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Searching for periodic sources with LIGO
General Relativity and Quantum Cosmology · Submitted 25 Feb 1997
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that for an all-sky, all-frequency search lasting T=10^7 s, this detection threshhold is at a level of 4 to 5 times h(3/yr), where h(3/yr) is the corresponding 99% confidence threshhold if one knows in advance the pulsar position and spin period.
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The abstract, sentence by sentence
We investigate the computational requirements for all-sky, all-frequency searches for gravitational waves from spinning neutron stars, using archived data from interferometric gravitational wave detectors such as LIGO. These sources are expected to be weak, so the optimal strategy involves coherent accumulaton of signal-to-noise using Fourier transforms of long stretches of data (months to years). Earth-motion-induced Doppler shifts, and intrinsic pulsar spindown, will reduce the narrow-band signal-to-noise by spreading power across many frequency bins; therefore, it is necessary to correct for these effects before performing the Fourier transform. The corrections can be implemented by a parametrized model, in which one does a search over a discrete set of parameter values. We define a metric on this parameter space, which can be used to determine the optimal spacing between points in a search; the metric is used to compute the number of independent parameter-space points Np that must be searched, as a function of observation time T. The number Np(T) depends on the maximum gravitational wave frequency and the minimum spindown age tau=f/(df/dt) that the search can detect. The signal-to-noise ratio required, in order to have 99% confidence of a detection, also depends on Np(T). We find that for an all-sky, all-frequency search lasting T=10^7 s, this detection threshhold is at a level of 4 to 5 times h(3/yr), where h(3/yr) is the corresponding 99% confidence threshhold if one knows in advance the pulsar position and spin period.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the computational requirements for all-sky, all-frequency searches for gravitational waves from spinning neutron stars, using archived data from interferometric gravitational wave detectors such as LIGO. | contribution 0.97 | 0.88 | 0.04 | asserted 0.93 |
| s1 | These sources are expected to be weak, so the optimal strategy involves coherent accumulaton of signal-to-noise using Fourier transforms of long stretches of data (months to years). | background 0.69 | 0.09 | 0.04 | asserted 0.63 |
| s2 | Earth-motion-induced Doppler shifts, and intrinsic pulsar spindown, will reduce the narrow-band signal-to-noise by spreading power across many frequency bins; therefore, it is necessary to correct for these effects before performing the Fourier transform. | background 0.73 | 0.11 | 0.03 | asserted 0.97 |
| s3 | The corrections can be implemented by a parametrized model, in which one does a search over a discrete set of parameter values. | method 0.99 | 0.16 | 0.03 | asserted 0.83 |
| s4 | We define a metric on this parameter space, which can be used to determine the optimal spacing between points in a search; the metric is used to compute the number of independent parameter-space points Np that must be searched, as a function of observation time T. | method 0.76 | 0.90 | 0.07 | asserted 1.00 |
| s5 | The number Np(T) depends on the maximum gravitational wave frequency and the minimum spindown age tau=f/(df/dt) that the search can detect. | method 0.56 | 0.72 | 0.06 | asserted 1.00 |
| s6 | The signal-to-noise ratio required, in order to have 99% confidence of a detection, also depends on Np(T). | method 0.46 | 0.49 | 0.07 | asserted 1.00 |
| s7 | We find that for an all-sky, all-frequency search lasting T=10^7 s, this detection threshhold is at a level of 4 to 5 times h(3/yr), where h(3/yr) is the corresponding 99% confidence threshhold if one knows in advance the pulsar position and spin period. | result 1.00 | 0.95 | 0.69 | asserted 1.00 |
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The paper
Original abstract
We investigate the computational requirements for all-sky, all-frequency searches for gravitational waves from spinning neutron stars, using archived data from interferometric gravitational wave detectors such as LIGO. These sources are expected to be weak, so the optimal strategy involves coherent accumulaton of signal-to-noise using Fourier transforms of long stretches of data (months to years). Earth-motion-induced Doppler shifts, and intrinsic pulsar spindown, will reduce the narrow-band signal-to-noise by spreading power across many frequency bins; therefore, it is necessary to correct for these effects before performing the Fourier transform. The corrections can be implemented by a parametrized model, in which one does a search over a discrete set of parameter values. We define a metric on this parameter space, which can be used to determine the optimal spacing between points in a search; the metric is used to compute the number of independent parameter-space points Np that must be searched, as a function of observation time T. The number Np(T) depends on the maximum gravitational wave frequency and the minimum spindown age tau=f/(df/dt) that the search can detect. The signal-to-noise ratio required, in order to have 99% confidence of a detection, also depends on Np(T). We find that for an all-sky, all-frequency search lasting T=10^7 s, this detection threshhold is at a level of 4 to 5 times h(3/yr), where h(3/yr) is the corresponding 99% confidence threshhold if one knows in advance the pulsar position and spin period.
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References
How the literature uses it
20 arXiv papers cite this in 47 sentences
Papers citing it · 29 sentences without a confident label
Uses its method or tool 4 papers
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Our analysis adopts a “stack–slide” type [ref] semi-coherent search implemented with the Global Correlation Transform (GCT) method [ref] .
Observational constraints on the spin/anisotropy of the CCOs of Cassiopeia A, Vela Jr. and G347.3-0.5 and a single surviving continuous gravitational wave candidate · The Einstein@Home Search · 1.00
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The search in [ref] is based on the Einstein@Home distributed computing framework and hierarchical search pipeline [ref] .
The G347.3-0.5 outlier from O3: a follow-up case study for continuous gravitational-wave candidates · Signal model and detection framework · 0.85
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Pragmatically, as done in [ref] , this can be calculated as [equation] which we refer to as the approximate number of unit-mismatch templates needed to cover a given search parameter space.
Hierarchical multi-stage MCMC follow-up of continuous gravitational wave candidates · The number of templates · 0.83
Compares with it 2 papers
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The number of templates in the bank was found to be in good agreement with the prediction of [ref] .
Parameter-space metric for all-sky semicoherent searches for gravitational-wave pulsars · Introduction · 0.93
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Given the idealized assumptions of [ref] , it is encouraging to see close agreement with the template estimation described in this section, which in turn is in good agreement with the practical implementation of lattice template placement described in Section [ref].
Lattice template placement for coherent all-sky searches for gravitational-wave pulsars · Counted and estimated number of templates · 0.99
Cites it as background 8 papers
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An important component of a wide-parameter-space $$-statistic search for gravitational-wave pulsars is the metric, or distance function, associated with the parameter space [ref] .
Lattice template placement for coherent all-sky searches for gravitational-wave pulsars · Introduction · 0.97
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First is the use of a parameter-space metric [ref] , which is used to determine the appropriate resolution of the bank of template signals such that the mismatch, or fractional loss in signal-to-noise ratio between any signal present in the data and its nearest template, never exceeds a prescribed maximum.
Implementing a semicoherent search for continuous gravitational waves using optimally-constructed template banks · Introduction · 0.92
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To achieve these constraints, the parameter space is associated with a metric, or distance function, $g$ [ref] .
Flat parameter-space metric for all-sky searches for gravitational-wave pulsars · Introduction · 0.81
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