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 http://www.ligo.org April APS Meeting (APR04) May 14, 2004 Denver, CO
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 Timedomain analysis method Injection of fake pulsars Results
CW sources Nearlymonochromatic continuous sources of gravitational waves include neutron stars with:  spin precession at ~frot
 excited oscillatory modes such as the rmode at 4/3 * frot
 nonaxisymmetric 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
Source model 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
 – polarization angle of signal
 – inclination angle of source with respect to line of sight
 0 – initial phase of pulsar; (t=0), and (t)= t0
CW search group efforts S2 Coherent searches  Timedomain method (optimal for parameter estimation)
 Target known pulsars with frequencies (2frot) in detector band
 Frequencydomain Fstatistic* method (optimal for blind detection)
 Allsky, broadband search, subset of S2 dataset
 Targeted searches (e.g. galactic core)
 LMXB (e.g. ScoX1) search
S2 Incoherent searches  Hough transform method
 Powerflux method
 Stackslide method
Future: Implement hierarchical analysis that layers coherent and incoherent methods Einstein@home initiative for 2005 World Year of Physics
First science run: S1 S1 run: 17 days (Aug 23Sep 9 02) Coincident run of four detectors, LIGO (L1, H1, H2), and GEO600 Two independent analysis methods (frequencydomain and timedomain) employed Set 95% upper limit values on continuous gravitational waves from single pulsar PSR J1939+2134, using LIGO and GEO IFO’s: best limit from Livingston IFO:
S2 expectations Coloured spectra: average amplitude detectable in time T (1% false alarm, 10% false dismissal rates):
Timedomain analysis method Perform timedomain complex heterodyne (demodulation) of the interferometer gravitational wave channel Lowpass 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 (cos0) 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:
Bayesian analysis 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):
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.
Analysis summary
S2 hardware signal injections Performed endtoend validation of analysis pipeline by injecting simultaneous fake continuouswave 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
Preliminary results for P1
Preliminary results for P2
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
Preliminary results for PSR B002172L
Preliminary results for the Crab pulsar
Preliminary upper limits for 28 known pulsars
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
Preliminary ellipticitylimits for 28 known pulsars
Summary and future outlook S2 analyses  Timedomain analysis of 28 known pulsars complete
 Broadband frequencydomain allsky search underway
 ScoX1 LMXB frequencydomain search near completion
 Incoherent searches reaching maturity, preliminary S2 results produced
S3 run  Timedomain analysis on more pulsars, including binaries
 Improved sensitivity LIGO/GEO run
 Oct 31 03 – Jan 9 04
 Approaching spindown limit for Crab pulsar
