User: hinder Date: 2012/03/12 10:57 AM

Modified: / ET.tex

Log: ET.tex: Rework discussion of NRAR error criteria according to referee comments

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File [modified]: ET.tex Delta lines: +16 -12 =================================================================== --- ET.tex 2012-03-12 15:56:23 UTC (rev 285) +++ ET.tex 2012-03-12 15:57:39 UTC (rev 286) @@ -2728,18 +2728,22 @@ %seems to be the one corresponding to an $8$-th order accurate finite %difference approximation. We also indicate on both plots the time at which the gravitational -wave frequency reaches $\omega=0.2/\mathrm{M}$. We follow a community standard, agreed -to over the course of the NRAR\cite{NRAR:web} collaboration, that constrains -the numerical resolution so that the accumulated phase error is not -larger than $0.05$ radians at a gravitational wave frequency of -$\omega=0.2/\mathrm{M}$. From the plot, we assert that the phase error between the -higher and high resolutions and the one between high and medium-high -resolutions satisfies this criterion, while the phase error between -the medium-high and medium resolutions barely satisfies the criterion; and the -one between medium and low resolutions does not. We conclude then -that the three highest resolution runs do have sufficient resolution -to extract waveforms for use in the construction of analytic waveform -templates. +wave frequency reaches $\omega=0.2/\mathrm{M}$. This reference time +has been suggested, for example in the NRAR\cite{NRAR:web} +collaboration, as a useful point at which errors can be compared +between codes. The suggestion is that the accumulated phase error +should not be larger than $0.05$ radians at this reference time, and +that this is roughly the scale of accuracy which might be useful for +comparisons with analytic approximation methods. From the plot, we +assert that the phase difference between the higher and high +resolutions and the one between high and medium-high resolutions +satisfies this criterion, while the phase difference between the +medium-high and medium resolutions barely satisfies the criterion; and +the one between medium and low resolutions does not. We conclude then +that the three highest resolution runs do have the suggested accuracy. +While the waveform shown here is too short for comparison with +analytic methods, we illustrate here that these sorts of comparisons +can be made using the toolkit.

\begin{figure} \includegraphics[width=0.45\textwidth]{tracks}