1. The search for continuous gravitational waves: analyses from LIGO’s second science run Michael Landry LIGO Hanford Observatory on behalf of the LIGO Scientific Collaboration April APS Meeting (APR04) May 1-4, 2004 Denver, CO
Photo credit: NASA/CXC/SAO

2. Talk overview Introduction to continuous wave (CW) sources
CW search group analysis efforts
Review of first science run (S1) results, and a look at expectations of the S2 run
Time-domain analysis method
Injection of fake pulsars
Results
Landry - April APS, 4 May 2004

3. CW sources
Nearly-monochromatic continuous sources of gravitational waves include neutron stars with:
spin precession at ~frot
excited oscillatory modes such as the r-mode at 4/3 * frot
non-axisymmetric distortion of crystalline structure, at 2frot
Limit our search to gravitational waves from a triaxial neutron star emitted at twice its rotational frequency (for the analysis presented here, only)
Signal would be frequency modulated by relative motion of detector and source, plus amplitude modulated by the motion of the antenna pattern of the detector
Landry - April APS, 4 May 2004

4. Source model The expected signal has the form:
PRD 58
063001
(1998)
F+ and Fx : strain antenna patterns of the detector to plus and cross polarization, bounded between -1 and 1
Here, signal parameters are:
h0 – amplitude of the gravitational wave signal
y – polarization angle of signal
i – inclination angle of source with respect to line of sight
f0 – initial phase of pulsar; F(t=0), and F(t)= f(t) + f0
Heterodyne, i.e. multiply by:
so that the expected demodulated signal is then:
Here, a = a(h0, y, i, f0), a vector of the signal parameters.
Landry - April APS, 4 May 2004

5. CW search group efforts
S2 Coherent searches
Time-domain method (optimal for parameter estimation)
Target known pulsars with frequencies (2frot) in detector band
Frequency-domain F-statistic* method (optimal for blind detection)
All-sky, broadband search, subset of S2 dataset
Targeted searches (e.g. galactic core)
LMXB (e.g. ScoX-1) search
S2 Incoherent searches
Hough transform method
Powerflux method
Stackslide method
Future: Implement hierarchical analysis that layers coherent and incoherent methods
initiative for 2005 World Year of Physics
*not the F-statistic associated with statistical literature (ratio of two variances), nor the F-test of the null hypothesis (See PRD (1998))
Landry - April APS, 4 May 2004

6. First science run: S1 S1 run: 17 days (Aug 23-Sep 9 02)
Coincident run of four detectors, LIGO (L1, H1, H2), and GEO600
Two independent analysis methods (frequency-domain and time-domain) employed
Set 95% upper limit values on continuous gravitational waves from single pulsar PSR J , using LIGO and GEO IFO’s: best limit from Livingston IFO:
Accepted for publication in Phys Rev D 69, (2004), preprint available, gr-qc/
Landry - April APS, 4 May 2004

7. S2 expectations
Coloured spectra: average amplitude detectable in time T (1% false alarm, 10% false dismissal rates):
Solid black lines: LIGO and GEO science requirement, for T=1 year
Circles: upper limits on gravitational waves from known EM pulsars, obtained from measured spindown (if spindown is entirely attributable to GW emission)
Only known, isolated targets shown here
GEO
LIGO
Landry - April APS, 4 May 2004

8. Time-domain analysis method
Perform time-domain complex heterodyne (demodulation) of the interferometer gravitational wave channel
Low-pass filter these data
The data is downsampled via averaging, yielding one value (“Bk”) of the complex time series, every 60 seconds
Determine the posterior probability distribution (pdf) of the parameters, given these data (Bk) and the model (yk)
Marginalize over nuisance parameters (cosi, j0, y) to leave the posterior distribution for the probability of h0 given the data, Bk
We define the 95% upper limit by
a value h95 satisfying: 1
PDF
Such an upper limit can be defined even when signal is present
h95
strain
Landry - April APS, 4 May 2004

9. Bayesian analysis likelihood prior posterior model noise
A Bayesian approach is used to determine the posterior
distribution of the probability of the unknown parameters via the
Likelihood (assuming gaussian noise within our narrow band):
The posterior pdf is
likelihood
prior
posterior
model
Bk’s are processed data
noise
Landry - April APS, 4 May 2004

10. Marginalizing over noise
As we estimate the noise level from the Bk no independent information is lost by treating it as another nuisance parameter over which to marginalize, i.e.
We assign Jeffreys prior to sigma, so that
giving a (marginalized) likelihood of
which can be evaluated analytically for gaussian noise.
Landry - April APS, 4 May 2004

