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A  2 veto for Continuous Wave Searches

Universitat de les Illes Balears. A  2 veto for Continuous Wave Searches. 12 th Gravitational Wave Data Analysis Workshop. December 2007. L. Sancho de la J. A.M. Sintes. (LIGO-G070826-00-Z). Outline. Motivation Hough Transform The  2 veto Results.

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A  2 veto for Continuous Wave Searches

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  1. Universitat de les Illes Balears A 2 veto for Continuous Wave Searches 12th Gravitational Wave Data Analysis Workshop December 2007 L. Sancho de la J. A.M. Sintes (LIGO-G070826-00-Z)

  2. Outline Motivation Hough Transform The 2 veto Results 12th Gravitational Wave Data Analysis Workshop (December 2007)

  3. + sensitive + computational cost  sensitive  computational cost Motivation • Type of source  Continuous Sources Motivation • Very small amplitude( h0  10-26 ) Hough Transform - Long integration time needed to build up enough SNR The 2 test - Relative motion of the detector with respect to the source (amplitude and frequency modulated) Results - System evolves during the observational period • Type of search All-sky search - Computational cost increases rapidly with total observation time. • Coherent Methods 2nd Stage: Follow up the candidates with higher resolution. (Matched filtering) Hierarchical Methods • Type of Methods  • Semi-Coherent Methods 1st Stage: Wide-parameter search with low resolution in parameter space. (Stack Slide, Power Flux, Hough) Reduce the number of candidates to be followed up Improve the sensitivity keeping the computational cost. 12th Gravitational Wave Data Analysis Workshop (December 2007)

  4. The Hough Transform Motivation • Robust pattern detection technique. Hough Transform The 2 test • We use the Hough Transform to find the pattern produced by the Doppler modulation (due to the relative motion of the detector with respect to the source) and spin-down of a GW signal in the time – frequency plane of our data: Results • For isolated NS the expected pattern depends on the parameters: 12th Gravitational Wave Data Analysis Workshop (December 2007)

  5. r f r0 f t Frequency t The Hough Transform • Procedure: Motivation Break up data (x(t) vs t) into segments. 1 Hough Transform The 2 test Results Take the FT of each segment and calculate the corresponding normalized power in each case (k ). 2 Select just those that are over a certain threshold th. 3 12th Gravitational Wave Data Analysis Workshop (December 2007)

  6. n n0   f f t t The Hough Transform • Procedure: Motivation Hough Transform The 2 test Results • To improve the sensitivity of the Hough search, the number count can be incremented not just by a factor +1, but rather by a weight ithat depends on the response function of the detector and the noise floor estimate  greater contribution at the more sensitive sky locations and from SFTs which have low noise. • The thresholds n0 and th are chosen based on the Neyman – Pearson criterion of minimizing the false dismissal(i.e. maximize the detection probability) for a given value of false alarm. 12th Gravitational Wave Data Analysis Workshop (December 2007)

  7. Hough Transform Statistics • The probability for any pixel on the time - frequency plane of being selected is: Motivation Signal absent Signal present Hough Transform SNR for a single SFT The 2 test Results • After performing the Hough Transform N SFTs, the probability that the pixel has a number count n is given by Without Weights With Weights Number Count Number Count Signal absent Signal present Signal absent Signal present Mean Mean Variance Variance 12th Gravitational Wave Data Analysis Workshop (December 2007)

  8. Need of the 2discriminator • We define the significance of a number count as Motivation ( andare the expected mean and variance for pure noise) Hough Transform The 2 test • The Hough significance will be large if the data stream contains the desired signal, but it can also be driven to large values by spurious noise. Results • We would like to discriminate which of those could actually be from a real signal. • It is important to reduce the number of candidates in a Hierarchical search  improvement in sensitivity for a given finite computational power. • Use the Hough Statistics information to veto the disturbances: Hypothesis: Data = random Gaussian Noise + Signal Construct a 2 test to validate this hypothesis 12th Gravitational Wave Data Analysis Workshop (December 2007)

  9. The 2 test for the Weighted Hough Transform 1) Divide the SFTs into p non-overlapping blocks of data 2) Analyze them separately 3) Construct a 2 statistic looking along the different blocks to see if the Hough number count accumulates in a way that is consistent with our hypothesis. Motivation TOTAL # SFTs Number count Sum weights N1 N2 N3 ... Np N n1 n2 n3 ... np n N Hough Transform The 2 test Results • If Signal present: small2 • If due to spurious noise: big 2 12th Gravitational Wave Data Analysis Workshop (December 2007)

  10. The 2 test: 2  significance plane characterization Gaussian Noise Motivation Hough Transform The 2 test Results p = 8 p = 16 12th Gravitational Wave Data Analysis Workshop (December 2007)

  11. The 2 test: 2  significance plane characterization Software Injected Signals Motivation Hough Transform The 2 test Results p = 8 p = 16 12th Gravitational Wave Data Analysis Workshop (December 2007)

  12. The 2 test: 2  significance plane characterization Software Injected Signals Motivation Hough Transform 91.1 – 99.9 Hz 101.1 – 101.9 Hz 252.1 – 252.9 Hz 420.1 – 420.9 Hz The 2 test Results • 1 month of LIGO data. • Example for p = 16. • 22 small 0.8 Hz bands between 50 and 1000 Hz were analyzed. • In each ‘quiet’ band we do 1000 Monte Carlo injections for different h0 values covering uniformly all the sky, f-band, spindown  [-1·10-9  0] Hz s-1, and pulsar orientations (9000 MC 91-100 Hz) • Find the best fit in the selected bands  fitting coefficients should be frequency dependent. 12th Gravitational Wave Data Analysis Workshop (December 2007)

  13. Results (on 1 month of LIGO data) • Loudest significance in every 0.25Hz band obtained with Hough: Motivation Hough Transform The 2 test Results Fig.29 of “B. Abbott et al., All-sky search for periodic gravitational waves in LIGO S4 data, 2007 (arXiv:0708.3818)” • Veto  92% of the frequency bins with significance greater than 7 12th Gravitational Wave Data Analysis Workshop (December 2007)

  14. Instrumental Disturbances • VIOLIN MODES: Motivation Hough Transform The 2 test Results 12th Gravitational Wave Data Analysis Workshop (December 2007)

  15. Hardware Injected Signals • PULSARS: (injected 50% of the time  look like disturbances!) Motivation Hough Transform Pulsar 3 Pulsar 2 The 2 test Pulsar 8 Results Pulsar 9 12th Gravitational Wave Data Analysis Workshop (December 2007)

  16. Conclusions and future work Motivation Hough Transform • We have developed a 2 veto for the Hough Transform in the CW search and we have characterized it in the presence of a signal and in the presence just of noise (Gaussian noise and also instrumental perturbations). The 2 test Results • We have proven the efficiency of this veto using 1month of LIGO data. • Under development : This 2veto is being implemented for an all-sky search using the LIGO S5 data. 12th Gravitational Wave Data Analysis Workshop (December 2007)

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