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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-G060499-00-W

  2. Gravitational Waves • Gravitation = metric tensor: • Weak Field Limit: • Gauge choice: • Quadrupole field: • At the detector: LIGO-G060499-00-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-G060499-00-W

  4. Inside LIGO LIGO-G060499-00-W

  5. LIGO-G060499-00-W

  6. Sources of Continuous Gravitational Waves Search methods can detected any type of periodic source. A B Upper limits are set on gravitational-wave amplitude, h0, of rotating triaxial ellipsoid. Credits: A. image by Jolien Creighton; LIGO Lab Document G030163-03-Z. B. image by M. Kramer; Press Release PR0003, University of Manchester - Jodrell Bank Observatory, 2 August 2000. C. image by Dana Berry/NASA; NASA News Release posted July 2, 2003 on Spaceflight Now. D. image from a simulation by Chad Hanna and Benjamin Owen; B. J. Owen's research page, Penn State University. Mountain on neutron star Precessing neutron star C Accreting neutron star D Oscillating neutron star LIGO-G060499-00-W LIGO-G060177-00-W

  7. Nature of gravitational wave signal • The GW signal from a triaxial pulsar can be modelled as • The unknown parameters are • h0 - amplitude of the gravitational wave signal •  - polarization angle of signal; embedded in Fx,+ •  - inclination angle of the pulsar • 0 - initial phase of pulsar (0) • In the targeted searches we currently only look for signals at twice the rotation frequency of the pulsars • For blind searches the location in the sky and the source’s frequency evolution are unknown. LIGO-G060499-00-W

  8. Amplitude Modulation Figure: D. Sigg LIGO-P980007-00-D Polarization Angle  Beam Pattern Response Functions: LIGO-G060499-00-W

  9. 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-G060499-00-W

  10. Phase and Frequency Modulation Phase at SSB: Phase at detector: Frequency at detector: df/dt : LIGO-G060499-00-W

  11. PRELIMINARY APS April 2006 Analysis of Hardware Injections Fake gravitational-wave signals corresponding to rotating neutron stars with varying degrees of asymmetry were injected for parts of the S4 run by actuating on one end mirror. Sky maps for the search for an injected signal with h0 ~ 7.5e-24 are below. Black stars show the fake signal’s sky position. DEC (degrees) DEC (degrees) RA (hours) RA (hours) LIGO-G060499-00-W LIGO-G060177-00-W

  12. All Sky Loudest Events 1000 SFTs, Fake Inst. Line & Noise: DEC (radians) LIGO-G060499-00-W RA (radians)

  13. Maximum Likelihood Likelihood of getting data x for model h for Gaussian Noise: Chi-squared Minimize Chi-squared = Maximize the Likelihood LIGO-G060499-00-W

  14. Coherent Matched Filtering F-statistic Jaranowski, Krolak, & Schutz gr-qc/9804014; Schutz & Papa gr-qc/9905018; Williams and Schutz gr-qc/9912029; Berukoff and Papa LAL Documentation LIGO-G060499-00-W

  15. Time Domain Coherent Search Using Bayesian Analysis Bayes’ Theorem: Likelihood: Posterior Probability: Confidence Interval: Prior LIGO-G060499-00-W

  16. Frequency Time Time Semi-coherent Methods • Break up data into 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 (advanced version includes weighted average of 1’s & 0’s). • PowerFlux: add power using weights that maximize SNR Track Doppler shift and df/dt LIGO-G060499-00-W LIGO-G060388-00-W

  17. Short Fourier Transforms (SFTs) & Periodograms: Hough Number Count & Weighted Number Count: StackSlide Power: Power Flux: LIGO-G060499-00-W

  18. 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-G060499-00-W Figure courtesy Anah Mourant, Caltech SURF student, 2003.

