S2 Fstat paper presentation isolated LIGO-G05XXXX-00-Z LSC meeting Boston, November 2005

Coherent wide parameter space searches for periodic gravitational waves in LIGO data: all-sky and Sco X-1 results Abstract I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS IV SIGNAL MODEL V ANALYSIS OF THE DATA VI RESULTS VII CONCLUSIONS ACKNOWLEDGEMENTS APPENDIX A,B,C

III ASTROPHYSICAL TARGETS Abstract I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS IV SIGNAL MODEL V ANALYSIS OF THE DATA VI RESULTS VII CONCLUSIONS ACKNOWLEDGEMENTS APPENDIX A,B,C

I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS Emission mechanisms Review emission mechanism and conclude that “the most likely sources of detectable GWs are isolated NSs through deformations and accreting NSs in binaries through deformations or r-modes.’’ IV SIGNAL MODEL V ANALYSIS OF THE DATA VI RESULTS VII CONCLUSIONS APPENDIX A,B,C

Maximum expected GW amplitude at the Earth I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS Emission mechanisms Isolated neutron stars Maximum expected GW amplitude at the Earth By extending an argument attributed to Blandford we conclude that h0max ~ 4E-24. Thus the current search is unlikely to make detection factor of o(15) worse. IV SIGNAL MODEL V ANALYSIS OF THE DATA VI RESULTS VII CONCLUSIONS APPENDIX A,B,C

Expected sensitivity of the S2 search I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS Emission mechanisms Isolated neutron stars Maximum expected GW amplitude at the Earth Expected sensitivity of the S2 search Typical sensitivity: h0 ~ 10-22 which corresponds to a reach of about 30pc at 260 Hz. IV SIGNAL MODEL V ANALYSIS OF THE DATA VI RESULTS VII CONCLUSIONS APPENDIX A,B,C

Distance (parsec) Astrophysical reach of the search: a methods illustration search Distance (parsec) signal frequency f0 (Hz) astrophysics expectations: h0 < 4E-24 (statistical argument)  our search is factors of o(20) less sensitive distance at which a pulsar could be detected versus its g.w. frequency for different e, at false alarm 1% and false dismissal 10% -- assuming frequency and position were known in advance. It’s S2: Sh no better than ~ 3 10-22 [Hz ]–1/2

Distance (parsec) Astrophysical reach of the search: this is mainly a methods paper. Distance (parsec) signal frequency f0 (Hz) h0= (4 pi^2 G /c^4) I f^2 e /d <h0> = sqrt [ 2F * Sh *25 /(4*Tobs)] e^2 = (5 c^5/32 G pi^4) fdot/I f^5

160-728.8 Hz, all-sky, fdot < 4e-10 Hz/s I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS Emission mechanisms Isolated neutron stars Maximum expected GW amplitude at the Earth Expected sensitivity of the S2 search IV SIGNAL MODEL 160-728.8 Hz, all-sky, fdot < 4e-10 Hz/s V ANALYSIS OF THE DATA VI RESULTS VII CONCLUSIONS APPENDIX A,B,C

Data selection for the isolated neutron stars search I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS IV SIGNAL MODEL V ANALYSIS OF THE DATA The detection statistic Pipeline FFTs and selection of the data Data selection for the isolated neutron stars search Difference in data selection is due to the fact that the Sco X-1 search is a targeted search in the sky. VI RESULTS VII CONCLUSIONS APPENDIX A,B,C

Data selection constrain: the spanned observation time < 13 hs The selection criteria depend only on Sh computed the average Sh over 10 hours of data by averaging 20 SFTs (Short (timebaseline) Fourier transform, 30 min timebaseline) constrain: the spanned observation time < 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 20 SFTs stretch over 10 hours starting @ 733803157 L1 : most sensitive 20 SFTs stretch over 12.75 hours starting @ 732489168

The H1 data: 892 sets found <Sh> ½ Average sqrt(Sh) over 20 SFTs (a set) in a small band. Different bands shown. <Sh> ½ Time during S2 run, in SFT-set order-number Average curves above over the different bands. minimum of the noise – chosen set Time during S2 run, in SFT-set order-number

The L1 data: 8 sets found <Sh> ½ Average sqrt(Sh) over 20 SFTs (a set) in a small band. Different bands shown. <Sh> ½ order # of the first SFT of the set Average curves above over the different bands. minimum of the noise – chosen set order # of the first SFT of the set

frequency spacing: 3E-6 Hz I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS IV SIGNAL MODEL V ANALYSIS OF THE DATA The detection statistic Pipeline FFTs and selection of the data Filter banks sky position: uniform area coverage on sphere. 31500 points. Derived by MonteCarlo simulations. frequency spacing: 3E-6 Hz VI RESULTS VII CONCLUSIONS APPENDIX A,B,C

L1 H1 m=1-Fobs/Fopt fraction of trials for which mismatch was < abscissa value (tot. number of trials: 100 000) m =1-Fobs/Fopt L1 mismatch m < 4% in 99% of trials H1 mismatch m < 2% in 99% of trials

Detail the single IFO search I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS IV SIGNAL MODEL V ANALYSIS OF THE DATA The detection statistic Pipeline FFTs and selection of the data Filter banks Single IFO search Detail the single IFO search Explain how the search is distributed to different processors Show distributions of events VI RESULTS VII CONCLUSIONS

