1. Bounding the strength of gravitational radiation from Sco-X1
C Messenger, V Re and A Vecchio
on behalf of the LSC
GWDAW 2004
Annecy, 15th – 18th December 2004

2. Scope of S2 analysis
Frequentist upper-limit on GWs from Sco X-1 using a coherent frequency domain approach
Using F-statistic as detection statistic (JKS 98)
GWs at 2 frot (mass quadrupole, not r-modes)
2 frequency window: 464 – 484 Hz (reasonably disturbed) and 604 – 624 Hz (reasonably clean)
Tobs = 6 hrs (set by computational resources)
Analyse L1 and H1 in coincidence L1
6 hours, 1 filter H2 H1
L1 (whole S2)
SCO X-1
GWDAW, Annecy 15th – 18th December, 2004

3. Analysis pipeline H1 F-Statistic L1 F-Statistic above threshold
Selection of
6 Hour dataset
S2 H1 data
S2 L1 data
Generate Orbital
template Bank
For L1
Generate Orbital
template Bank
For H1
S2 L1 data
subset
S2 H1 data
subset
H1 6 hour
Template bank
L1 6 hour
Template bank
Generate PDF’s
Via MC injection
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”
H1 F-Statistic
above threshold
L1 F-Statistic
above threshold
Find Coincidence events
Coincident
Results
Calculate Upper
Limits per band
Find loudest
event per band
Follow up
candidates
GWDAW, Annecy 15th – 18th December, 2004

4. Sco X-1 parameter space
The latest observations of Sco X-1 were made by Steeghs and Cesares in 2001.
They publish the following ephemeris for the low mass companion.
The orbit is assumed circular (e<10-3)
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)
GWDAW, Annecy 15th – 18th December, 2004

5. Computational Costs 2 weeks 6 hours
Number of Orbital filters scales as Tobs3(Tobs<P), const(Tobs>P)
Frequency filters scales as Tobs
Code speed scales as Tobs
The Computational time scales as Tobs5
Additional parameter space dimensions become important for Tobs>106 (inc spin up/down, period error, eccentricity)
2 weeks
Using Tsunami
(200 node
Beowulf cluster)
For 1 s errors
In parameters
6 hours
GWDAW, Annecy 15th – 18th December, 2004

6. 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
GWDAW, Annecy 15th – 18th December, 2004

7. The frequency resolution
Using the projected metric to lay orbital templates takes advantage of frequency – orbital correlations.
A mismatch in orbital parameters can be compensated for by a mismatch in frequency.
We find 1/(5Tobs) is approximately continuous ?
GWDAW, Annecy 15th – 18th December, 2004

8. Coincidence events
The orbital template bank guarantees a >90% match with the closest filter.
If a signal is detected in a detector we can therefore identify a region around an orbital filter within which the true signal is sure to lie.
Now find the possible orbital filters in the second detector that could be the closest.
The coincidence detection is based on geometric arguments only.
Remember that the frequency could be mismatched up to +/- 15 frequency bins.
~200 possible coincident locations per event.
GWDAW, Annecy 15th – 18th December, 2004

9. Understanding the search
ARTIFICIAL
DATA
GWDAW, Annecy 15th – 18th December, 2004

10. Selecting the optimal 6hr
We construct the following measure of detector sensitivity to a particular sky position
GWDAW, Annecy 15th – 18th December, 2004

11. The current status We have analysed a 1/5 of the total parameter space
S1 paper
~ 20
We have analysed a 1/5 of the total parameter space
The preliminary results are consistent with statistics
We are undergoing an LSC code review
Getting a better understanding of the coincidence statistics
Ready to set frequentist upper limits via Monte-Carlo injections into the data set.
GWDAW, Annecy 15th – 18th December, 2004

12. Future work Short term targets Longer term targets
Complete LSC code review (Organise growing number of codes + documentation)
Analyse the entire search bandwidth (40 Hz)
Longer term targets
Implement a suitable veto strategy (Fstat shape test, Fstat time domain test, …)
Follow up loudest candidate(s) and hopefully veto them out (observe for longer ?)
Start applying our understanding to the incoherent stacking approach (Virginia Re, Greg Mendell)
Apply the coherent approach to other LMXB’s (Dominic Kasprzyk)
GWDAW, Annecy 15th – 18th December, 2004