LIGO-G W The Search For Periodic Gravitational Waves Gregory Mendell, LIGO Hanford Observatory on behalf of the LIGO Scientific Collaboration The Laser Interferometer Gravitational-Wave Observatory Supported by the United States National Science Foundation

LIGO-G W Gravitational Waves Gravitation = metric tensor: Weak Field Limit: Gauge choice: Quadrupole field: At the detector:

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

LIGO-G W Inside LIGO

LIGO-G W

LIGO-G W Sources of Continuous Gravitational Waves Mountain on neutron star Precessing neutron star Accreting neutron star Oscillating neutron star AB C D Credits: A. image by Jolien Creighton; LIGO Lab Document G Z. B. image by M. Kramer; Press Release PR0003, University of Manchester - Jodrell Bank Observatory, 2 August 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. Search methods can detected any type of periodic source. Upper limits are set on gravitational-wave amplitude, h 0, of rotating triaxial ellipsoid.

LIGO-G W Nature of gravitational wave signal The GW signal from a triaxial pulsar can be modelled as The unknown parameters are h 0 - amplitude of the gravitational wave signal  - polarization angle of signal; embedded in F x, +  - 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-G W Figure: D. Sigg LIGO-P D Amplitude Modulation Beam Pattern Response Functions: Polarization Angle 

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

LIGO-G W Phase and Frequency Modulation Phase at SSB: Phase at detector: Frequency at detector: df/dt :

LIGO-G W Analysis of Hardware Injections RA (hours) DEC (degrees) PRELIMINARY APS April 2006 LIGO-G W 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 h 0 ~ 7.5e-24 are below. Black stars show the fake signal’s sky position.

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

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

LIGO-G W Coherent Matched Filtering Jaranowski, Krolak, & Schutz gr-qc/ ; Schutz & Papa gr- qc/ ; Williams and Schutz gr-qc/ ; Berukoff and Papa LAL Documentation F-statistic

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

LIGO-G W Semi-coherent Methods Time Frequency Time Track Doppler shift and df/dt LIGO-G W 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

LIGO-G W Short Fourier Transforms (SFTs) & Periodograms: Hough Number Count & Weighted Number Count: StackSlide Power: Power Flux:

LIGO-G W Frequentist Confidence Region 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 Matlab simulation for signal: Figure courtesy Anah Mourant, Caltech SURF student, 2003.

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

LIGO-G W Frequentist Population-based Confidence Region From The Loudest Event.

LIGO-G W 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-G W The back of the envelope please… For a triaxial ellipsoid (or think of  I as a way of scaling a the time varying quadrupole Q): Maximum expected ellipticities: Solid quark stars: Hybrid hyperon/heutron stars or buried B fields: Neutron stars with fluid core and solid crust: Estimated strain: h = 4  2 (G/c 4 )  If 2 /r ~ 2  2  (v esc 2 /c 2 )(v R 2 /c 2 )(R/r) ~10 –25 (  /10 -6 )(I/10 45 g. cm 2 ) (f/300 Hz) 2 (1kpc/r)

LIGO-G W Results 1. S1 coherent time-domain and F-stat search targeting pulsar J : The LIGO Scientific Collaboration, Phys.Rev. D69 (2004) ; gr- qc/ Best UL: h_0 < 1.4  ;  < 2.9  (10 45 g. cm 2 /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) ;gr-qc/ Best UL: h_0 < 1.7  ; Best UL  < 4.5e  S2 semi-coherent all-sky, Hz, Hough search: LIGO Scientific Collaboration, Phys.Rev. D72 (2005) ; gr-qc/ Best UL: h_0 < 4.4  S3 coherent all-sky, Hz and Sco X-1, Hz & Hz, F-stat search: LIGO Scientific Collaboration, submitted to Phys. Rev. D (2006); gr-qc/ Best all-sky UL: h_0 < 6.6e-23 ; Best Sco X-1 UL: h_0 < 1.7e-22

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

LIGO-G W S5 targeted h 0 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 (f gw = 59.6 Hz, dist = 2.0 kpc)  h 0 = 3.0x10 -24,  = 1.6x10 -3  Assumes I = kgm 2 Sensitivity curves use: Crab pulsar Frequency (Hz) h0h0 PRELIMINARY APS April 2006

LIGO-G W S3 Results PRELIMINARY

LIGO-G W Many searches are underway. You can join via Like 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. has many times more computing power at low cost.

LIGO-G W End

LIGO-G W 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 Advanced LIGO will have 10x sensitivity, better a lower frequencies. Using signal recycling can further improve sensitivity in a narrow frequency band.

LIGO-G W S3 Results PRELIMINARY

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

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

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

LIGO-G W Astrophysical Sources Black HolesDense Stars Supernovae Stochastic Background Photos:

LIGO-G W Neutron and Strange-quark Stars neutronstars_4.html NASA/CXC/SAO

LIGO-G W 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-G W S4 StackSlide “Loudest Events” Hz LIGO-Gxxxxxx-00-W 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(f H1 - f L1 ) > 1.1e-4*f0 StackSlide Power Frequency (Hz) APS April 2006 PRELIMINARY

LIGO-G W S4 StackSlide “Loudest Events” Hz LIGO-Gxxxxxx-00-W StackSlide Power Frequency (Hz) APS April 2006 PRELIMINARY FakePulsar3=> FakePulsar8=> <=Follow-up Indicates Instrument Line 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(f H1 - f L1 ) > 1.1e-4*f0

LIGO-G W LIGO-Gxxxxxx-00-W Best: 4.4e-24 For Hz Band PRELIMINARY Frequency (Hz) S4 StackSlide h 0 95% Confidence All Sky Upper Limits Hz APS April 2006 Note that h 0 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. Best: 5.4e-24 For Hz Band h 0 Upper Limit

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

LIGO-G W PowerFlux S5 H Hz (no spindown) PRELIMINARY APS April 2006

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

LIGO-G W Sensitivity of Periodic Search Techniques False alarm & false dismissal rates determine SNR of detectable signal. Coherent matched filtering tracks phase. Incoherent power averaging tracks frequency only. Optimal search needs templates per 1 Hz for 1 yr of data; Hierarchical approach needed. 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-G W S2 Time Domain Search Results Best h o UL = 1.7 x Best ellipticity UL = 4.5 x (I = gcm 2 ) LIGO Scientific Collaboration & The Pulsar Group, Jodrell Bank Observatory, gr-qc/ , Phys. Rev. Lett. 94 (2005)

LIGO-G W S2 All-sky Hough Search Results Best h o Upper Limit = 4.43 x LIGO Scientific Collaboration, gr-qc/ , submitted to Phys. Rev. D (2005).

LIGO-G W 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/ , submitted to Phys. Rev. D (2005); and LIGO Scientific Collaboration, S2 Maximum Likelihood Search, in prepartion.

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