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

2. 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

3. 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

4. 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

5. 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

6. 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 ~ 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

7. 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 ~ [Hz ]–1/2

8. 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

9. 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
Hz, all-sky, fdot < 4e-10 Hz/s
V ANALYSIS OF THE DATA
VI RESULTS
VII CONCLUSIONS
APPENDIX A,B,C

10. 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

11. 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
L1 : most sensitive 20 SFTs stretch over hours

12. 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

13. 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

14. 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 points. Derived by MonteCarlo simulations.
frequency spacing: 3E-6 Hz
VI RESULTS
VII CONCLUSIONS
APPENDIX A,B,C

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

16. 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

17. Single IFO events
247 Hz
Hz, violin mode

18. 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

19. 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) ] }

20. 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

21. 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%

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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 Hz, Hz, Hz,
Hz and Hz.

28. Results for the isolated pulsar search
Hz : 10th harmonic of a key operating in the data acquisition system.
Hz and Hz are lines present only in L1, which have disappeared in S3.
Hz and 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

29. Results for the isolated pulsar search

30. 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).

31. 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 h presentation.

32. 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: Hz