1. Coherent wide parameter space searches for gravitational waves from neutron stars using LIGO S2 data
Xavier Siemens, for the LIGO Scientific Collaboration University of Wisconsin -- Milwaukee

2. Interferometer network
LIGO Hanford WA
(4km & 2km)
LIGO Livingston LA
(4km)
GEO (600m)

3. The Signal Frequency f of signal in Solar System Barycenter (SSB)
A gravitational wave incident on an interferometer produces a changing differential arm length
We search for gravitational waves generated by rotating neutron stars with deviations from axisymmetry.
Signal is essentially monochromatic but Doppler shifted due to motion of the detector relative to the source
For example, isolated neutron star parameters:
Frequency f of signal in Solar System Barycenter (SSB)
Rate of change of frequency df/dt in SSB
Sky coordinates (, ) of source
Strain amplitude h0
Spin-axis inclination 
Phase, Polarization , 
Phase evolution
Amplitude modulation

4. The Searches Coherent searches: Incoherent searches:
For the first science run the LSC continuous wave group looked using two different coherent searches at a single isolated pulsar (J ). [Abbott et al., Phys. Rev. D ,2004]
For the second and third science runs we are pursuing a number of different approaches to the problem:
(NASA/CXC/SAO)
Coherent searches:
- Time-domain: Targeted [Abbott et al., gr-qc/ ] Markov Chain Monte Carlo - Frequency-domain: Isolated Binary, Sco X-1
Searches over narrow parameter space
Searches over wide parameter space
Ultimately, would like to combine these two in a hierarchical scheme
Incoherent searches:
+ Hough transform Stack-Slide + Powerflux
Excess power, wide parameter space searches

5. Wide Parameter Space Coherent Searches
Detection statistic: = log of the likelihood maximized over the nuisance parameters [Jaranowski, Krolak and Schutz, PRD58 (1998) ; Jaranowski and Krolak, PRD59 (1999) ]
Noise only: is a random variable that follows a distribution with 4 degrees of freedom
Noise+Signal: distribution has a non-centrality parameter

6. Scope of analyses Isolated neutron stars:
10 hours most sensitive S2 data Hanford 4k (H1) and Livingston 4k (L1) IFOs
All-sky search: ~ 3e4 sky position templates
Wide frequency band: 160 Hz- 760 Hz
Coincidence between L1 and H1 events
Templates without spin-down  maximum spin-down
2.5 x Hz/s.
Set upper limits in 1.2Hz bands
Binary neutron stars:
Dedicated Sco-X1 search
6 hour coherent integration of best S2 data (set by computational resources)
2 frequency windows: 464 – 484 Hz (strong spectral features) and 604 – 624 Hz (reasonably clean)
Search over uncertainties in orbital parameter space of
Sco-X1
Analyse L1 and H1 in coincidence
Set upper limits in 1Hz bands

7. Data analysis pipeline I
H1 data
L1 data
Binary search: 6 hours
Isolated: 10 hours
Isolated template bank: sky locations and frequencies
Binary template bank: orbital parameters and frequencies
Isolated search does an additional veto involving the shape of the F-statistic as a function of frequency
Compute F statistic
over template bank
Generate list of candidates above threshold
Compute F statistic
over template bank
Generate list of candidates above threshold
Parameter space consistency?
YES NO
Coincident Candidates
Rejected Candidates
Follow-up or Upper limit based on loudest event

8. Data analysis pipeline II
Coincidences
Coincidence has the effect of lowering the values of the detection statistic in both data sets when they are due to noise. More importantly, outliers produced by spectral disturbances are also more readily vetoed with a coincidence scheme.

9. Expected results Software and results currently under LSC review.
Based on the LIGO noise curve for S2 and the integration time we expect the upper limits on the strain for the all-sky isolated search to be in the range of several x10-23 to a few x10-22 depending on the noise character in the different bands.
For the binary search we expect upper limits in the range of a few x10-22
(Artist’s impression: NASA)