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Results from TOBAs Cross correlation analysis to search for a Stochastic Gravitational Wave Background. University of Tokyo Ayaka Shoda M. Ando, K. Okada, K. Ishidoshiro , W. Kokuyama , Y. Aso , K. Tsubono. Prototype TOBA. 20-cm small torsion bar - PowerPoint PPT Presentation


Results from TOBAs New Upper Limit on a Stochastic Gravitational Wave Background

Results from TOBAs Cross correlation analysis to search for a Stochastic Gravitational Wave BackgroundUniversity of TokyoAyaka Shoda

M. Ando, K. Okada, K. Ishidoshiro, W. Kokuyama, Y. Aso, K. TsubonoPrototype TOBA

20cm20-cm small torsion barSuspended by the flux pinning effectof the superconductorRotation monitor: laser Michelson interferometerActuator: coil-magnet actuatorPrototype TOBA

SuperconductorTest massLaser sourceInterferometerPrevious Result

For the detection of a stochastic gravitational-wave background, simultaneous observation is necessary.Upper limit on a stochastic GW background


KyotoTokyoDATE: 21:30 7:30, Oct. 29, 2011Sampling frequency: 500 Hz, the direction of the test mass: north-southSimultaneous ObservationData Quality

Equivalent Strain Noise SpectraTokyoKyoto

SeismicMagnetic couplingData Quality

1098765432110-6SpectrogramTokyoKyotoGlitchesThe data should be selectedCross Correlation AnalysisConceptdifficult to predict the waveform of a stochastic GW backgroundSearch the coherent signal on the data of the two detectors.

Correlation Value: The signal of i-th detector

: The optimal filter (Weighting function)

Cross Correlation AnalysisIf not detectedDivide the time series data into 200sec long segmentsDelete 10% of the segments whose noise level is worstChoose the analyzed frequency band as 0.035 0.84 HzInject mock signals into the real data and calculate the detection efficiency

Detection threshold for false alarm rate 5%


ResultHistogram and Cross correlation valueResult upper limit

NEW!!4 times better

Extend exploredfrequency band95 % confidence upper limit

SummaryEstablished the pipeline of the cross correlation analysis with TOBAsThe stochastic GW background signal is not detected.Update the upper limit on a stochastic GW background at 0.035~0.840 Hz:

Backup slides

Data Selection Divide time series data into several segments Remove the segments in which RMS is big Calculate cross correlation with the survived segmentsTokyoKyotosegmentTimeCross Correlation Value

Optimal Filtera filter which maximizes the signal-to-noise ratio

Pi ( f ): PSD of i-th detectorOverlap reduction function: a function which represents the difference of response to the GWs between two detectorsIn the case of TOBAs, same as the interferometers oneIn this case,

Optimal filter

The frequency band where the optimal filter is the biggest is chosen as the analyzed frequency band.Optimal filter = big when the sensitivity to a stochastic GW background is goodUpper Limit

Mock signalHow big a stochastic GW background can we detect if it would come tothis data set?

Make a mock signal of a stochastic GW backgroundInject the signal into the observational dataPerform same analysis as explained above95% confidence upper limitRepeat 1-3 to compute the rate at which we detect the mock signal.Detection efficiencyReceiver operating characteristicDetection efficiency0.95The amplitude of injected signals

Parameter TuningThere are some parameters whose optimal values are depend on the data qualityThe length of the segmentsThe amount of the segments removed by data selectionThe bandwidth of the analyzed frequency bandDetermined by the time shifted data.200 sec10 %0.8 HzThe values which make the upper limit calculated with time shifted data best is used.Summary of Analysis

Data selection

whiteningThe analyzed frequencyband is excluded fromRMS calculation The indicator of the noise level = Whitened RMSAvoid making the resultintentionally betterCross correlation anlysis21

signalGW signalnoiseCross correlation value

Noise is reduced

Cross correlationvalueFourier transformationDetection Criteria

/TsegProbability distribution of /Tseg azaBy the Neuman-Peason criterion,Note: we do not know the sign of the two signal.

Signal is presentSignal is absentaa: false alarm rateHistogram of /Tseg calculated with time shifted data

Signal detectionHow to decide :

/TsegzaCalculate with diversely time shifted dataHistogram of calculated Histogram of when the signal is absent.

a: false alarm rateb: false dismissal rate23NoGW signalwithGW signal

Future plan24

This cross correlation analysis 1 year observation



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