The search for continuous gravitational waves: analyses from LIGO s second science run

Transcription

1 The search for continuous gravitational waves: analyses from LIGO s second science run Michael Landry LIGO Hanford Observatory on behalf of the LIGO Scientific Collaboration April APS Meeting (APR04) May 1-4, 2004 Denver, CO Photo credit: NASA/CXC/SAO

2 Talk overview Introduction to continuous wave (CW) sources CW search group analysis efforts Review of first science run (S1) results, and a look at expectations of the S2 run Time-domain analysis method Injection of fake pulsars Results Landry - April APS, 4 May

3 CW sources Nearly-monochromatic continuous sources of gravitational waves include neutron stars with:» spin precession at ~f rot» excited oscillatory modes such as the r-mode at 4/3 * f rot» non-axisymmetric distortion of crystalline structure, at 2f rot Limit our search to gravitational waves from a triaxial neutron star emitted at twice its rotational frequency (for the analysis presented here, only) Signal would be frequency modulated by relative motion of detector and source, plus amplitude modulated by the motion of the antenna pattern of the detector Landry - April APS, 4 May

4 Source model The expected signal has the form: 2 1+ cos ι h() t = F+ ( t; ψ) h0 cos Φ( t) F ( t; ψ) h0cosιsin Φ( t) 2 F + and F x : strain antenna patterns of the detector to plus and cross polarization, bounded between -1 and 1 Here, signal parameters are:» h 0 amplitude of the gravitational wave signal» ψ polarization angle of signal» ι inclination angle of source with respect to line of sight PRD (1998)» φ 0 initial phase of pulsar; Φ(t=0), and Φ(t)= φ(t) + φ 0 i () t Heterodyne, i.e. multiply by: e φ so that the expected demodulated signal is then: iφ 0 iφ 0 ( t ; a) = F ( t ; ψ ) h ( 1+ cos ι) i F ( t ; ψ ) h ( cosι) e y k + k 0 e k 0 2 Here, a = a(h 0, ψ, ι, φ 0 ), a vector of the signal parameters. Landry - April APS, 4 May

5 CW search group efforts S2 Coherent searches» Time-domain method (optimal for parameter estimation) Target known pulsars with frequencies (2f rot ) in detector band» Frequency-domain F-statistic* method (optimal for blind detection) All-sky, broadband search, subset of S2 dataset Targeted searches (e.g. galactic core) LMXB (e.g. ScoX-1) search S2 Incoherent searches» Hough transform method» Powerflux method» Stackslide method Future: Implement hierarchical analysis that layers coherent and incoherent methods Einstein@home initiative for 2005 World Year of Physics *not the F-statistic associated with statistical literature (ratio of two variances), nor the F-test of the null hypothesis (See PRD (1998)) Landry - April APS, 4 May

6 First science run: S1 S1 run: 17 days (Aug 23-Sep 9 02) Coincident run of four detectors, LIGO (L1, H1, H2), and GEO600 Two independent analysis methods (frequency-domain and timedomain) employed Set 95% upper limit values on continuous gravitational waves from single pulsar PSR J , using LIGO and GEO IFO s: best limit from Livingston IFO: h 0 < (1.4 ± 0.1) 10 Accepted for publication in Phys Rev D 69, (2004), preprint available, gr-qc/ Landry - April APS, 4 May

7 S2 expectations Coloured spectra: average amplitude detectable in time T (1% false alarm, 10% false dismissal rates): h0 = 11.4 Sh( f ) / T Solid black lines: LIGO and GEO science requirement, for T=1 year Circles: upper limits on gravitational waves from known EM pulsars, obtained from measured spindown (if spindown is entirely attributable to GW emission) Only known, isolated targets shown here GEO LIGO Landry - April APS, 4 May

8 Time-domain analysis method Perform time-domain complex heterodyne (demodulation) of the interferometer gravitational wave channel Low-pass filter these data The data is downsampled via averaging, yielding one value ( B k ) of the complex time series, every 60 seconds Determine the posterior probability distribution (pdf) of the parameters, given these data (B k ) and the model (y k ) Marginalize over nuisance parameters (cosι, ϕ 0, ψ) to leave the posterior distribution for the probability of h 0 given the data, B k We define the 95% upper limit by 1 a value h 95 satisfying: 95% 0 = h h0 = 0 ( a all data) dφ dψd cosι 0.95 dh0 p 0 Such an upper limit can be defined even when signal is present PDF 0 h 95 strain Landry - April APS, 4 May

9 Bayesian analysis A Bayesian approach is used to determine the posterior distribution of the probability of the unknown parameters via the Likelihood (assuming gaussian noise within our narrow band): The posterior pdf is p ( a) ( a { B }) p( a) p { B } k posterior prior likelihood k model B ( ) 2 k y t k;a 2 p( { Bk} a, σ k) exp - = exp -χ /2 2 k 2σ k B k s are processed data noise Landry - April APS, 4 May

