1. Sco-X1search : S2 results
C Messenger, V Re and A Vecchio
on behalf of LSC-PULG
LIGO Scientific Collaboration Meeting
UMich, 4th – 5th June 2005

2. Outline Astrophysical scenario Data Analysis Pipeline S2 results
Data-set selection
Parameter space &Template bank
F-statistic Search
Coincidence test
Injections
Upperlimits
Work in progress and future plans
UMich LSC Meeting, 4th – 5th June 2005

3. Accreting neutron stars
Conjecture for LMXBs: GWs are the limiting physics that prevents NSs from being spun-up to the braking frequency
Two models:
Density fluctuations – “mountain” on neutron star (Bildsten, 1998; Ushomirsky, Cutler, Bildsten, 2000; Cutler, 2002)
fgw = 2 frot
R-modes (Andersson et al, 1999; Wagoner, 2002)
fgw = 4/3 frot
(from Cutler and Thorne 2000)
UMich LSC Meeting, 4th – 5th June 2005

4. Data analysis pipeline
Data-set selection
Template bank generation
F-statistic Search
Coincidence test
Chi-squared test
Injections & Upperlimits
UMich LSC Meeting, 4th – 5th June 2005

5. S2 results : Data-set selection
LLO
LHO
Tstart
7324
Tend
# SFT
192
Tspan
18535
20302
Tobs
Data-set selected based on sensitivity factor
Factor in the noise floor across the search band & sky position sensitivity
Limited to 6 hour maximum observation span (Tcomp a Tspan5)
UMich LSC Meeting, 4th – 5th June 2005

6. S2 results : Parameter Space & Template bank
2+1 dimensional parameter space
2 orbital parameters (Projected Semi-Major axis & Periapse passage)
+ Intrinsic GW emission frequency
Orbital period NOT a search parameter for coherent observation times < 1 week
Spin down NOT a search parameter for coherent observation times < 1 month
Projected Semi-Major Axis {1.44 +/- 0.18} (sec) at 1 sigma
Time of periapsis { /- 299} (GPS sec) at 1 sigma
Frequency range split into 2 bands {474 +/- 10 & 614 +/- 10} Hz
METRIC used to place filters in orbital parameter space (frequency projected out) & frequency space (independent of orbital parameters)
UMich LSC Meeting, 4th – 5th June 2005

7. S2 results : F-statistic search
The F-Statistic in the presence of Gaussian noise should be Chi2_4 distributed
We have “good” and “bad” bands.
The “bad” bands deviate significantly from the expected distribution in the tails resulting in statistically unlikely large values.
Usually due to large “spikes” not removed by the running median.
UMich LSC Meeting, 4th – 5th June 2005

8. S2 results : Coincidence test
The method involves finding orbital templates that could be common closest filters to a possible signal.
Have to search a finite range of frequencies around possible event frequency.
UMich LSC Meeting, 4th – 5th June 2005

9. S2 results : Candidate Events
The parameter space contains features after coincidence appearing as planes of events at constant frequency.
Event densities in orbital parameter space appear isotropic
UMich LSC Meeting, 4th – 5th June 2005

10. S2 results : Injections & ULs
Upperlimits are ~4x1022 in both bands.
Coincidence analysis helps us in the case where one detector is “clean” and one detector is “not clean”.
UL’s around the 60 Hz power line harmonic at 480 Hz are dominated by very large loudest events inconsistent with the statistics.
UMich LSC Meeting, 4th – 5th June 2005

11. Work in Progress & future plans
Improvements in h0 sensitivity are obtainable with better data-set selection (taking into account injection distributions) – Note that the upper limits are correct (fingers crossed) for the data set we used.
This coherent pipeline is clearly not the way to search for GW’s from Sco-X1 (but we knew that).
An incoherent approach (Virginia Re, Greg Mendell) is the way forward.
This approach is currently suitable for other LMXB’s (Domonic Kasprzyk) with smaller orbital parameter and frequency uncertainties (giving far longer observation times)
Maybe need to use a different noise floor estimate at power line harmonic(s) ?
Extend the frequency band to fill the gap
UMich LSC Meeting, 4th – 5th June 2005