Single IFO events 247 Hz 343.6 Hz, violin mode

Define joint significance of coincident events I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS IV SIGNAL MODEL V ANALYSIS OF THE DATA The detection statistic Pipeline FFTs and selection of the data Filter banks Single IFO search Coincidence analysis Define joint significance of coincident events Statistics before and after coincidence Compare with fake noise VI RESULTS VII CONCLUSIONS

Joint significance used to rank coincidences we measure loudness of a value of the detection statistic on the theoretical distribution of the noise false alarm s(2F*): joint false alarm of two values of 2F, one measured in H1 and one in L1 is defined as Pfa(FH1 , 2FL1 ) = pfa (2FH1) * pfa (2FL1). joint significance : 1 - Pfa(FH1 , 2FL1 ) which has the same ranking as - { log [pfa (2FH1) ] + log [pfa (2FL1) ] }

Loudest (over whole sky and 1.2 Hz bands) single IFO search In gaussian stationary noise: mL1 = 45.7 mH1 = 41.7 The values are different due to the different data set and location of the detectors. Our data is affected by spectral contamination. Not surprising. m 2F <100 = 52.2 m 2F <100 = 46.6

Loudest (over whole sky and 1.2 Hz bands) coincident search 2F <100 = 52.2 after coincidence: 2F <100 = 39.5 15% h0 sensitivity improvement In GSN 11% 2F <100 = 46.6 after coincidence: 2F <100 = 32.2 20% h0 sensitivity improvement In GSN 17%

Loudest coincident templates 2 nearby points per 1.2 Hz band: the loudest coincident template in H1 and L1 higher concentration at the poles, where instrumental lines have signature of signals Southern Hemisphere Northen Hemisphere

I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS IV SIGNAL MODEL V ANALYSIS OF THE DATA The detection statistic Pipeline FFTs and selection of the data Filter banks Single IFO search Coincidence analysis Upper limits Detail procedure of MonteCarlo injections and searches of a population of signals. VI RESULTS VII CONCLUSIONS

Setting the upper limit h0 injected Confidence Various sets of injections are performed. Each set consists of at least 3200 injections. For each set we derive a value of the confidence versus the injected h0. Each set is a blue dot. From the various sets we do a linear fit and read off the h0 corresponding to C=0.95

Recover well hardware injected pulsars (TableII) I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS IV SIGNAL MODEL V ANALYSIS OF THE DATA The detection statistic Pipeline FFTs and selection of the data Filter banks Single IFO search Coincidence analysis Upper limits Hardware injections Recover well hardware injected pulsars (TableII) VI RESULTS VII CONCLUSIONS

VI RESULTS I INTRODUCTION II INSTRUMENTS AND THE SECOND SCIENCE RUN III ASTROPHYSICAL TARGETS IV SIGNAL MODEL V ANALYSIS OF THE DATA The detection statistic Pipeline FFTs and selection of the data Filter banks Single IFO search Coincidence analysis Upper limits Hardware injections VI RESULTS VII CONCLUSIONS

Results for the isolated pulsar search Green line: 90th percentile upper limit values cyan circles: 90th percentile most significant events. red crosses: ratios R of F values too high or too low to be compatible w. same source. magenta lines: 1.2 Hz bands excluded because loudest event is due to a known instrumental noise feature. Lines detailed in appendix B. 95% h0 upper limit Only 5 events remain unexplained in the 90th percentile: @ 160.00 Hz, 546.03 Hz, 564.02 Hz, 626.80 Hz and 700.51 Hz.

Results for the isolated pulsar search 160.00 Hz : 10th harmonic of a key operating in the data acquisition system. 626.80 Hz and 700.51 Hz are lines present only in L1, which have disappeared in S3. 546.02 Hz and 626.80 Hz appear clearly only in H1 in S2 and in subsequent runs. In S3 the amplitude of both lines decreases by a factor of 10. This is a behaviour which is not consistent with the model of the signal that we are searching for. 95% h0 upper limit

Results for the isolated pulsar search

Results for the isolated pulsar search: broad agreement with expectations. With GSN: This is what the red curve shows. So there is good agreement between observations and expectations. The ratio of measured to expected never exceeds 4.4 and the 90th percentile level is 1.7 Departures from expectations depend on estimate of noise (Sn).

Conclusions The sensitivity of the searches makes it extremely unlikely to detect anything. Main goal of paper is to demonstrate an analysis method on real data Pipeline presented is considerably more complex than any other coherent search previusoly performed This is a necessary dry-run for one of the two steps of a hierarchical procedure. We do not attempt any follow-up. This is an upper-limit paper – but we have taken the time to understand our loudest events. Most constraining 95% confidence upper limits: 6.6E-23 for the isolated, 580 Hz band, all-sky search 1.7E-22 for the Sco X-1 search Previously published upper limits from coherent searches: 0.76 Hz search, all-sky, coherent over 48 hrs, 1 spin-down parameter: 90% confidence 1E-22 No cleaning performed here: wanted to characterize the effects of spectral artifacts Future: merge into a hierarchical scheme. This is already happening – e.g. S3 E @ h presentation.

Results for the isolated pulsar search red lines : 1.2 Hz bands excluded because MC did not converge due to high spectral noise (power lines) magenta lines: 1.2 Hz bands excluded because loudest event is due to a known instrumental noise feature. 95% h0 upper limit Most constraining UL: 6.6E-23 @ 265.6-266.8 Hz