Transcript Montreal_07_pstr

Searches for continuous gravitational waves with LIGO and GEO600
M. Landry for the LIGO Scientific Collaboration
LIGO Hanford Observatory, Richland WA 99352
California Institute of Technology
http://www.ligo.org
The experiment
Fig 1. LIGO Scientific Collaboration (LSC) gravitational wave observatories. The
Laser Interferometer Gravitational Wave Observatory (LIGO) is composed of two
sites, LIGO Livingston (Lousiana, LA) and LIGO Hanford (Richland, WA). A single
four-km power-recycled Michelson (denoted L1) occupies the Livingston vacuum
envelope, while 2 similar detectors (4km and 2km machines, denoted H1 and H2)
occupy the Hanford vacuum. The GEO600 machine is a 600m folded Michelson
interferometer located in Hannover, Germany,.
power recycling
mirror
g.w. output
port
Fig 2. Core optic configuration of LIGO
interferometers. Optical cavities are
coupled in the form of a power-recycled
Michelson to Fabry-Perot cavities
comprising long (4km or 2km) arms.
Known pulsars are targeted in searches for
gravitational waves at twice the spin frequency of the
star. Radio timing data provided by the Jodrell Bank
Pulsar Group (M. Kramer and A.G. Lyne) are used to
model the phase evolution of the gravitational wave. In
terms of the strain h seen at the detector:
Gravitational waves are distortions in the space-time metric
predicted by Einstein’s General Theory of Relativity. Current
searches for astrophysically generated gravitational waves
include the ground-based kilometric interferometers GEO600
and LIGO. The detectors’ sensitive band includes audio
frequencies from a few tens of Hz to several kHz.
Spinning compact objects such as neutron or quark stars
should be a source continuous gravitational waves (CW) in
the audio band. Quasi-sinusoidal gravitational waves
detected from pulsars would be Doppler modulated by
relative motions of the detector and star, and amplitude
modulated by the sweeping of the detector beam pattern
(variations in detector sensitivity as a function of position)
across the sky. These modulations provide an effective filter
to match against data when searching for a signal, but
dramatically increases the number of templates one must
search.
Fig 3. Progression of strain sensitivities of the LIGO
interferometers. Curves are strain-equivalent noise output of the
gravitational wave channel of the most sensitive interferometer
during each science run, S1 (2002), through to the present S5 run.
The black curve is the design noise curve (science requirement),
whereby sensitivity is limited at low frequencies by seismic noise,
middle frequencies by thermal noise of test masses and suspension
systems, and at high frequencies by the shot noise of the laser.
Evident in the strain curves are stationary and quasi-stationary
discrete line noise sources such as 60Hz and harmonics from
power lines, ~345Hz and harmonics from test mass recoil due to
suspension wire violin modes, and injected calibration lines.
Targeted searches
 1  cos2  
h  t   F  t;  h 0 
 cos (t )  F  t;  h 0 cos sin (t )
2


F+ and Fx : strain antenna patterns of the detector plus and
cross polarization, bounded between -1 and 1
Parameters of the signal are:
h0 – amplitude of the gravitational wave signal
 – polarization angle of signal
 – inclination angle of source with respect to line of sight
f0 – initial phase of pulsar; (t=0), and (t)= f(t) + f0
Photo credit: NASA/CXC/SAO
Radio timing data: M. Kramer, A.G. Lyne
Jodrell Bank Pulsar Group
Fig 4. Upper limits on gravitational wave emission from known pulsars, using
thirteen months of S5 data. The black curve indicates the expected sensitivity for
the three LIGO interferometers operating at design sensitivity for one year. Blue
stars indicate robust upper limits for which we have good timing data from radio
observations. Green stars represent pulsars for which radio timing data may have
accumulated phase errors (hence requiring new radio observations). Black triangles
are indirect upper limits on gravitational wave emission derived from observed
pulsar spindown. Note the Crab spindown near 59.6Hz has been surpassed.
Supernova remnant Cas A
Credit: NASA/CXC/GSFC/U. Hwang et al.
Fig 5. Searches for continuous waves over a wider parameter
space than a single template are underway on specific, interesting
objects of known sky position such as the Crab pulsar and
supernova remnant Cas A. The search method employed is a fully
coherent one (see the F-statistic method, below), and the
parameter space includes f and f-dot. An area search of the
galactic center will be launched soon.
sources: see B. Owen talk
see J. Betzwieser poster
All-sky searches
Fully coherent analyses of LIGO and GEO data are
made by matched filtering in the frequency domain.
The optimal detection statistic (maximum likelihood) is
the so-called F-statistic, as described in Jaranowski,
Królak and Schutz, PRD 58 063001 (1998).
All-sky coherent searches are made over large
parameter spaces including frequency (typically the
most sensitive band of the instrument, from 501500Hz), spindown, and all sky positions. Due to
computational constraints, the stretches of data
analyzed coherently are limited to ~25h, although many
such segments are analyzed and compared.
The hierarchical search
Fig 7. The Einstein@home screensaver package. Built
atop the Berkeley Open Infrastructure for Network
Computing, or BOINC, Einstein@home provides roughly
70TFlops of distributed computing resources for LSC CW
searches. The current CW search running under
Einstein@home is a hierarchical one employing interleaved
passes of the coherent F-statistic algorithm and the
semicoherent Hough transform algorithm.
40 Years of Pulsars
Semi-coherent methods
The LSC has three semi-coherent search algorithms
(Powerflux, Stackslide and Hough transform) that take
short Fourier transforms (SFTs) of data as input,
account for Doppler shifts and spindown, and then form
sums over power (or weighted 1’s and 0’s in the case
of Hough). The sums are weighted according to the
antenna patterns F+ and Fx, shown below:
Frequency
Coherent methods
All-sky, blind searches for gravitational waves from
unknown pulsars are computationally limited. For an
observation time T, the required computing power of a
coherent search over sky position, frequency, and
spindown scales as T6 while sensitivity scales as only
T1/2. The addition of orbital parameters in the case of
binary searches, or higher derivatives for younger
sources add powers of T. The computational challenge
requires distributed computing and optimal search
methods. The best sensitivity can be achieved by a
hierarchical search, in which data is passed by layers
of both coherent and semi-coherent search algorithms.
Time
see R. Prix poster
McGill University, Aug 12-17, 2007
Time
Fig 6. Typical method employed by semi-coherent searches. The
output of the gravitational wave channel of a given interferometer is
partitioned into 30m short Fourier Transforms (SFTs). Doppler and
spindown effects are accounted for, and then a sum of either power or
weighted 1’s and 0’s is performed.
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