Transcript G070826-00 - DCC

A 2 veto for Continuous Wave Searches
12th Gravitational Wave Data
Analysis Workshop
December 2007
L. Sancho de la J.
A.M. Sintes
(LIGO-G070826-00-Z)
Universitat de les
Illes Balears
Outline
Motivation
Hough Transform
The 2 veto
Results
12th Gravitational Wave Data Analysis Workshop (December 2007)
Motivation
Motivation
 Type of source  Continuous Sources
Hough Transform
- Very small amplitude ( h0  10-26 )
The 2 test
- Long integration time needed to build up enough SNR
Results
- Relative motion of the detector with respect to the source (amplitude and frequency modulated)
- System evolves during the observational period
 Type of search  All-sky search
- Computational cost increases rapidly with total observation time.
• Coherent Methods
nd
+ Stage:
sensitive
2(Matched
Follow up the candidates
filtering)
+ computational
cost
with
higher resolution.
 Type of Methods 
Hierarchical
Methods
• Semi-Coherent Methods
st Stage: Wide-parameter search with
1(Stack
 sensitive
Slide, Power Flux, Hough)
low
resolution in parameter
space.
 computational
cost
Reduce the number of candidates to be followed up  Improve the sensitivity keeping the computational cost.
12th Gravitational Wave Data Analysis Workshop (December 2007)
The Hough Transform
Motivation
Hough Transform
 Robust pattern detection technique.
The 2 test
Results
 We use the Hough Transform to find the pattern produced by the Doppler
modulation (due to the relative motion of the detector with respect to the source)
and spin-down of a GW signal in the time – frequency plane of our data:
 For isolated NS the expected pattern depends on the parameters:
12th Gravitational Wave Data Analysis Workshop (December 2007)
The Hough Transform
Motivation
 Procedure:
Hough Transform
1
Break up data (x(t) vs t) into segments.
Tobs
The 2 test
Results
T 
2
3
Tobs
N
Take the FT of each segment and calculate the corresponding normalized
power in each case (k ).
Select just those that are over a certain threshold th.

0
f
Frequency
t
12th Gravitational Wave Data Analysis Workshop (December 2007)
The Hough Transform
Motivation
 Procedure:
Hough Transform
The 2 test
Results
n
f
t
n0


 To improve the sensitivity of the Hough search, the number count can be incremented not
just by a factor +1, but rather by a weight i that depends on the response function of the
detector and the noise floor estimate  greater contribution at the more sensitive sky
f
locations and from SFTs which have low noise.
 The thresholds n0 and th are chosen based on the Neyman – Pearson criterion of
minimizing the false dismissal (i.e. maximize the detection probability) for a given value of
t
false alarm.
12th Gravitational Wave Data Analysis Workshop (December 2007)
Hough Transform Statistics
Motivation
 The probability for any pixel on the time - frequency plane of being selected is:
Hough Transform
The 2 test
q  e th
Signal absent
p
Signal present


  e  1 
th
th 
22 
kk  O  kk 
2
SNR for a
single SFT

k 
2
~
4 h ( fk )
Tcoh S n ( f k )
Results
 After performing the Hough Transform N SFTs, the probability that the pixel
has a number count n is given by
Without Weights
With Weights
N
N
Number Count
n   ni
Number Count
p n  
1
2 2
Signal absent
Signal absent
Mean
Variance
n Nq
Signal present
n  N
 2  N q (1  q )  2  N (1  )
Mean
n Nq
N
Variance
 2   i2 q (1  q )
i 1
12th Gravitational Wave Data Analysis Workshop (December 2007)

i 1
i 1
N
N n
p(n)    p n 1  p 
n
N
n   i ni

e
i 1
i
N
n  n 2
2 2
Signal present
n  qN 
N
q th
2
N
 
i 1
i
 2   i2i 1  i 
i 1
i
Need of the 2 discriminator
Motivation
Hough Transform
The 2 test
Results
 We define the significance of a number count as
n n
s
( n and  are the expected mean and
variance for pure noise)

