The search for continuous gravitational waves: analyses from LIGO

1
The search for continuous gravitational waves
analyses from LIGOs second science run Michael
LandryLIGO Hanford Observatoryon behalf of the
LIGO Scientific Collaborationhttp//www.ligo.org
April APS Meeting (APR04)May 1-4,
2004Denver, CO
Photo credit NASA/CXC/SAO
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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

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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

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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(t0), 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.
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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
• Einstein_at_home 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 58 063001
(1998))
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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
  J19392134, using LIGO and GEO IFOs best limit
  from Livingston IFO

• Accepted for publication in Phys Rev D 69, 082004
  (2004), preprint available, gr-qc/0308050

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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 T1 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
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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 0
Such an upper limit can be defined even when
signal is present
h95
strain
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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)

The posterior pdf is
likelihood
prior
posterior
model
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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.
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Analysis summary
Heterodyne, lowpass, average, calibrate Bk
Raw Data
Compute likelihoods
Model yk
uniform priors on h0(gt0), cosi, j0, y
Compute pdf for h0
Compute upper limits
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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

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Preliminary results for P1

• Parameters of P1

• P1 Constant Intrinsic Frequency
• Sky position 0.3766960246 latitude (radians)
• 5.1471621319 longitude (radians)
• Signal parameters are defined at SSB GPS time
• 733967667.026112310 which corresponds to a
  wavefront passing
• LHO at GPS time 733967713.000000000
• LLO at GPS time 733967713.007730720
• In the SSB the signal is defined by
• f 1279.123456789012 Hz
• fdot 0
• phi 0
• psi 0
• iota p/2
• h0 2.0 x 10-21

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Preliminary results for P2

• Parameters for P2

P2 Spinning Down Sky position 1.23456789012345
latitude (radians) 2.345678901234567890
longitude (radians) Signal parameters are defined
at SSB GPS time SSB 733967751.522490380, which
corresponds to a wavefront passing LHO at GPS
time 733967713.000000000 LLO at GPS time
733967713.001640320 In the SSB at that moment the
signal is defined by f1288.901234567890123 fdot
-10-8 phase2 pi (f dt1/2 fdot
dt2...) phi 0 psi 0 iota p/2 h0 2.0 x
10-21
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Pulsar timing

• Analyzed 28 known isolated pulsars with 2frot gt
  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 gt 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

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Preliminaryresults for PSR B0021-72L

• Posterior probability density for PSR J1910-5959D
• Flat prior for h0 (h0gt0), Jeffreys prior for s,
  i.e. p(s) ? 1/s

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Preliminaryresults for the Crab pulsar

• Posterior probability density for PSR B053121
• Crab pulsar heterodyned to take timing noise into
  account
• Flat prior for h0 (h0gt0), Jeffreys prior for s,
  i.e. p(s) ? 1/s

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Preliminaryupper limits for 28 known pulsars
h0 UL range Pulsar
10-23-10-22 J19392134, B195132, J19131011, B053121
10-24-10-23 B0021-72C, B0021-72D, B0021-72F, B0021-72G, B0021-72L, B0021-72M, B0021-72N, J0711-6830, B1820-30A, J1730-2304, J1721-2457, J1629-6902, J1910-5959E, J2124-3358, J1910-5959C, J00300451, J1024-0719, J1910-5959D, J23222057, B151602A, J1748-2446C, J1910-5959B, J1744-1134, B1821-24
Blue timing checked by Jodrell Bank Purple ATNF
catalogue
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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

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Preliminary ellipticity limits for 28 known
pulsars
? UL range Pulsar
10-2-10-1 B195132, J19131011, B053121
10-3-10-2 -
10-4-10-3 B1821-24, B0021-72D, J1910-5959D, B151602A, J1748-2446C, J1910-5959B
10-5-10-4 J19392134, B0021-72C, B0021-72F, B0021-72L, B0021-72G, B0021-72M, B0021-72N, B1820-30A, J0711-6830, J1730-2304, J1721-2457, J1629-6902, J1910-5959E, J1910-5959C, J23222057
10-6-10-5 J1024-0719, J2124-3358, J00300451, J1744-1134
Blue timing checked by Jodrell Bank Purple ATNF
catalogue
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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 31 03 Jan 9 04
• Approaching spindown limit for Crab pulsar