It has been emphasized [202] that the direct use of time domain errors obtained in numerical
simulations can be deceptive in assessing the accuracy standards for model waveforms to be suitable for
gravitational-wave data analysis. For this reason, the frequency domain accuracy requirements have been
translated into requirements on the time domain error norms, so that they can be readily enforced in
practice [203
, 204
, 201].
There are two distinct criteria for waveform accuracy: (i) Insufficient accuracy can lead to an unacceptable fraction of signals to pass undetected through the corresponding matched-filter; (ii) the accuracy affects whether a detected waveform can be used to measure the physical properties of the source, e.g., mass and spin, to a level commensurate with the accuracy of the observational data. Accuracy standards for model waveforms have been formulated to prevent these potential losses in the detection of gravitational waves and the measurement of their scientific content.
For a numerical waveform with strain component , the time domain error is measured by
The error can also be measured in terms of time derivatives of the strain. The first time derivative corresponds to the error in the news
and the second time derivative corresponds to the Weyl component error In [203], it was shown that sufficient conditions to satisfy data analysis criteria for detection and
measurement can be formulated in terms of any of the error norms
, i.e., in
terms of the strain, the news or the Weyl component. The accuracy requirement for detection is
The values of for the inspiral and merger of non-spinning equal-mass black holes have been
calculated in [203] for the advanced LIGO noise spectrum. As the total mass of the binary varies from
,
varies between
,
varies between
and
varies
between
. Thus, only the error
in the news can satisfy the criteria over the entire mass
range. The error in the strain
provides the easiest way to satisfy the criteria in the low mass case
and the error in the Weyl component
provides the easiest way to satisfy the criteria in
the high mass case
.
http://www.livingreviews.org/lrr-2012-2 |
Living Rev. Relativity 15, (2012), 2
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