1. 1 Status of Power-Flux * Search for Continuous-Wave Sources Dave Chin, Vladimir Dergachev, Keith Riles (University of Michigan) LIGO Scientific Collaboration Meeting LIGO Livingston Observatory March 15-18, 2004 *The analysis formerly known as “unbiased” G040076-00-Z

2. 2 Analysis Procedure Compute raw powers for intervals over entire data run (30-minute SFT’s  0.5 mHz binning) Define sky/polarization bins [RA,  For each sky/polarization bin and each 0.5 Hz band, define log 10 (power) matrix (900 freq bins  ~2000 SFT’s) where: –Each power corrected for antenna-pattern: 1 / |F +/× | 2 –Power weighted by inverse noise: 1/ σ 2 where σ ~  Option to avoid discarding high-noise SFT’s –Alternatives: unweighted mean or median with SFT vetoing (results shown here)

3. 3 Analysis Procedure (cont.) Decompose matrix into sum of SFT and frequency vectors plus residuals with zero median per row & column  Diagnostic of anomalous bins & SFT’s  Remove large-outlying SFTs (option)  Flag but do not remove large-outlying frequency bins  Flag bins with poor K-S statistic for residual Order SFT’s in ascending corrected power Stack bins of corrected power with 1/noise weighting until last SFT added increases expected standard deviation of median over band of cumulative stacks Recompute matrix from retained SFT’s, including Doppler frequency shifts (“sliding”)

4. 4 Analysis Procedure (cont.) Use Monte Carlo simulations (software injections) to estimate biases and errors on upper limits (to do) Recent Changes from Previous Baseline Analysis Added “sliding”  Improves performance, negligible additional computing cost Included antenna pattern correction in power estimation (instead of post-computation efficiency correction)  Better handles non-stationary noise Tried inverse-noise weighting of power contributions  Option for non-stationary noise, but less effective than expected  Computational cost of extra SFT’s make truncation attractive

5. 5 Snapshot of Analysis Most analysis elements in place – will present preliminary S2 limits for a selected 0.5 Hz band at selected sky point for “+” polarization

6. 6 Sample frequency band: H1 650.0-650.5 Hz Matrix decomposition – SFT median vector (no antenna-pattern correction) Chronological orderSorted by median power

7. 7 Sample frequency band: H1 650.0-650.5 Hz Matrix decomposition – Frequency median vector (no antenna-pattern correction) [log 10 (power) contribution]

8. 8 Sample frequency band: H1 650.0-650.5 Hz Matrix decomposition – Residuals for all bins (no antenna-pattern correction) H1 data: Stationary noise simulation Non-stationary noise simulation

9. 9 Sample frequency band: H1 650.0-650.5 Hz Matrix decomp.: Estimated error vs ordered SFT (no antenna-pattern correction) Stop here

10. 10 Sample frequency band: H1 650.0-650.5 Hz Now bin the sky and include antenna pattern (arbitrary sampling of 264 sky locations) Stop here  Antenna pattern strongly affects sample of SFT’s retained (prefers low-noise SFT’s with favorable orientation)

11. 11 Sample frequency band: H1 650.0-650.5 Hz Sample of SFT’s kept/discarded in the analysis KEEP DISCARD SFT index (time)

12. 12 Sample frequency band: H1 650.0-650.5 Hz Median of SFT powers in the band with Doppler corrections: (similar to stack-slide) Edge effects due to Doppler shifts  Exclude left/right ~0.1 Hz One sky point (of 264):

13. 13 Sample frequency band: H1 650.0-650.5 Hz Set limits on total power flux in each frequency bin (for now, define 90% CL as [measured + 1.3 σ band ], where “measured” is constrained to be non-negative; do it right later) Measured median powers: Mean-subtracted powers + 1.3 sigma: Min upper limit

14. 14 Sample frequency band: H1 650.0-650.5 Hz Convert “power flux” limit to strain amplitude limit: (pile-up at left edge due to ultra-conservative truncation of excess power at zero) Reminder Limits apply to One sky location One polarization One band No Monte Carlo efficiency correction Preliminary Limits h + < 2-4 × 10 -23

15. 15 Summary Have demonstrated a pipeline for obtaining limits in presence of non-stationary noise Implemented antenna pattern & Doppler modulations But much work to do: Signal injection tests – evaluate required sky binning Deal with strong instrumental lines Deal with colored noise (fit? Running median?) Logistics of full search over ~2kHz and polarization Multiple IFO’s