  19. Bayesian Confidence Region Matlab simulation for signal: Uniform Prior: x Figures courtesy Anah Mourant, Caltech SURF student, 2003. LIGO-G060499-00-W

  20. Frequentist Population-based Confidence Region From The Loudest Event. LIGO-G060499-00-W

  21. GWs from triaxial pulsar • For upper limits have to select a model. (This is not needed for detection!) • Ellipticity, , measures asymmetry in triaxially shaped pulsar equatorial ellipticity LIGO-G060499-00-W

  22. The back of the envelope please… For a triaxial ellipsoid (or think of Ias a way of scaling a the time varying quadrupole Q): • Maximum expected ellipticities: • Solid quark stars: 10-4 • Hybrid hyperon/heutron stars or buried B fields: 10-5 • Neutron stars with fluid core and solid crust: 10-6 • Estimated strain: • h = 42(G/c4) If 2/r • ~ 22(vesc2/c2)(vR2/c2)(R/r) • ~10–25(/10-6)(I/1045 g.cm2) (f/300 Hz)2 (1kpc/r) LIGO-G060499-00-W

  23. Results 1. S1 coherent time-domain and F-stat search targeting pulsar J1939+2134: The LIGO Scientific Collaboration, Phys.Rev. D69 (2004) 082004; gr-qc/0308050 Best UL: h_0 < 1.4  10-22;  < 2.9 10-4 (1045 g.cm2/I) 2. S2 coherent time-domain search targeting 28 pulsars: The LIGO Scientific Collaboration: B. Abbott, et al, M. Kramer, A.G. Lyne, Phys.Rev.Lett. 94 (2005) 181103;gr-qc/0410007 Best UL: h_0 < 1.7 10-24; Best UL  < 4.5e  10-6 3. S2 semi-coherent all-sky, 200-400 Hz, Hough search: LIGO Scientific Collaboration, Phys.Rev. D72 (2005) 102004; gr-qc/0508065 Best UL: h_0 < 4.4 10-23 4. S3 coherent all-sky, 160-728.8 Hz and Sco X-1, 464-484 Hz & 604-624 Hz, F-stat search: LIGO Scientific Collaboration, submitted to Phys. Rev. D (2006); gr-qc/0605028 Best all-sky UL: h_0 < 6.6e-23 ; Best Sco X-1 UL: h_0 < 1.7e-22 LIGO-G060499-00-W

  24. Preliminary Results and Plans 5. S3 Einstein@Home search: preliminary S3 results posted at http://einstein.phys.uwm.edu/. Final S3 and S4 results in preparation. Initial start of S5 search is running. 6. S3/S4 Targested search including pulsars: 32 isolated and 44 in binaries; results in preparation. April 2005 APS Best UL: h_0 < few  10-25, and  < 10-6 for one pulsar 7. S4 all-sky, 50-1000 Hz, PowerFlux, StackSlide, Hough search: results in preparation; S5 preliminary all-sky PowerFlux search April 2005 APS Best UL: h_0 < few  10-24. 8. Start of S5 preliminary coherent time-domain targeted pulsar search: Best UL h0 < few  10-25; Best  UL: < few x 10-7 9. S4/S5 F-stat targeted isolated x-ray sources: RX J1856.5-3754 (nearest known NS) and Cas A (youngest known NS) search started. 10. S5 Multi-IFO PowerFlux & Multi-IFO Hierarchical Einstein@Home Search under development. LIGO-G060499-00-W

  25. PRELIMINARY APS April 2006 S5 targeted h0 Results • Spin-down upper limit calculated with intrinsic spin-down value if available i.e. corrected for Shklovskii transverse velocity effect • Closest to spin-down upper limit • Crab pulsar ~ 2.1 times greater than spin-down (fgw = 59.6 Hz, dist = 2.0 kpc) • h0 = 3.0x10-24, e = 1.6x10-3 • Assumes I = 1038 kgm2 • Sensitivity curves use: Crab pulsar h0 Frequency (Hz) LIGO-G060499-00-W

  26. PRELIMINARY Einstein@Home S3 Results LIGO-G060499-00-W

  27. 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-G060499-00-W

  28. End LIGO-G060499-00-W

  29. S5 And Future Prospects • PowerFlux will give quick views of S5 data, and provide candidates for follow-up if any unexplained signals turn up. • Hierarchical searches, with coincidence, other vetoes, and follow-up searches, will improve sensitivity. • Divide data into ~30 hr segments and generate coherent F-statistic for each. • Apply StackSlide/Hough of the F-statistic segments. • Automatic follow-up of candidates will be done. • The code will run under Einstein@Home. • Advanced LIGO will have 10x sensitivity, better a lower frequencies. Using signal recycling can further improve sensitivity in a narrow frequency band. LIGO-G060499-00-W