12. Data analysis Source position: known Orbital motion
Circular orbit to a very good approximation
Search with discrete mesh over 3 orbital parameters (period, projected orbit semi-major axis, initial phase)
Phase Doppler shift much more severe than for isolated sources
Signal confined to a single bin for Tobs < 150 sec (Sco X-1)
.Df ~ 0.2 Hz (Sco X-1)
P: binary period
q = m2/mNS
GWDAW8, 17th – 20th December A Vecchio – Accreting neutron stars

13. Data analysis (con’t) Intrinsic change in GW frequency (“spin down”)
System is in equilibrium – GW emission balances accretion torque: frequency makes a “random walk” as the accretion rate (Mdot) changes in time
We can not model this frequency evolution using low-order polinomial in time
However, the signal is confined to a single frequency by for Tobs < 2 weeks
Rotation frequency, and therefore GW frequency, not very well known: Df ~ 1 – 40 Hz
t: time scale over which torque doubles or turns off
GWDAW8, 17th – 20th December A Vecchio – Accreting neutron stars

14. Computationally bound search
Computational load comes from two poorly constrained set of parameters:
Emission frequency: search over a fairly large bandwidth (tens of Hz)
Orbital parameters (Sco X-1: N_filt ~ 106 for 1 day of coherent integration)
Long integration times
Search strategy:
Hierarchical: simplest approach is to use a “stack-slide” search (Brady and T Creighton, 1999)
Coherent integration over Tc
Concatenate incoherently M chunks of length Tc (total observation time = M Tc)
Stack-slide search code development is well underway
GWDAW8, 17th – 20th December A Vecchio – Accreting neutron stars

15. Approach for S2 analysis
Target Sco X-1 (the brightest source)
The analysis can be extended in a straightforward way (in principle) to the other LMXBs
Only coherent analysis (the core of the entire search strategy) over:
Relevant band for emission at twice the rotation frequency (but if enough processing power is available we’ll explore band for 4/3 rotation frequency)
The longest possible observation time for available computational resources (Tsunami: 200 CPUs)
T(coherent) < 1/2 day
Frequency domain analysis (different flavour of analysis carried out for S1)
GWDAW8, 17th – 20th December A Vecchio – Accreting neutron stars

16. Scorpius X-1
Neutron star in a binary system accreting from a low-mass (0.42 M_sun) companion
Distance: 2.8 (+/- 0.2) kpc
Orbital parameters
Period: (1) day = 18.9 hrs
Projected semi-major axis: sec < a < sec
“Initial” orbital phase: Da = 0.1 rad
Circular orbit (e < 10-3)
Rotation frequency from twin kHz QPOs (van der Klis et al, 1997; van der Klis, 2000)
232 – 242 Hz
302 – 312 Hz
GWDAW8, 17th – 20th December A Vecchio – Accreting neutron stars

17. S2 preliminary analysis
One-stage coherent FD analysis (F statistic)
Tobs = 3 hrs (set by Tanalysis = 1 week on 100 CPUs)
Same data segment for L1, H1 and H2
Search carried out over:
Wide frequency band
“lower band”: 464 – 484 Hz
“upper band”: 604 – 624 Hz
Discrete mesh over 2D parameter space (10% mismatch)
Period known to high accuracy (not a search parameter for Tobs < 1 month)
Mesh on a and a: 39,487 filters (upper-band)
Frequentist upper-limits on ten 4 Hz wide bands covering the relevant frequency range
GWDAW8, 17th – 20th December A Vecchio – Accreting neutron stars

18. Expected sensitivity for S2
We will set an upper-limit on Sco X-1 using the most sensitive S2 data stretch ~ 6 hrs long from L1, H1 and H2 (in coincidence)
The analysis – search and Monte Carlo’s – will take ~6 weeks on 200 CPUs (Tsunami, B’ham cluster)
The expected “angle-averaged” upper-limit at 95% confidence will depend on the frequency band
h0(95%) ~ a few x (on “clean” band)
h0(95%) ~ (on “noisy” band(s), which we know are there)
We are implementing Itoh’s veto to reject spurious events
GWDAW8, 17th – 20th December A Vecchio – Accreting neutron stars

19. Conclusions Coherent search analysis pipeline is in place
S2 analysis is in progress
However, any further sensitivity improvement rely on
Lower detector noise (expected)
Hierarchical search approach (well underway)
Future plans
Full stack-slide analysis code ready for S3 analysis
Place upper-limits on other accreting neutron stars
Place upper-limits on emission at 4/3 frot
GWDAW8, 17th – 20th December A Vecchio – Accreting neutron stars