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The Search For Periodic Gravitational Waves

The L aser I nterferometer G ravitational-Wave O bservatory. The Search For Periodic Gravitational Waves. http://www.ligo.caltech.edu. Gregory Mendell, LIGO Hanford Observatory on behalf of the LIGO Scientific Collaboration. Supported by the United States National Science Foundation.

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The Search For Periodic Gravitational Waves

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  1. The Laser Interferometer Gravitational-Wave Observatory The Search For Periodic Gravitational Waves http://www.ligo.caltech.edu Gregory Mendell, LIGO Hanford Observatory on behalf of the LIGO Scientific Collaboration Supported by the United States National Science Foundation LIGO-G050492-00-W

  2. Gravitational Waves • Gravitation = metric tensor: • Weak Field Limit: • Gauge choice: • Quadrupole field: • At the detector: LIGO-G050492-00-W

  3. Laser Interferometer Gravitational-wave Detection Gravitational-wave Strain: free masses • LIGO’s arms: L = 4 km. • Sensitivity: L nominally around 10-18 m. (Depending on frequency and duration of the signal this can be much larger or much smaller!) suspended test masses LIGO-G050492-00-W

  4. Inside LIGO LIGO-G050492-00-W

  5. Calibration • Measure open loop gain G, input unity gain to model • Extract gain of sensing function C=G/AD from model • Produce response function at time of the calibration, R=(1+G)/C • Now, to extrapolate for future times, monitor single calibration line in AS_Q error signal, plus any changes in gain beta, and form alphas • Can then produce R at any later time t, given alpha and beta at t • A photon calibrator, using radiation pressure, gives results consistent with the standard calibration. LIGO-G050492-00-W

  6. Noise Amp. Spectral Density: [Sn(f)]1/2 LIGO-G050492-00-W

  7. LMXBs Astrophysical Sources Pulsars Black Holes Stochastic Background Supernovae LIGO-G050492-00-W Photos: http://antwrp.gsfc.nasa.gov; http://imagine.gsfc.nasa.gov

  8. Neutron and Strange-quark Stars http://chandra.harvard.edu/resources/illustrations/neutronstars_4.html NASA/CXC/SAO LIGO-G050492-00-W

  9. Wobbling star Accreting star “Mountain” on star Oscillating star Continuous Periodic Gravitational-Wave Sources Free precession wobble angle  Mountain mass & height: MR2 Low-mass x-ray binary: balance GW torque with accretion torque . Unstable vibrations with amplitude A A. Vecchio on behalf of the LIGO Scientific Collaboration : GR17 – 22nd July, 2004 LIGO-G050492-00-W

  10. The back of the envelope please… Approximate form of the Quadrupole Formula For fr = 200 Hz, M = 1.4 M, R = 106 cm, r = 1 kpc = 3  1021 cm: • Triaxial ellipsoid: h ~ (G/c4) MR24fr2/r ~ 10–26 (for ellipticity ~ 10–6) • Precession: h ~ (G/c4) sin (2)  MR2fr2/r ~ 10-27 (for ellipticity ~ 10-6, wobble angle  = /4) • LMXB Sco-X1: h ~ 10-26 (balance GW torque with accretion torque) • R-modes: h ~ (G/c4) MA2R2 (16/9) fr2/r ~ 10–26 (for saturation amplitude A ~ 10–3) • Pulsar Glitch h ~ (G/c4) MA2R2fr2/r ~ 10 –32 ( for glitch amplitude A ~ 10–6) LIGO-G050492-00-W

  11. Estimate for population of objects spinning down due to gravitational waves Blanford (1984) as cited by Thorne in 300 Years of Gravitation; see also LIGO Scientific Collaboration, gr-qc/0508065, submitted to Phys. Rev. D (2005); and LIGO Scientific Collaboration, S2 Maximum Likelihood Search, in prepartion. LIGO-G050492-00-W

  12. Periodic Signals GW approaching from direction n Solar System Barycenter T = arrival time at SSB t = arrival time at detector Relativistic corrections are included in the actual code. LIGO-G050492-00-W

  13. Phase and Frequency Modulation Phase at SSB: Phase at detector: Frequency at detector: df/dt : LIGO-G050492-00-W

  14. Amplitude Modulation Figure: D. Sigg LIGO-P980007-00-D Polarization Angle  Beam Pattern Response Functions: LIGO-G050492-00-W

  15. Maximum Likelihood Likelihood of getting data x for model h for Gaussian Noise: Chi-squared Minimize Chi-squared = Maximize the Likelihood LIGO-G050492-00-W

  16. Coherent Matched Filtering Jaranowski, Krolak, & Schutz gr-qc/9804014; Schutz & Papa gr-qc/9905018; Williams and Schutz gr-qc/9912029; Berukoff and Papa LAL Documentation LIGO-G050492-00-W