  30. PRELIMINARY Einstein@Home S3 Results LIGO-G060499-00-W

  31. Line Avoiding: Doppler Skybands (e.g., for no-spindown) Skyband 10 (worst) Skyband 0 (good) LIGO-G060499-00-W

  32. All Sky Loudest Events 1000 SFTs, Fake Pulsar & Noise: DEC (radians) LIGO-G060499-00-W RA (radians)

  33. Dealing With Instrument Lines: Cleaning Spectral Density [1/Sqrt(Hz)] Frequency (Hz) LIGO-G060499-00-W LIGO-Gxxxxxx-00-W

  34. Astrophysical Sources Black Holes Dense Stars Stochastic Background Supernovae LIGO-G060499-00-W Photos: http://antwrp.gsfc.nasa.gov; http://imagine.gsfc.nasa.gov

  35. Neutron and Strange-quark Stars http://chandra.harvard.edu/resources/illustrations/neutronstars_4.html NASA/CXC/SAO LIGO-G060499-00-W

  36. 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-G060499-00-W

  37. APS April 2006 PRELIMINARY S4 StackSlide “Loudest Events” 50-225 Hz • Searched 450 freq. per .25 Hz band, 51 values of df/dt, between 0 & -1e-8 Hz/s, up to 82,120 sky positions (up to 2e9 templates). The expected loudest StackSlide Power was ~ 1.22 (SNR ~ 7) • Veto bands affected by harmonics of 60 Hz. • Simple cut: if SNR > 7 in only one IFO veto; if in both IFOs, veto if abs(fH1-fL1) > 1.1e-4*f0 StackSlide Power StackSlide Power Frequency (Hz) LIGO-G060499-00-W LIGO-Gxxxxxx-00-W

  38. APS April 2006 PRELIMINARY S4 StackSlide “Loudest Events” 50-225 Hz • Searched 450 freq. per .25 Hz band, 51 values of df/dt, between 0 & -1e-8 Hz/s, up to 82,120 sky positions (up to 2e9 templates). The expected loudest StackSlide Power was ~ 1.22 (SNR ~ 7) • Veto bands affected by harmonics of 60 Hz. • Simple cut: if SNR > 7 in only one IFO veto; if in both IFOs, veto if abs(fH1-fL1) > 1.1e-4*f0 FakePulsar3=> FakePulsar8=> StackSlide Power <=Follow-up Indicates Instrument Line FakePulsar8=> StackSlide Power FakePulsar3=> <=Follow-up Indicates Instrument Line Frequency (Hz) LIGO-G060499-00-W LIGO-Gxxxxxx-00-W

  39. APS April 2006 PRELIMINARY S4 StackSlide h0 95% Confidence All Sky Upper Limits 50-225 Hz Best: 4.4e-24 For 139.5-139.75 Hz Band Note that h0 is the gravitational-wave amplitude for a rotating triaxial ellipsoid. Monte Carlo injections of triaxial sources over the search parameter space & source orientations set the ULs. h0 Upper Limit Best: 5.4e-24 For 140.75-141.0 Hz Band h0 Upper Limit LIGO-G060499-00-W LIGO-Gxxxxxx-00-W Frequency (Hz)

  40. PRELIMINARY APS April 2006 PowerFlux 95% CL limits – S4 H1 (50-1000 Hz) Linear amplitude (=0.5*h0worst-pulsar-orient.) Doppler Skyband 0 Color coding BLUE – Non-Gaussian Diamond – Wand. Line Green – Upper Limit Red point – Loose Candidate (SNR > 7) LIGO-G060499-00-W

  41. PRELIMINARY APS April 2006 PowerFlux S5 H1 40-800 Hz(no spindown) LIGO-G060499-00-W

  42. PRELIMINARY Detector artifacts worse at low frequencies for L1 39.87 Hz comb (RF oscillator) APS April 2006 95% CL limits – L1 (50-1000 Hz) *For APS Linear amplitude (=0.5*h0worst-pulsar-orient.) Doppler Skyband 0 Color coding BLUE – Non-Gaussian Diamond – Wand. Line Green – Upper Limit Red point – Loose Candidate (SNR > 7) LIGO-G060499-00-W

  43. 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-G060499-00-W

  44. 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-G060499-00-W

  45. 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-G060499-00-W

  46. 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-G060499-00-W

  47. Simulation:What might detection sound or look like? Play Me (AM & FM modulation greatly exaggerated!) LIGO-G060499-00-W

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