hrs (H1-H2)

(10/31/03 – 01/09/04)

*[The LIGO Collaboration, PRD 69, 122004, (2004)]

PRELIMINARY


LSC/SB 21

Summary The current best IFO-IFO upper-limit (published) is from S1: 23 (+/-4.6)

» S2 bettered it to 0.018 (+0.007- 0.003) (PRELIMINARY)» The S3 studies are set to improve that

H1-H2 is the most sensitive pair, but it also suffers from cross-correlated terrestrial noise. H1-H2 coherence found weak in most frequency bands, except ~120Hz and ~180Hz; steps taken to excise these bands from analysis (in addition to frequency masking of certain lines).

The observed properties of the search statistics for the H1-H2 and H1-L1 pairs, after correcting for biases and known systematics, were found to closely fit the expected ones.

It now remains to run the search pipeline on the S3 science data to obtain upper-limits / confidence belts for a constant

Beyond current analysis:» Search for (f) ~ n(f/f0)n

» Targeted searches


LSC/SB 22

H1-L1 analysis: Long-duration features in CC-statistics (S2)

S2 data was treated as“playground”for S3, esp., to check forlong-durationtrends.

bounding the strength of a stochastic gw background in ligo’s s3 data

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