1. A.M. Sintes for the pulgroup
First all-sky upper limits from LIGO on the strength of periodic gravitational waves using the Hough transform LIGO-P R
A.M. Sintes
for the pulgroup
LSC Meeting, 4-5 June 2005
University of Michigan Ann Arbor

2. Content I. Introduction II. The second science run
III. Astrophysical targets
IV. The expected waveform
V. The Hough transform
VI. The search
The SFT data
The parameter space
The implementation of the Hough transform
Number counts from L1, H1 and H2
VII. Upper limits
VIII. Hardware injections
IX. Conclusions
A. The bias in the running median
B. The number count outliers

3. II. The second science run. Feb. 14-Apr
II. The second science run. Feb.14-Apr.14,2003 Sensitivity of the Hough search
Characteristic amplitude detectable from a known generic source with a 10% false dismissal and 1% false alarm rate using the Hough transform
III. Astrophysics expectation h0 less than 4x10-24

4. IV. The expected waveform
Expected waveform from an isolated spinning NS is sinusoidal with small spin-down:
Doppler frequency modulation due to motion of Earth and amplitude modulation due to detector antenna pattern.
For setting upper limits only, we assume the emission mechanism is due to deviations of the pulsar’s shape from perfect axial symmetry, fGW=2fr

5. V. The Hough transform Time-frequency pattern
We use the HT to find a pattern produced by the Doppler modulation & spin-down of a GW signal in the time-frequency plane of our data.
For isolated NS the expected pattern depends on: {a,d, f0, fn} n d a

6. V. The Hough transform Frequency Time
Break up data into N segments, take the Fourier transforms, select frequency bins
p(r|h, Sn) is a 2 distribution with 2 degrees of freedom
Frequency
Time
After performing the HT using N SFTs, the probability that a point in parameter space has a number count n is given by a binomial distribution
Optimal choice rth=1.6 , q=0.20
The relation between nth and the false alarm a for candidate selection

7. VI. The search A. The SFT data, B. Parameter space
Input data: S2 (Feb 14- Apr 14, 2003)
Calibrated 30 minutes SFTs produced according to v.05 DQ segments on June 10, 2004
L1: N=687; H1: N=1761; H2: N=1384
Search for isolated pulsars
frequency band 200 – 400 Hz (Δf = 1/1800 Hz = 5.55×10 – 4 Hz)
1 spin-down parameter (11 values: Δf1 = –1.1×10– 10 Hz s– 1)
Templates:
1.5×105 sky locations for the whole 300 Hz Hz Hz

8. VI.C Implementation of the HT
HMs can be obtained by summing the appropiate PHMs
PHMs can be reused for different values of frequency and spin-down
Make use of LUTs to construct PHMs
Use of PHMDs instead of PHMs
Full-sky search for the entire S2 run, on 200 CPUs on the Merlin AEI, each analyzing 1 Hz band, and distributed using Condor lasted less than half a day (3 IFOs)

9. VI.D Number counts from L1, H1, H2 Number count distribution
blue: Hz
green: Hz
asterisks: theoretical

10. Known spectral disturbances: 200-400 Hz
Calibration lines
n*60 Hz power lines
n*16 Hz due to data acquisition
Mechanical resonances: violin modes
Comb ~37 Hz, with side lobes ~0.7Hz, due to synthesized oscillators
n*0.25 Hz

11. L1 kk H1 H2

12. Histograms of the maximum number count
Raw output
After the frequency veto

13. B. Outliers present in the Hough maps
~1012 number of templates in the 200 Hz. Threshold at a=10-13, corresponding to a threshold in the number count of: 216 for L1, 480 for H1, and 390 for H2
3 x Hz
4 x Hz
5 x Hz
n× Hz detected in association with VME controller hardware used during S2

14. L1
Noise spectrum √Sn
Outliers stand above the background noise level. However we have not determined in a conclusive manner their physical cause . H1 H2

15. VII. Frequentist upper limit
Perform the Hough transform for a set of points in parameter space l={a,d,f0,fi} S , given the data:
HT: S  N
l  n(l)
Determine the maximum number count n*
n* = max (n(l)): l  S
Determine the probability distribution p(n|h0) for a range of h0
The 95% frequentist upper limit h095% is the value such that for repeated trials with a signal h0 h095%, we would obtain n  n* more than 95% of the time
Compute p(n|h0) via Monte Carlo signal injections

16. Number count distribution for signal injections
L1: Hz, n* = injections
p(n|h0) ideally binomial for a target search, but:
Non stationarity in the noise
Amplitude modulation of the signal for different SFTs
Different sensitivity for different sky locations and pulsar orientations
Random mismatch between signal & templates
‘smear’ out the binomial distributions
0.1%
30.5%
87.0% 1

17. Monte-Carlo & Confidence level
L1: Hz
0.02x10-23, 0.5% error
1.5% error

18. UL accuracy for 5000 injections
L1: Hz 0.1x10-23→ 2.2%
H1: Hz 0.1x10-23→ 2.0%
injections %
5000 injections →accuracy better than 3% in the 95% confidence UL for h0

19. Measured PDF: p(n|h0inject)
L1: Hz h0inject =4.422x10-23 C=94.95%, n* =202
H1: Hz h0inject =4.883x10-23 C=95.04%, n* =455
H2: Hz h0inject =8.328x10-23 C=95.02%, n* =367
100,000 injections

20. Hough S2: 95 % confidence UL

21. Best all-sky UL on h0

22. Astrophysical reach

23. VIII. Hardware injections (12 h)
Data: 14 SFTs for L1 17 SFTs for H1 13 SFTs for H2
P1: Constant Intrinsic Frequency
Sky position: Dec (radians)
RA (radians)
f = Hz
fdot = 0, phi = 0, psi = 0, iota = p/2
h0 = 2.0 x 10-21
P2: Spinning Down
Sky pos.: Dec (radians)
RA (radians)
f= Hz
fdot = Hz s-1, L1 H1 H2

24. Hough S2: UL Summary Detector L1 H1 H2 Frequency (Hz) 200-201 259-260
Best S2 upper limit for a targeted coherent search was 1.7×10-24 for PSR J D
26 times worse
Detector L1 H1 H2
Frequency (Hz)
h095%
4.43x10-23
4.88x10-23
8.32x10-23