15-18 December 2004 GWDAW-9 Annecy 1 All-Sky broad band search for continuous waves using LIGO S2 data Yousuke Itoh 1 for the LIGO Scientific Collaboration 1 Albert-Einstein-Institute, Golm, Germany G Z

GWDAW-9 2 S2 Frequentist coherent search For S1: set upper limit on a single known pulsar »Targeted search (J ), ~ 2 weeks data »95 % UL: 2e-21 (GEO), 2.7e-22 (L1), 5.4e-22 (H1), 4e-22 (H2) (Phys. Rev. D ,2004) For S2: perform a wide parameters-space search »All-sky search: ~ 3e4 sky templates »Wide frequency band: Hz »Set an upper limit on each 1 Hz band »Coincidence analysis between two IFOs »10 hours good sensitivity data »Templates without spin-down  maximum spin-down 2.5e-11 Hz/s.

GWDAW-9 3 S2 Frequentist coherent search For S2: perform a wide parameters-space search »Computational cost  Tobs = 10 hours data Given a F statistic value ( Jaranowski, Królak, and Schutz Phys. Rev. D (1998) ), assuming it equals to the optimal signal to noise ratio defined in the JKS paper, the corresponding strain h0 of a signal averaged over the sky position and the nuisance parameters is: Correspondingly to this, the visible distance to a pulsar having ellipticity=1e-5, signal frequency=300 Hz, is 27 pc. »Practically, our aims are to establish a search pipeline, develop various techniques and solve problems arising during implementation(s) and tests of the pipeline in the application of it on the real data.

GWDAW S2 Search Pipeline This pipe line is executed on each 1 Hz band S2 10 hours data

GWDAW-9 5 Compute F stat. over bank of filters and frequency ranges. store results above threshold S2 Search Pipeline This pipe line is executed on each 1 Hz band

GWDAW Take a pair of candidates from two IFOs. Ask if the pair is coincident in the parameters space. Any candidate events in the step 2 that can not find a coincident pair in the step 3 will be rejected. 3 S2 Search Pipeline This pipe line is executed on each 1 Hz band

GWDAW Take a coincident pair generated in the step 3. If either or both of the two events in the pair are loud-enough, perform a chi-square test on the event(s). If either failed the test, reject the pair. Otherwise keep the pair as a coincident candidate. 4 S2 Search Pipeline This pipe line is executed on each 1 Hz band

GWDAW-9 8 x x x x x x x x x x x x x h 0 95% f0f ………………….460 | x || We have one such collection for every 1 Hz BAND

GWDAW-9 9 New in S2: Data selection computed the average Sh on 10 hours of data, every 30 minutes, when possible. constrain: the spanned observation time must not greater than 13 hs did this in various bands took the 10 hours stretch for which the average over the different bands is smallest H1: most sensitive 10 hours stretch over hours L1 : most sensitive 10 hours stretch over hours Note: we don’t care that the observations be simultaneous. We can do coincidences between data sets taken at different times.

GWDAW-9 10 New in S2: Noise power spectrum Sh Frequency in Hz Distribution of F statistic: running mean Dist. of F: running median Mean Outliers affect much and F statistic does not follow the chisquare distribution. Median Outliers affect little and F stat. follows the chisquare dist. 2F Observed noise PDF Distortion in PDF Theoretically expected PDF for white Gaussian.

GWDAW-9 11 New in S2: Frequency domain cluster identification 2F Frequency (Hz) Injected Signal Zoom up Single candidate event If the frequencies of two peaks are less than df Hz apart, they are considered to consist of a single candidate event. df = 1.4e-4 Hz by MC. At a fixed R.A. and Dec. Threshold on 2F

GWDAW-9 12 veto signal Injected damped sinusoid New in S2: F statistic shape veto Procedure Generate a veto signal from MLE parameters of the candidate (outlier). Compare the profiles of the outlier and the veto signal. Reference: GWDAW8 Class. Quant. Grav. 21 S1667, 2004 Frequency in Hz 2F Simulated pulsar signal veto signal

