All-sky search of EXPLORER d ata

1. All-sky search of EXPLORER data Andrzej Królak Albert Einstein Institute Golm on leave from Institute of Mathematics Warsaw Annecy 17/12/2004

2. All-sky Search of the EXPLORER Data EXPLORER resonant bar detector The EXPLORER detector is operated by Italian group ROG led by Eugenio Coccia. The analysis is performed by a team consisting of Pia Astone, Kazik Borkowski, Piotr Jaranowski, Andrzej Królak, Maciej Piętka and is carried out on the basis of Memorandum of Understanding between the ROG group and Institute of Mathematics of the Polish Academy of Sciences. http://www.astro.uni.torun.pl/~kb/AllSky/AllSky.html Annecy 17/12/2004

3. Collaboration with VIRGO project Three searches for continuous sources of GW were performed. Each consisted of analysis of 2 days of EXPLORER data. Numerical calculation for two searches were performedby a network of computers in Bologna and Rome under an agreement between Rog Collaboration and the VIRGO project group in Rome led by Fulvio Ricci. Annecy 17/12/2004

4. Response of the detector to a continuous GW signals. GW Annecy 17/12/2004

5. Linear parameterization Response of the detector • For observation time of a few days and a few Hz bandwidth linear representation is an adequate approximation. Annecy 17/12/2004

6. Maximum likelihood detection F-statistic Annecy 17/12/2004

7. False alarm probability For a linear phase model F is a homogeneous random field Characteristic correlation hyper ellipse Taylor expansion Number of cells in the parameter space: Reduced Fisher information matrix False alarm probability Annecy 17/12/2004

8. Grid of templates in the parameter space Expectation value of the statistics when the signal is present in the data Taylor expansion Signal-to-noise loss Find a regular grid so that each element of the grid is inscribed into hyperellipsoid Annecy 17/12/2004

9. Spectral density of EXPLORER data Annecy 17/12/2004

10. Statistical analysis of 13-day set of data taken by EXPLORER detector in November 1991 Annecy 17/12/2004

11. Parameters of search I • Parameters of the data: • Modified Julian Date of the first sample: 48580.7908507 • Length of observation time: 2 days • Bandwidth of the search: 920.9992 -- 921.7598 Hz • Parameters of the search: • Spin down range: -9.1762 10-8 -- +9.1762 10-8 Hz s-1 • No. of spin downs 2868 • Sky positions: All sky, no. of pointings 31915 • No. of filters = 183064440 • Sensitivity of the search • Spectral density (two-sided) = 10-21/√Hz Annecy 17/12/2004

12. Parameters of search II: The same as search I except that Modified Julian Date of the first sample: 48591.6456387 Parameters of search III: The same as search I except that Modified Julian Date of the first sample: 48582.7853901 Annecy 17/12/2004

13. Candidate statistics If there is no noise F has χ2distribution with 4 degrees of freedom. Search I Annecy 17/12/2004

14. Search II Annecy 17/12/2004

15. Search III Annecy 17/12/2004

16. Results of the searches No. of triggers max SNR (astro) SI 37349 8.19 SII 21549 8.29 SIII 42626 8.45 Annecy 17/12/2004

17. Trigger verification • Transformation from parameters (p0,p1,A,B) to astrophysical parameters (f, f1, δ,α) . • Search on a small grid around astrophysical parameters. • Search in a different 2-day stretch of data. • Search in a 4-day stretch of data containing the original 2-day stretch. Annecy 17/12/2004

18. Trigger verification: examples Annecy 17/12/2004

19. Annecy 17/12/2004

20. Additional verification • 1. Search for signals with parameters of the trigger in the whole 13 day long data set • (Signal-to-noise should theoretically increase by 250%!) • 2. Search for coincidences among triggers • for various searches Annecy 17/12/2004

21. Original verification Annecy 17/12/2004

22. Addition verification in all data Annecy 17/12/2004

23. Upper limit 99% confidence upper limit Annecy 17/12/2004

24. Upper limit for the 3 searches Annecy 17/12/2004