  17. Time Domain Coherent Search Using Bayesian Analysis Bayes’ Theorem: Likelihood: Posterior Probability: Confidence Interval: Prior LIGO-G050492-00-W

  18. Frequency Time Incoherent Power Averaging • Break up data into M segments; FFT each segment. • Track the frequency. • StackSlide: add the power weighted by the noise inverse. • Hough: add 1 or 0 if power is above/below a cutoff. • PowerFlux: add power using weights that maximize SNR LIGO-G050492-00-W

  19. Incoherent Methods Short Fourier Transforms (SFTs): Periodogram: Hough Number Count: StackSlide Power: Power Flux: LIGO-G050492-00-W

  20. False alarm & false dismissal rates determine SNR of detectable signal. • Coherent matched filtering tracks phase. • Incoherent power averaging tracks frequency only. • Optimal search needs 1023 templates per 1 Hz for 1 yr of data; Hierarchical approach needed. Sensitivity of PeriodicSearch Techniques These are for 1% false alarm & 10% false dismissal rates, an average sky position and source orientation. A hierarchical search employs a much large false alarm rate, then use coincidence and other vetoes to maximize sensitivity and narrow follow-up searches to the most promising candidates. LIGO-G050492-00-W

  21. Fake Pulsar vs. Fake Instrument Line Power averaging reduces noise variance. Pulsar SNR increases with time. Frequency demodulation broadens instrument line. SNR decreases with time. LIGO-G050492-00-W

  22. All Sky Loudest Events 1000 SFTs, Fake Pulsar & Noise: DEC (radians) LIGO-G050492-00-W RA (radians)

  23. All Sky Loudest Events 1000 SFTs, Fake Inst. Line & Noise: DEC (radians) LIGO-G050492-00-W RA (radians)

  24. Instrument lines in the S2 data. LIGO Scientific Collaboration, gr-qc/0508065, submitted to Phys. Rev. D (2005). LIGO-G050492-00-W

  25. Frequentist Confidence Region Matlab simulation for signal: • Estimate parameters by maximizing likelihood or minimizing chi-squared • Injected signal with estimated parameters into many synthetic sets of noise. • Re-estimate the parameters from each injection LIGO-G050492-00-W Figure courtesy Anah Mourant, Caltech SURF student, 2003.

  26. Bayesian Confidence Region Matlab simulation for signal: Uniform Prior: x Figures courtesy Anah Mourant, Caltech SURF student, 2003. LIGO-G050492-00-W

  27. Frequentist Confidence Region For A Source Population From The Loudest Event. LIGO-G050492-00-W

  28. LIGO Scientific Collaboration & The Pulsar Group, Jodrell Bank Observatory, gr-qc/0410007, Phys. Rev. Lett. 94 (2005) 181103. S2 Time Domain Search Results Best ho UL = 1.7 x10-24. Best ellipticity UL = 4.5 x 10-6(I = 1045 gcm2) LIGO-G050492-00-W

  29. Detection of Fake HW Injected Signals LIGO Scientific Collaboration & The Pulsar Group, Jodrell Bank Observatory, gr-qc/0410007, Phys. Rev. Lett. 94 (2005) 181103; LIGO Scientific Collaborationgr-qc/0508065, submitted to Phys. Rev. D (2005). LIGO-G050492-00-W

  30. S2 All-sky Hough Search Results LIGO Scientific Collaboration, gr-qc/0508065, submitted to Phys. Rev. D (2005). Best ho Upper Limit = 4.43 x10-23 LIGO-G050492-00-W

  31. Many searches are underway. You can join via Einstein@home: http://einstein.phys.uwm.edu/ • Like SETI@home, but for LIGO/GEO matched filter search for GWs from rotating compact stars. • Support for Windows, Mac OSX, and Linux clients • Our own clusters have thousands of CPUs. • Einstein@home has many times more computing power at low cost. LIGO-G050492-00-W

  32. Summary and Future Prospects • Initial LIGO is searching for highly deformed, rotating, highly compact stars in the solar neighborhood of the galaxy. • Four Science Runs Have Been Completed. The fifth Science Run is scheduled to begin next month and last over one year at or very near design sensitivity. • Advanced LIGO will search with ~10x the sensitivity of initial LIGO. It will be sensitive to more moderately deformed, rotating, highly compact stars throughout the galaxy. • Hierarchical searches, with coincidence and other vetoes, and follow-up targeted searches, are several ways to improve sensitivity beyond back-of-the envelope estimates presented in this talk. • Advanced LIGO using signal recycling can further improve sensitivity in a narrow frequency band. LIGO-G050492-00-W

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