10 Marginalizing over noise As we estimate the noise level from the B k no independent information is lost by treating it as another nuisance parameter over which to marginalize, i.e. p p ( B ) ( ) k} a p { Bk}, σ j a d j { σ 0 p 0 We assign Jeffreys prior to sigma, so that giving a (marginalized) likelihood of 1 ( σ a),( σ > 0) ( B ) ( ) ( ) k} a p σ j a p { Bk} a, σ j d j { σ which can be evaluated analytically for gaussian noise. j σ j j Where σ is constant for each 30 j B k, i.e. 30m Landry - April APS, 4 May

11 Analysis summary Raw Data Heterodyne, lowpass, average, calibrate: B k Compute likelihoods 1 p( { B k } a) n B k y k k 2 n Model: y k uniform priors on h 0 (>0), cosι, ϕ 0, ψ p Compute pdf for h 0 ( a) ( a { B }) p( a) p { B } k k Compute upper limits Landry - April APS, 4 May

12 S2 hardware signal injections Performed end-to-end validation of analysis pipeline by injecting simultaneous fake continuous-wave signals into interferometers Two simulated pulsars were injected in the LIGO interferometers for a period of ~ 12 hours during S2 Fake signal is sum of two pulsars, P1 and P2 All the parameters of the injected signals were successfully inferred from the data Landry - April APS, 4 May

13 Preliminary results for P1 Parameters of P1: P1: Constant Intrinsic Frequency Sky position: latitude (radians) longitude (radians) Signal parameters are defined at SSB GPS time which corresponds to a wavefront passing: LHO at GPS time LLO at GPS time In the SSB the signal is defined by f = Hz fdot = 0 phi = 0 psi = 0 iota = π/2 h 0 = 2.0 x Landry - April APS, 4 May

14 Preliminary results for P2 Parameters for P2: P2: Spinning Down Sky position: latitude (radians) longitude (radians) Signal parameters are defined at SSB GPS time: SSB , which corresponds to a wavefront passing: LHO at GPS time LLO at GPS time In the SSB at that moment the signal is defined by f= fdot = [phase=2 pi (f dt+1/2 fdot dt^2+...)] phi = 0 psi = 0 iota = π/2 h 0 = 2.0 x Landry - April APS, 4 May

15 Pulsar timing Analyzed 28 known isolated pulsars with 2f rot > 50 Hz.» Timing information has been provided using radio observations collected over S2/S3 for 18 of the pulsars (Michael Kramer, Jodrell Bank).» Timing information from the Australia Telescope National Facility (ATNF) catalogue used for 10 pulsars An additional 10 isolated pulsars are known with 2f rot > 50 Hz but the uncertainty in their spin parameters is such that a search over frequency is warranted Crab pulsar heterodyned to take timing noise into account Landry - April APS, 4 May

16 Preliminary results for PSR B L Posterior probability density for PSR J D Flat prior for h 0 (h 0 >0), Jeffreys prior for σ, i.e. p(σ) 1/σ L1 H1 H2 joint Landry - April APS, 4 May

17 Preliminary results for the Crab pulsar Posterior probability density for PSR B Crab pulsar heterodyned to take timing noise into account Flat prior for h 0 (h 0 >0), Jeffreys prior for σ, i.e. p(σ) 1/σ L1 H1 H2 joint Landry - April APS, 4 May

18 Preliminary upper limits for 28 known pulsars h 0 UL range Pulsar J , B , J , B B C, B D, B F, B G, B L, B M, B N, J , B A, J , J , J , J E, J , J C, J , J , J D, J , B A, J C, J B, J , B Blue: timing checked by Jodrell Bank Purple: ATNF catalogue Landry - April APS, 4 May

19 Equatorial Ellipticity Results on h 0 can be interpreted as upper limit on equatorial ellipticity Ellipticity scales with the difference in radii along x and y axes I ε = xx I I zz yy 4 c r h π G f gw I zz ε = Distance r to pulsar is known, I zz is assumed to be typical, g cm 2 Landry - April APS, 4 May

20 Preliminary ellipticity limits for 28 known pulsars ε UL range Pulsar B , J , B B , B D, J D, B A, J C, J B J , B C, B F, B L, B G, B M, B N, B A, J , J , J , J , J E, J C, J J , J , J , J Blue: timing checked by Jodrell Bank Purple: ATNF catalogue Landry - April APS, 4 May

21 Summary and future outlook S2 analyses» Time-domain analysis of 28 known pulsars complete» Broadband frequency-domain all-sky search underway» ScoX-1 LMXB frequency-domain search near completion» Incoherent searches reaching maturity, preliminary S2 results produced S3 run» Time-domain analysis on more pulsars, including binaries» Improved sensitivity LIGO/GEO run» Oct Jan 9 04» Approaching spindown limit for Crab pulsar Landry - April APS, 4 May