McGill University, Aug 12-17, 2007

1. Frequency Time Time The experiment Searches for continuous gravitational waves with LIGO and GEO600M. Landry for the LIGO Scientific CollaborationLIGO Hanford Observatory, Richland WA 99352California Institute of Technologyhttp://www.ligo.org 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 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,. 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. Fabry-Perot cavity 4km 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. g.w. output port power recycling mirror Targeted searches 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: 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 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 Supernova remnant Cas A Credit: NASA/CXC/GSFC/U. Hwang et al. Photo credit: NASA/CXC/SAO Radio timing data: M. Kramer, A.G. Lyne Jodrell Bank Pulsar Group 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. 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. sources: see B. Owen talk see J. Betzwieser poster All-sky searches Semi-coherent methods 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. 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: 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 50-1500Hz), 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. 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. see R. Prix poster 40 Years of Pulsars McGill University, Aug 12-17, 2007 G070594-00-Z