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
G040543-00-Z
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
L1
10-19
6 hours, 1 filter
[Jaranowski,Krolak,Schutz, PRD,58,063001,(1998)]
•
•
GWs at 2 frot (mass quadrupole
[L.Bildsten, ApJ.Lett,501,L89 (1998)], not yet rmodes [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,
10-21
10-23
Annu. Rev. Astron. Astrophys, 2000. 38:717-60]
•
•
•
Also search orbital parameter space of
Sco-X1
Tobs = 6 hrs (set by computational
resources)
Analyse L1 and H1 in coincidence
GWDAW, Annecy 15th – 18th December, 2004
H2
H1
L1 (whole S2)
10-25
SCO-X1
G040543-00-Z
Analysis pipeline
Selection of
6 Hour dataset
S2 L1 data
S2 L1 data
subset
Generate Orbital
template Bank
For L1
L1 F-Statistic
above threshold
L1 6 hour
Template bank
S2 H1 data
S2 H1 data
subset
Generate PDF’s
Via MC injection
Compute F statistic over
bank of filters and
frequency range
Store results above “threshold”
Generate Orbital
template Bank
For H1
H1 6 hour
Template bank
Compute F statistic over
bank of filters and
frequency range
Store results above “threshold”
H1 F-Statistic
above threshold
Find Coincidence events
Find loudest
event per band
Coincident
Results
GWDAW, Annecy 15th – 18th December, 2004
Calculate Upper
Limits per band
Follow up
candidates
G040543-00-Z
Selecting the optimal 6hr
We construct the following measure of
detector sensitivity to a particular sky position
GWDAW, Annecy 15th – 18th December, 2004
h0 
5 Sh ( f )
( A  B)T
G040543-00-Z
Sco-X1 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,568:273-278,2002]
T0 ( HJD )  2451358.568(3)  0.787313(1) E
• The orbit has eccentricity<10-3 ] 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 731163327+/-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, 2000. 38:717-60]
GWDAW, Annecy 15th – 18th December, 2004
G040543-00-Z
Computational Costs
The scaling of computational
time with observation time :
T<P
P<T<106
# Orbital
Templates
T3
constant
# Frequency
Templates
T
T
CPU time per
template
T
T
Computational
time
T5
T2
2 weeks
6 hours
Using Tsunami
(200 node
Beowulf cluster)
For 1s errors
In parameters
• 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, 2004
G040543-00-Z
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, 63,122001 (1998)]
GWDAW, Annecy 15th – 18th December, 2004
G040543-00-Z
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, 2004
G040543-00-Z
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 2
>90% in
Detector 1
• 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, 2004
G040543-00-Z
The search sensitivity
~ 20
S1 paper
• 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, 2004
G040543-00-Z
Status and future work
• Currently
– 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, 2004
G040543-00-Z