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

where is the error in the numerical approximation and , i.e., is the norm, which in principle should be integrated over the complete time domain of the model waveform obtained by splicing a perturbative chirp waveform to a numerical waveform for the inspiral and merger.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 errorIn [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

and the requirement for measurement is Here is the optimal signal-to-noise ratio of the detector, defined by are dimensionless factors introduced in [203] to rescale the traditional signal-to-noise ratio in making the transition from frequency domain standards to time domain standards; determines the fraction of detections lost due to template mismatch, cf. Equation (14) of [204]; and corrects for error introduced in detector calibration. These requirements for detection and measurement, for either conservatively overstate the basic frequency domain requirements by replacing by its minimum value in transforming to the time domain.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 .

Living Rev. Relativity 15, (2012), 2
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