1. Searching for accreting neutron stars
C Messenger, V Re and A Vecchio
on behalf of LSC-PULG
8th Gravitational Waves Data Analysis Workshop
UWM, 17th – 20th December 2003

2. Outline Astrophysical scenario Data analysis Expected S2 sensitivity
General
Approach for LIGO S2 data set
Expected S2 sensitivity
Work in progress and future plans
GWDAW8, 17th – 20th December A Vecchio – Accreting neutron stars

3. Astrophysical scenario
Observational evidence that rotation frequencies in Low Mass X-Ray Binaries (LMXB) are
Well below NS breaking frequency
Clustered in a narrow (237 Hz – 619 Hz) frequency range (Bildsten, 1998; Chakrabarty et al, 2003)
Currently, two are the proposed mechanisms:
Magnetic braking (Wang and Zang, 1997), but need for fine tuning of parameters
Gravitational waves (Bildsten, 1998)
GWDAW8, 17th – 20th December A Vecchio – Accreting neutron stars

4. GWs from 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)
GWDAW8, 17th – 20th December A Vecchio – Accreting neutron stars

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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