1. Bounding the strength of gravitational radiation from Sco-X1
C Messenger
on behalf of the LSC pulsar group
GWDAW 2004
Annecy, 15th – 18th December 2004
G Z

2. Scope of S2 analysis
AIM : Set frequentist upper-limit on GWs on a wide parameter space using coherent frequency domain approach
Sco-X1 is an LMXB -> GW emission mechanism supported via accretion [R.V.Wagoner, ApJ. 278,345 (1984)]
Using F-statistic as detection statistic [Jaranowski,Krolak,Schutz, PRD,58,063001,(1998)]
GWs at 2 frot (mass quadrupole [L.Bildsten, ApJ.Lett,501,L89 (1998)], not yet r-modes [Andersson et al, ,ApJ 516,307 (99)])
2 frequency windows: 464 – 484 Hz (strong spectral features) and 604 – 624 Hz (reasonably clean) [Van der Klis, Annu. Rev. Astron. Astrophys, :717-60]
Also search orbital parameter space of Sco-X1
Tobs = 6 hrs (set by computational resources)
Analyse L1 and H1 in coincidence H1
L1 (whole S2) L1 H2
SCO X-1
6 hours, 1 filter
GWDAW, Annecy 15th – 18th December, G Z

3. Analysis pipeline H1 F-Statistic L1 F-Statistic above threshold
Selection of
6 Hour dataset
S2 H1 data
S2 L1 data
S2 L1 data
subset
S2 H1 data
subset
Generate Orbital
template Bank
For H1
H1 6 hour
Template bank
Generate Orbital
template Bank
For L1
L1 6 hour
Template bank
Generate PDF’s
Via MC injection
H1 F-Statistic
above threshold
L1 F-Statistic
above threshold
Compute F statistic over
bank of filters and
frequency range
Store results above “threshold”
Compute F statistic over
bank of filters and
frequency range
Store results above “threshold”
Find Coincidence events
Calculate Upper
Limits per band
Find loudest
event per band
Coincident
Results
Follow up
candidates
GWDAW, Annecy 15th – 18th December, G Z

4. Selecting the optimal 6hr
We construct the following measure of detector sensitivity to a particular sky position
GWDAW, Annecy 15th – 18th December, G Z

5. Sco X-1 parameter space
The orbital ephemeris is taken from the latest (and first) direct observations of the lower mass object within Sco X-1 [Steeghs and Cesares, ApJ,568: ,2002]
The orbit has eccentricity< ] Search for circular orbit (e=0)
The period (P) is known very well and is NOT be a search parameter
The Search parameters are :
The projected orbital semi-major axis is (4.33+/-0.52) X 108 m
The time of periapse passage (SSB frame) is /-299 sec
The GW frequency is not well known and the current model predicts two possible bands, (464<f0<484) and (604<f0<624) Hz. [Van der Klis, Annu. Rev. Astron. Astrophys, :717-60]
GWDAW, Annecy 15th – 18th December, G Z

6. Computational Costs T3 T T5 T2 2 weeks 6 hours
The scaling of computational time with observation time :
T<P
P<T<106
# Orbital Templates T3
constant
# Frequency Templates T
CPU time per template
Computational time T5 T2
Using Tsunami
(200 node
Beowulf cluster)
For 1s errors
In parameters
2 weeks
6 hours
This scaling limits this coherent search to an observation time of ~6 hours
Additional parameter space dimensions become important for T>106 (inc spin up/down, period error, eccentricity)
GWDAW, Annecy 15th – 18th December, G Z

7. Orbital templates
Templates are laid in an approximately “flat” 2D space by choosing a sensible parameterisation.
The template bank covers the uncertainty in the value of the projected semi-major axis and the time of periapse passage.
The template placement is governed by the parameter space metric [Brady et al, PRD 57,2101 (1998), Dhurandhar and Vecchio, PRD, 63, (1998)]
GWDAW, Annecy 15th – 18th December, G Z

8. The frequency resolution
Using the projected metric to lay orbital templates takes advantage of frequency – orbital parameter correlations.
A mismatch in orbital parameters can be compensated for by a mismatch in frequency.
We find that a frequency resolution of 1/(5Tobs) approximates a continuous frequency spectrum.
A consequence of this approach is that the detection template and signal can differ in frequency by up to +/15 bins
GWDAW, Annecy 15th – 18th December, G Z

9. Coincidence events
The orbital template bank guarantees a >90% match with the closest filter.
If a signal triggers a template we can identify a region around that template within which the true signal lies.
>90% in
Detector 1
Detector 2
Now find the possible closest templates in the second detector.
The coincidence detection is based on geometric arguments only.
Typically ~8 possible orbital and ~30 possible frequency coincidence locations
~200 possible coincident locations per event.
GWDAW, Annecy 15th – 18th December, G Z

10. The search sensitivity
S1 paper
~ 20
The “11.4” factor is based on a false alarm rate of 1% and a false dismissal rate of 10% for a single filter search
We use ~108 per 1 Hz band
This significantly increases the chances of “seeing” something large just from the noise.
Therefore we require stronger signals to obtain the same false dismissal and false alarm rates.
GWDAW, Annecy 15th – 18th December, G Z

11. Status and future work Currently Targets
We have analysed 1/5th of the parameter space
Completing LSC code review (Organising and checking the growing number of codes + documentation)
Ready to run the pipeline on the full parameter space and set frequentist upper limits via Monte-Carlo injections.
Targets
Implement suitable veto strategies (Fstat shape test, Fstat time domain test, …)
Follow up loudest candidate(s) with an aim to veto them out (observe for longer ?, observe another data stretch ?, …)
Start applying our understanding to the incoherent stacking approach (see poster by Virginia Re)
Apply the coherent approach to other LMXB parameter space searches.
GWDAW, Annecy 15th – 18th December, G Z