10/06/2003LSC WIDE COLLOQUIUM1 LSC Pulsar Group and P Shawhan, S Marka, and S Koranda presented by B...

10/06/2003 LSC WIDE COLLOQUIUM 1

LSC Pulsar Group and P Shawhan, S Marka, and S Koranda

presented by B Allen, R Dupuis, N Christensen, and X Siemens

S2 Hardware Pulsar Injections


Why Do Hardware Injections?• Provides end-to-end validation of search code:

– Gain confidence about tricky things like floating point dynamic range in filtering process

– Helps algorithm/code developers in testing– Provide a fixed point of reference to return to

• Challenges in the pulsar case:– Realistic signals must last for hours (~107 cycles). This is unlike the

burst (seconds) and inspiral (tens of seconds) case.– Would like to avoid the “SB” scenario where the simulated signal

dominates the data– Getting the correct initial phase relationship at the different detector

sites can be tricky (specifics later)• Simpler in pulsar case:

– Calibration: signal is at a “single” frequency


S2 Pulsar Injection Parameters

• Signal is sum of two different pulsars, P1 and P2

P1: Constant Intrinsic FrequencySky position: 0.3766960246 latitude (radians)

5.1471621319 longitude (radians)Signal parameters are defined at SSB GPS time733967667.026112310 which corresponds to a wavefront passing:LHO at GPS time 733967713.000000000LLO at GPS time 733967713.007730720In the SSB the signal is defined byf = 1279.123456789012 Hzfdot = 0phi = 0A+ = 1.0 x 10-21

Ax = 0 [equivalent to iota=pi/2]

P2: Spinning DownSky position: 1.23456789012345 latitude (radians)

2.345678901234567890 longitude (radians)Signal parameters are defined at SSB GPS time:SSB 733967751.522490380, which corresponds to awavefront passing:LHO at GPS time 733967713.000000000LLO at GPS time 733967713.001640320In the SSB at that moment the signal is defined byf=1288.901234567890123fdot = -10-8 [phase=2 pi (f dt+1/2 fdot dt^2+...)]phi = 0A+ = 1.0 x 10-21

Ax = 0 [equivalent to iota=pi/2]


How was simulated signal made?• 12 hours of strain data was produced (with overall 1021

normalization factor) using LAL routines:

• 144 files (5 minutes each) were produced. Each file contains 16384*300+1 4-byte IEEE 754 floats:

– Key 1234.5 (4 bytes)– Sample 0 xxxxxx (4 bytes)– Sample 1 yyyyyy (4 bytes)– …

• Time range was 00:00 –12:00 UTC April 10th• The 2.8 GB of injection data was shipped to each site• More details of signals in LIGO DCC: LIGO-G030479-00-Z

S2_pulsar_LHO_733968013.datS2_pulsar_LHO_733968313.datS2_pulsar_LHO_733968613.dat… and so on.


Simulated strain: Detector Response Function

April 10th 04:00 UTC is:LHO: 8 pm April 9th

LLO: 10 pm April 9th

April 10th 10:00 UTC is:LHO: 2 am April 10th

LLO: 4 am April 10th

simulated source ispassing near a zero ofthe antenna pattern.


How and When?

• More than 9 hours of pulsar injections into L1, H1 and H2– Start 18:19 PDT on April 9– Stop 04:03 PDT on April 10

• Instruments were in lock for almost the entire time• Pulsar plus calibration line summed into DARM_CTRL• ETM_X and ETM_Y used for other injections• Strain/DARM_CTRL calibrations worked out at 1284 Hz, halfway

between two signals. NOTE: THESE WERE SUBSEQUENTLY REVISED FOR H1 AND H2 – SO AT THOSE DETECTORS THE OVERALL STRAIN FACTOR WAS NOT 1.e-21!

• Injections started at 733974613 (01:50:00 UTC April 10) and continued until 734007889 (11:04:36 UTC April 10) with some minor interruptions (loss of lock, realignment, computer restarted because of lack of memory).


Time Domain Bayesian Analysis

• For each signal all parameters were successfully inferred (except a constant 90 degrees phase shift)

• Four plots were produced for each signal:1. posterior probability density function of h0 given the data (marginalized over the

other parameters)

2. confidence contour plot of \cos\iota vs h0 with levels at 67%, 95%, 99%, and 99.9%

3. confidence contour plot of polarisation angle \psi vs h0 with levels at 67%, 95%,

99%, and 99.9%

4. confidence contour plot of phase \phi_0 vs h0 with levels at 67%, 95%, 99%, and

99.9%

• Coherent analysis using data from all sites showed that phase was conserved between sites

• Full results (with larger images) are posted at http://www.astro.gla.ac.uk/users/rejean/lsc/S2injections (lsc/lsconly)


Results for signal P1

L1:

p(h0| Bk) p(h0,cos | Bk) p(h0,0 | Bk) p(h0, | Bk)

H1:

H2:


Results for signal P2p(h0| Bk) p(h0,cos | Bk) p(h0,0 | Bk) p(h0, | Bk)

L1:

H1:

H2:


Joint Coherent Analysis

p(a|all data) = p(a|H1) p(a|H2) p(a|L1)

