Searching for gravitational radiation from Scorpius X-1: Limits from the second LIGO science run

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Searching for gravitational radiation from Scorpius X-1: Limits from the second LIGO science run

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Searching for gravitational radiation from Scorpius X-1: Limits from the second LIGO science run

Alberto Vecchio

on behalf of the LIGO Scientific Collaboration

GWDAW10 - UTB, 14th - 17th December, 2005

LIGO - G05xxxx

- Analyses carried out by the LSC Pulsar group
- Coherent wide parameter space searches: several astrophysical targets
- This talk: Scorpius X-1 (low-mass X-ray binary)

- Second LIGO science run (S2)
- Method and results from the Sco X-1 analysis using S2 data
- Ongoing work and future plans

- Search strategies (and pipelines) for continuous GWs:
- Time domain analysis: optimal for “single filter” (or very limited parameter space) targets, such as radio pulsars
- e.g. S2 analysis of 28 radio pulsars: PRL 94, 181103 (2005)

- Coherent matched-filter based frequency domain analysis: optimal sensitivity for large parameter space (but computationally intensive) - this talk
- “Same” software as that used in E@h (Bruce Allen’s talk)

- Semi-coherent analysis: computationally efficient, but reduced sensitivity
- Hough transform: e.g. all-sky, fdot, isolated neutron stars analysis using S2 data: PRD 72, 102004 (2005)
- Power flux
- Stack-slide

- Time domain analysis: optimal for “single filter” (or very limited parameter space) targets, such as radio pulsars
- We have been integrating these fundamental building blocks into hierarchical pipelines: best sensitivity for fixed computational resources

- Previous analyses:
- S1 analysis targeted at PSR J1939+2134 (“single filter”): h095% = 1.4 0.1 x 10-22 (PRD 69, 082004 (2004))
- Explorer data: all-sky, fdot, 0.76 Hz frequency band 922 Hz: h090% = 1.0 x 10-22 (Astone et al, 2005)

- Analyses of (a small sub-set of) S2 LIGO data:
- Wide parameter space
- Blind search for isolated neutron stars (all sky, no spindown + frequency band 160 -728.8 Hz) [presented at Amaldi6]
- Scorpius X-1: low-mass X-ray binary (orbital parameters + frequency bands 464 - 484 HZ & 604 - 624 Hz)

- Search “in coincidence” (H1 and L1 data)
- Lots of technical and implementation issues

- Wide parameter space
- Notice: the “time domain pipeline” is a coherent pipeline designed in a different framework and (currently) not suitable to probe a wide parameter space

Braking

mechanism

is needed

to explain

lack of

sources

here

- Braking due to GW’s (Bildsten, 1998):
- Accretion replenishes angular momentum lost to GWs
- GW torque scales as 5: fairly insensitive to physical parameters
- clustering of frequencies

- S2: Feb. - Apr. 2003: 59 days
- Duty cycle:
- H1: 74%
- H2: 58%
- L1: 37%
Predicted Sco X-1 signal amplitude:

Known parameters:

Sky position (no search over sky)

Period (for T < 1 month)

No spin-down (for T < 1 week)

Search parameters:

Orbit: projected semi-major axis and “time of periapse passage”

Frequency

Possibly eccentricity (we set e = 0 in templates for S2 search)

Number of templates

1018

1014

1012

1010

108

106

104

102

S2 analysis

For Tspan < orbital period, the time of the analysis scales as:

This is a computationally limited search

103 104 105 106

Observation time Tspan /sec

- Coherent analysis: F-statistic (Jaranowski, Krolak, and Schutz, 1998)
- Integration time: the “best” 6 hours of data
- L1 and H1 in coincidence
- Parameter space (3-dimensional):
- 1- region of the two relevant orbital parameters
- 40 Hz frequency band (464 - 484 Hz and 604 - 624 Hz)

- Frequentist upper-limit based on joint significance

Time transformations:

From SSB time T to detector time t (depends on position in the sky):

From SSB time T to source time tp (depends on orbital parameters)

GW phase (in source frame): monochromatic over the observation time

464 - 484 Hz

604 - 624 Hz

L1

- SFTs: 60 sec
- Two 20 Hz bands
- Use best data segment with Tspan < 6 h
- Source position
- Noise floor
- Amount of data with Tspan

H1

1/50 of the whole parameter space

- 2 dimensional filter banks (orbit) + frequency
- Overall max mismatch 0.1
- Orbital bank (using metric) for each detector and 1 Hz wide band
- Frequency sampled at 1/(5 Tspan)

- Number of filters (2 orbital param. x frequency) for detectors and bands:
- L1: 464 - 484 Hz : (3 391 - 3 668) x 1 875 500
- L1: 604 - 624 Hz : (5 738 - 6107) x 1 875 500
- H1: 464 - 484 Hz : (6 681 - 7 236) x 2 154 000
- H1: 604 - 624 Hz : (11 309 - 12 032) x 2 154 000

465 Hz - 466 Hz

Example of expected vs actual distribution of the values of 2F in single interferometer output

L1

“Good” band

“Bad” band (not the worse!)

H1

Illustration of coincidence analysis (orbital filters)

- We test for templates in H1 and L1 to be consistent with same astrophysical signal:
- a. Orbital parameters
- b. Frequency: 40 frequency bins

Orbital parameter 2

Orbital parameter 1

Before coincidence

464 - 484 Hz

604 - 624 Hz

Mean value of loudest 2F (excluding 3 disturbed bands) for each 1 Hz band before and after coincidence:

<2 F>L1 = 40.8

<2 F>L1 = 28.6

<2 F>H1 = 45.4

<2 F>H1 = 33.5

After coincidence

614-615 Hz

614-615 Hz

- Coincident templates at the end of the pipeline are ranked according to their joint significance:
- We inject in software a population of signals with constant amplitude h0 and random parameters (orbit, frequency and nuisance parameters) and detect them with the same pipeline
- The upper-limit (on amplitude) h095% corresponds to the amplitude of the population that in 95% of the injections produces a more significant coincidence than the most significant coincident template found in the actual analysis

464 - 484 Hz

604 - 624 Hz

Best upper-limit:

h095% = 1.73 (0.02 + 0.16) x 10-22

- Errors:
- MonteCarlo: 1-3%
- Calibration: 9%

h095% = 2 x 10-22

Upper limit on ellipticity (assuming Sco X-1 distance of 2.8 kpc):

010-4

10-3

5x10-4

e = 5x10-3

469-470

464-466

614-615

479-480

e = 10-4 e = 5 x 10-4 e = 10-3 e = 5 x 10-3

C = 0.95 C = 0.95 C = 0.88 C = 0.50

For e > 5 x 10-4 the pipeline looses efficiency: the fitting factor of templates with signal is < 1

- Coherent analyses in coincidence of S2 data over a wide parameter space:
- Blind search for isolated neutron stars over 10 hours of data: all sky, no spindowns, frequency band 160 -728.8 Hz
- Scorpius X-1 over 6 hours of data: orbital parameters and frequency bands 464 - 484 Hz & 604 - 624 Hz

- First (preliminary) upper limit on gravitational radiation from Sco X-1: h095% ~ 2 x 10-22 and 95% ~ 5 x 10-4
- Future work:
- Pipeline: incorporated as coherent stage into hierarchical search schemes
- Accreting neutron stars:
- Same pipeline used to target X-ray accreting milli-second neutron stars (source parameters much better known) over whole S4/5
- Hierarchical search using whole S4/5 aimed at Sco X-1 and the other low mass x-ray binaries
- How close can we get to the predicted signal strength?