 The Hough significance will be large if the data stream contains the desired
signal, but it can also be driven to large values by spurious noise.
 We would like to discriminate which of those could actually be from a real signal.
 It is important to reduce the number of candidates in a Hierarchical search 
improvement in sensitivity for a given finite computational power.
 Use the Hough Statistics information to veto the disturbances:
Hypothesis: Data = random Gaussian Noise + Signal
Construct a 2 test to validate this hypothesis
12th Gravitational Wave Data Analysis Workshop (December 2007)
The 2 test for the Weighted Hough Transform
Motivation
1) Divide the SFTs into p non-overlapping blocks of data
TOTAL
Hough Transform
The 2 test
Results
# SFTs
N1
N2
N3
...
Np
N
Number count
n1
n2
n3
...
np
n
N
p
N
Sum weights

N
p

N
p

N
p

2) Analyze them separately
3) Construct a 2 statistic looking along the different blocks to see if the Hough number count
accumulates in a way that is consistent with our hypothesis.
 
 If Signal present: small 2
12th Gravitational Wave Data Analysis Workshop (December 2007)
n
N
 If due to spurious noise: big 2
The 2 test: 2  significance plane characterization
 2  p 1
Gaussian Noise
Motivation
  2p
Hough Transform
 2  7.32
The 2 test
  3.98
Results
p=8
 2  15.57
  5.80
p = 16
12th Gravitational Wave Data Analysis Workshop (December 2007)
The 2 test: 2  significance plane characterization
Software Injected Signals
Motivation
Hough Transform
The 2 test
Results
p=8
p = 16
12th Gravitational Wave Data Analysis Workshop (December 2007)
The 2 test: 2  significance plane characterization
Motivation
Software Injected Signals
Hough Transform
91.1 – 99.9 Hz
101.1 – 101.9 Hz
252.1 – 252.9 Hz
420.1 – 420.9 Hz
The 2 test
Results
 1 month of LIGO data.
 Example for p = 16.
 22 small 0.8 Hz bands between 50 and 1000 Hz were analyzed.
 In each ‘quiet’ band we do 1000 Monte Carlo injections for different h0 values covering uniformly
all the sky, f-band, spindown  [-1·10-9  0] Hz s-1, and pulsar orientations (9000 MC 91-100 Hz)
 Find the best fit in the selected bands  fitting coefficients should be frequency dependent.
12th Gravitational Wave Data Analysis Workshop (December 2007)
Results (on 1 month of LIGO data)
Motivation
 Loudest significance in every 0.25Hz band obtained with Hough:
Hough Transform
The 2 test
Results
Fig.29 of “B. Abbott et al., All-sky search for periodic gravitational waves in LIGO S4 data, 2007 (arXiv:0708.3818)”
 Veto  92% of the frequency bins with significance greater than 7
12th Gravitational Wave Data Analysis Workshop (December 2007)
Instrumental Disturbances
Motivation
 VIOLIN MODES:
Hough Transform
The 2 test
Results
12th Gravitational Wave Data Analysis Workshop (December 2007)
Hardware Injected Signals
Motivation
 PULSARS: (injected 50% of the time  look like disturbances!)
Hough Transform
The 2 test
Pulsar 3
Pulsar 8
Pulsar 2
Results
Pulsar 9
12th Gravitational Wave Data Analysis Workshop (December 2007)
Conclusions and future work
Motivation
Hough Transform
The 2 test
Results
 We have developed a 2 veto for the Hough Transform in the CW search and we have
characterized it in the presence of a signal and in the presence just of noise (Gaussian
noise and also instrumental perturbations).
 We have proven the efficiency of this veto using 1month of LIGO data.
 Under development : This 2 veto is being implemented for an all-sky search using the
LIGO S5 data.
12th Gravitational Wave Data Analysis Workshop (December 2007)