Signal P1 Signal P2

individual IFOs

all IFOs


4 and 5 Parameter Search Works WellAnd Has Been Tested

• Parameters : f0, cos(i), y, h

0, and then df

• Tested on synthesized data (4 and 5 parameters)• Tested on the S2 Injected Signals (4 parameters)• Use likelihood and priors of the time-domain search

as MCMC starting point.• df uncertain to 1/60 Hz. For a 5 Hz search, run on 300

nodes• 10 hours cpu for 10 days of data

Markov Chain Monte Carlo Results


4 Parameters: S2 Injection: It Works!

Signal 1 as seen in H1 above. Exact match with time domain search. Full results posted at http://physics.carleton.edu/Research/ligo/S2injectCW.htmlFound h

0, , and cos, but off due presumably to a time definition


Signal 1 at H1Signal 1:Parameters of injected signal:RA = 5.1471621319 radDEC = 0.3766960246 radf0 = 1279.123456789012 Hzfdot = 0.0psi = 0.0phi=0.0cos(iota)=0.0h0 = 2.0e-21 (± calibration errors)

MCMC Result (h0 scaled by 10-22)The Statistics Are: Mean Standard Deviation h0 20.97711 1.44419 psi -0.02704 0.02424 phi -0.66802 0.03438 cosiota -0.04865 0.02474

Quantiles for each variable: 2.5% 97.5%h0 18.17624 23.817896psi -0.07318 0.019197phi -0.73427 -0.601182cosiota -0.09867 -0.001396


Signal 2 at L1

Signal 1 as seen in L1 above. Exact match with time domain search.


Signal 1 at L1Signal 1:Parameters of injected signal:RA = 5.1471621319 radDEC = 0.3766960246 radf0 = 1279.123456789012 Hzfdot = 0.0psi = 0.0phi=0.0cos(iota)=0.0h0 = 2.0e-21 (± calibration errors)

MCMC Results (h0 scaled by 10-22)The statistics are: Mean Standard Deviation h0 19.00456 1.44050 psi -0.08483 0.03439 phi -0.82187 0.04071 cosiota -0.07484 0.03583

Quantiles for each variable: 2.5% 97.5%h0 16.2522 21.889774psi -0.1460 -0.011781phi -0.9026 -0.743842cosiota -0.1473 -0.005469


Signal 2 at H2

Signal 2 as seen in H2 above. Exact match with time domain search.


Signal 2 at H2

Signal 2:Parameters of injected signal:RA = 2.345678901234567890DEC = 1.23456789012345f0 = 1288.901234567890123 Hzfdot = -1.0e-8 Hz/spsi = 0.0h0 = 2.0e-21 (± calibration errors)phase = 0.0cos(iota)=0.0

MCMC Results (h0 scaled by 10-22)The statistics are: Mean SD h0 19.132891 0.91848 psi -0.008155 0.02172 phi -0.753110 0.02425 cosiota 0.061423 0.02135 Quantiles for each variable:

2.5% 97.5%h0 17.24495 21.02338psi -0.05211 0.03266phi -0.80178 -0.70678cosiota 0.02091 0.10527


6 Parameter Search: Road to a SN1987A Search

• Parameters : df, dfdot, f0, cos(i), psi, and h

0

• Test on synthesized data has commenced• Different Technique - “Delayed Rejection in

Reversible Jump Metropolis-Hastings”, plus other tricks.

• Will soon test on S2 injected signal 2 where dfdot is non-zero

• New manpower - John Veitch @ Glasgow


Generated PDFs from the parameters h0, df, and

dfdot. In this example from the 6 parameter problem the true values for the critical parameters were h

0=10.0,

df = 0.0078125, and dfdot = 2x10-10. The priors we uniform -10-9Hz/s<dfdot<10-9 Hz/sand -1/60 Hz < df < 1/60 Hz

6 Parameter Search


S2 Frequency DomainInjection Results

The signal in the data (green 60s SFTs, red 1800s SFTs)

Signal I Signal I

Signal IISignal II

Hz

Hz

Hz

Hz

hS

hS hS

hS


Results

21

0

0

1

0

21

2

2.3 10

cos(

L1-Expect2 10

cos(

) 0.034

Signa

4.6

1.8 10

cos( )

l I ( )

Signal II (

0.00063

0.

F=282

F=248

) 0.00.0

55

)

o

o

o

h

h

h

2

2

10

21

1

0

0

1.8 10

cos( ) 0.0

H1-Expect1.6 10

cos( ) 0

41

Sign

1.3

1.7 10

co

al I ( )

Signal I

s(

I

) 0.03

0.

F=175

F=614( )

6

.00.

9

0

o

o

o

h

h

h

21

0

0

1

0

21

2

1.7 10

cos( ) 0.027

H2-Expect1.7 1

2.

Si

8

0c

1.6 10

cos( ) 0.00

g

5

nal

os( ) 0.00

I ( )

Signal II (

F=69

F=370

8

.

.

2

)

1

0

1

o

o

o

h

h

h


• Still have problems with phase of the signal …

• 1800s SFTs (which I did not show results for) have equally good results (they are calibrated with calibration factors averaged every 30 mins)

• Overall results are very encouraging

FD Conclusions


What about S3?

• The Pulsar Group will to provide a fast real-time function that can be called, which will return h(t). Will be used to do pulsar injections during entire S3 run (~5 pulsars, parameters TBD).

• Uta Weiland (GEO Hannover) is writing a routine for this purpose for GEO pulsar injections. Can only inject 1 pulsar.

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