OutlineLength Sensing and ControlGravitational-Wave DataCalibrationGravitational-Wave Strain DataOutlineBasic PrinciplesOutlineThe Gravitational Wave Signal TableauSignal ClassesShort-duration, Known Waveforms: Inspirals, etc.Basic Matched FilteringSource Parameters vs. Signal ParametersOptimal Matched Filtering in Frequency DomainMatched Filtering Susceptibility to GlitchesWaveform Consistency TestsTemplate Bank ConstructionTemplate Bank Construction in (t0,t3) spaceEllipses in Mass SpaceDifferent Bank Layout MethodsUncertain Waveforms for High-Mass InspiralsTemplates for Detection vs. Parameter EstimationSignal ClassesContinuous, Known Waveform: GW from Spinning Neutron StarsContinuous GW Signals at EarthSearch Methods for CW signalsSearch for Gravitational Waves from Known PulsarsWide Parameter Space SearchesGetting by with a Little Help from Our FriendsSemi-Coherent Search MethodsHierarchical SearchSignal ClassesShort-duration, Unknown Waveform: Gravitational-Wave Bursts“Excess Power” Search MethodsCross-Correlation MethodsSignal ClassesContinuous, Unknown Waveform: Stochastic Gravitational WavesSky Map of Stochastic Gravitational Waves: “Radiometer”OutlineVariable Data QualityNon-Stationary Noise / GlitchesOutlineBig Science!Gravitational-WaveData Analysis Peter ShawhanPhysics 798GApril 12, 2007U of Maryland Phys 798G, 12 April 20072Outline► Gravitational-wave data► General data analysis principles► Specific data analysis methods► Classification of signals► Methods for each class of signals► Idiosyncracies of real detectors► The gravitational-wave communityU of Maryland Phys 798G, 12 April 20073Length Sensing and ControlU of Maryland Phys 798G, 12 April 20074Gravitational-Wave DataInstantaneous estimate of strain for each moment in timei.e. demodulated channel sensitive to arm length difference(Or, for resonant detector: displacement sensed by transducer)Digitized time series recorded in computer filesLIGO / GEO sampling rate: 16384 HzVIRGO sampling rate: 20000 HzSynchronized with GPS timeCommon “frame” file format (*.gwf)Many auxiliary channels recorded tooInterferometric sensing and controlEnvironmental sensors (accelerometers, microphones, magnetometers,…)Interferometer configuration and facilities housekeeping dataTotal data volume: a few megabytes per second per interferometerU of Maryland Phys 798G, 12 April 20075CalibrationMonitor P(f) continuously with “calibration lines”Sinusoidal arm length variations with known absolute amplitudeApply frequency-dependent correction factor to get GW strainGW READOUT)()()(1)READOUTGW(fSfPfGh+×=U of Maryland Phys 798G, 12 April 20076Gravitational-Wave Strain DataU of Maryland Phys 798G, 12 April 20077Outline► Gravitational-wave data► General data analysis principles► Specific data analysis methods► Classification of signals► Methods for each class of signals► Idiosyncracies of real detectors► The gravitational-wave communityU of Maryland Phys 798G, 12 April 20078Basic PrinciplesGravitational wave sources are rare and/or intrinsically weakNeed highly sensitive detectorsA detectable signal will most likely be near threshold of detectabilityClaiming the first detection will be a big dealPast detection claims failed to be confirmedWant to set a high standard of evidenceRequire consistency among multiple detectorsIndividual detectors may glitchRequire coincidence or cross-coherence of some sortAllow for relative time delay, different antenna response, sensitivitiesEstimate false alarm rate (“background”) using time-shifted dataU of Maryland Phys 798G, 12 April 20079Outline► Gravitational-wave data► General data analysis principles► Specific data analysis methods► Classification of signals► Methods for each class of signals► Idiosyncracies of real detectors► The gravitational-wave communityU of Maryland Phys 798G, 12 April 200710The Gravitational WaveSignal TableauWaveform knownWaveform unknownShort duration Long durationLow-mass inspiralAsymmetric spinning NSHigh-mass inspiralBinary mergerNS / BH ringdownCosmic string cusp / kinkStellar core collapseCosmological stochastic backgroundMany overlapping signalsRotation-driven instability??? ??? ???U of Maryland Phys 798G, 12 April 200711Signal ClassesWaveform knownWaveform unknownShort duration Long durationLow-mass inspiralAsymmetric spinning NSHigh-mass inspiralBinary mergerNS / BH ringdownCosmic string cusp / kinkStellar core collapseCosmological stochastic backgroundMany overlapping signalsRotation-driven instability??? ??? ???U of Maryland Phys 798G, 12 April 200712Short-duration, Known Waveforms:Inspirals, etc.Known well, or fairly well, in some parametrized spacee.g. post-Newtonian expansion (assumes negligible spins)whereh(t) () ()()()()L+⎟⎠⎞⎜⎝⎛+++−⎟⎠⎞⎜⎝⎛+++=Ψ−−−−3/123/213/5144617100854291016064305867364158341133674396512832fmfmfmfmtffcπηηηπηππηηπηπ1PN1.5PN2PNKnown waveform ⇒Use matched filteringU of Maryland Phys 798G, 12 April 200713Basic Matched FilteringU of Maryland Phys 798G, 12 April 200714Source Parameters vs.Signal ParametersInspiral source parametersMasses (m1, m2)SpinsOrbital phase at coalescenceInclination of orbital planeSky locationDistance→ Simply multiplicative→ Assume negligible for now→ Simply multiplicative for a given detector→ Maximize analytically when filteringFilter with orthogonal templates, take quadrature sumU of Maryland Phys 798G, 12 April 200715Optimal Matched Filteringin Frequency DomainLook for maximum of |z(t)| above some threshold Î triggerSearch overlapping intervalsto cover science segment,avoid wrap-around effectsEstimate power spectrum frombin-by-bin median of fifteen256-sec data segmentsdfefSfhfstztfinπ20*)()(~)(~4)(∫∞=Template, generated in freq. domainusing stationary phase approx.Dataafter FFTNoise power spectral densityU of Maryland Phys 798G, 12 April 200716Matched FilteringSusceptibility to GlitchesU of Maryland Phys 798G, 12 April 200717Waveform Consistency TestsChi-squared testDivide template into p parts,calculateTests using filter outpute.g. time above thresholdTimeFrequency∑=−=pllptztzpt122/)()()(χU of Maryland Phys 798G, 12 April 200718Template Bank ConstructionHow did we come up with this set of templates???U of Maryland Phys 798G, 12 April 200719Template Bank Constructionin (τ0,τ3) spaceητητ//3/233/50−−∝∝mmU of Maryland Phys 798G, 12 April 200720Ellipses in Mass SpaceU of Maryland