11. Analysis summary Heterodyne, lowpass, average, calibrate: Bk Raw Data
Compute likelihoods
Model: yk
uniform priors
on h0(>0), cosi,
j0, y
Compute pdf for h0
Compute upper limits
Landry - April APS, 4 May 2004

12. S2 hardware signal injections
Performed end-to-end validation of analysis pipeline by injecting simultaneous fake continuous-wave signals into interferometers
Two simulated pulsars were injected in the LIGO interferometers for a period of ~ 12 hours during S2
Fake signal is sum of two pulsars, P1 and P2
All the parameters of the injected signals were successfully inferred from the data
Landry - April APS, 4 May 2004

13. Preliminary results for P1
Parameters of P1:
P1: Constant Intrinsic Frequency
Sky position: latitude (radians)
longitude (radians)
Signal parameters are defined at SSB GPS time
which corresponds to a wavefront passing:
LHO at GPS time
LLO at GPS time
In the SSB the signal is defined by
f = Hz
fdot = 0
phi = 0
psi = 0
iota = p/2
h0 = 2.0 x 10-21
Landry - April APS, 4 May 2004

14. Preliminary results for P2
Parameters for P2:
P2: Spinning Down
Sky position: latitude (radians)
longitude (radians)
Signal parameters are defined at SSB GPS time:
SSB , which corresponds to a
wavefront passing:
LHO at GPS time
LLO at GPS time
In the SSB at that moment the signal is defined by f=
fdot = [phase=2 pi (f dt+1/2 fdot dt^2+...)]
phi = 0
psi = 0
iota = p/2
h0 = 2.0 x 10-21
Landry - April APS, 4 May 2004

15. Pulsar timing
Analyzed 28 known isolated pulsars with 2frot > 50 Hz.
Timing information has been provided using radio observations collected over S2/S3 for 18 of the pulsars (Michael Kramer, Jodrell Bank).
Timing information from the Australia Telescope National Facility (ATNF) catalogue used for 10 pulsars
An additional 10 isolated pulsars are known with 2frot > 50 Hz but the uncertainty in their spin parameters is such that a search over frequency is warranted
Crab pulsar heterodyned to take timing noise into account
Landry - April APS, 4 May 2004

16. Preliminary results for PSR B0021-72L
Posterior probability density for PSR J D
Flat prior for h0 (h0>0), Jeffreys prior for s, i.e. p(s)  1/s L1 H1 H2
joint
Landry - April APS, 4 May 2004

17. Preliminary results for the Crab pulsar
Posterior probability density for PSR B
Crab pulsar heterodyned to take timing noise into account
Flat prior for h0 (h0>0), Jeffreys prior for s, i.e. p(s)  1/s L1 H1 H2
joint
Landry - April APS, 4 May 2004

18. Preliminary upper limits for 28 known pulsars
h0 UL range
Pulsar
J , B , J , B
B C, B D, B F, B G, B L, B M, B N, J , B A, J , J , J , J E, J , J C, J , J , J D, J , B A, J C, J B, J , B
Blue: timing checked by Jodrell Bank
Purple: ATNF catalogue
Landry - April APS, 4 May 2004

19. Equatorial Ellipticity
Results on h0 can be interpreted as upper limit on equatorial ellipticity
Ellipticity scales with the difference in radii along x and y axes
Distance r to pulsar is known, Izz is assumed to be typical, 1045 g cm2
Landry - April APS, 4 May 2004

20. Preliminary ellipticity limits for 28 known pulsars
 UL range
Pulsar
B , J , B -
B , B D, J D, B A, J C, J B
J , B C, B F, B L, B G, B M, B N, B A, J , J , J , J , J E, J C, J
J , J , J , J
Blue: timing checked by Jodrell Bank
Purple: ATNF catalogue
Landry - April APS, 4 May 2004

21. Summary and future outlook
S2 analyses
Time-domain analysis of 28 known pulsars complete
Broadband frequency-domain all-sky search underway
ScoX-1 LMXB frequency-domain search near completion
Incoherent searches reaching maturity, preliminary S2 results produced
S3 run
Time-domain analysis on more pulsars, including binaries
Improved sensitivity LIGO/GEO run
Oct – Jan 9 04
Approaching spindown limit for Crab pulsar
Landry - April APS, 4 May 2004