GWDAW-9 13 New in S2: Grid in the parameters space Equal spacing in frequency and pseudo isotropic grid for the sky template. Spacing in frequency, R.A, Dec. are determined by Monte Carlo: df = 1/8/(10 hours) Hz grid spacing = 0.02 radians both in R.A. and Dec. at the equator Then, maximum loss in F = 5 % for LLO and 2 % for LHO, 99 % of the MC trials, loss in F is less than 2 % for LLO and 0.5 % for LHO. Cumulative probability distribution of loss in F % of the trials with loss < x value (Loss in F) = 1 – Fobs/Fmax 0 0 % 100 % 5 % loss 2 % loss

GWDAW-9 14 New in S2: Coincidence analysis If a candidate event in one IFO are less than a certain distance in the parameters space away from a candidate event in the other IFO, these two candidate events are coincident. Significance of an event = False Alarm rate “Joint significance” of a coincident events pair LLO i and LHO j Loudest coincident event: = the coincident event having the smallest Joint significance Set an upper limit based on the loudest coincidence event event in each 1 Hz band.

GWDAW-9 15 Pulsar signal software injection Declination Right Ascension 2F All sky color map (LLO) Declination Right Ascension 2F All sky color map (LHO) Signal f = Hz R.A. = Dec. = Loudest LLO Only f = Hz R.A.= Dec.= Fmax=812.2 Loudest LHO Only f = Hz R.A.=3.494 Dec.= Fmax=146.1

GWDAW-9 16 LHO Loudest f = Hz R.A.=3.494 Dec.= Fmax=146.1 LLO Loudest f = Hz R.A.= Dec.= Fmax=812.2 LLO Loudest Coincident Loudest f = Hz Hz R.A.= Dec.= Fmax= LHO Loudest Coincident Loudest f = Hz R.A.= Dec.= Fmax= Coincidence analysis (cont’d) R.A. from 3.41 to 3.58 radians Dec. from to radians 2F Contour plot near the injected signal Coincidence window df=0.001 Hz (Angular distance)=0.028 rad. (one grid spacing) Loudest coincident pair Our (rather-restrictive-in-the-sky-location) coincidence-window gives us a better estimate of the signal sky location (at least for this example.)

GWDAW-9 17 if a signal is injected in the data from a random source (uniformly located on the sky, in frequency and in nuisance parameters) with h 0 = h 0 95% (or greater), then in 95% (or greater) of the injections the signal produces at the output of our pipeline a more significant coincidence than the most significant event that we have found in the actual analysis. It is in this sense that we say that h 0 95% is the 95% confidence strain upper limit value for the population of astrophysical signals used in the injections. Upper limit statement

GWDAW-9 18 Upper limit statement Pipeline LHO dataLLO data i-th injection of a signal with parameters randomly chosen but fixed h 0. i-th Joint Significance JS i Monte Carlo injection loop i=1 to N MC k = {Number of trials in which JS i is larger than the observed joint significance of the loudest coincident event} Compute p=k/N MC h 0 is the 100p % upper limit for the populations of the astrophysical signals used in injection.

GWDAW-9 19 What we expect Internal review and vetting of this search is not yet completed… COINCIDENCES LOWER THE LOUDEST EVENT: L1, 2F < 100: Mean single loudest = 49.0 mean coincident loudest = 34.2 H1, 2F < 100: Mean single loudest = 45.7 mean coincident loudest = 34.5 Based on the LIGO S2 noise curve, we expect the 95 % upper limit on the strain to be about several 10^-23 in quiet bands and a few 10^-22 in noisy bands. NOTE: This analysis : 10 hours blind search, 95 % UL ~10^-22. S1 : ~2 weeks targeted search, 95%UL ~ a few 10^-22. Several techniques have been developed in parallel and will be used in the future searches. More elaborate coincidence window see Prix’s poster. Metric based template placement Code speed-up