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Ewan D. Barr edited considerations.tex
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Ideally the upper DM limit for each band should be defined by the top frequency of that band. While practically speaking this is feasible for SKA1\_Mid, the large amount of memory required to do this across the whole SKA1\_Low band ($>100$ GB) is restrictive and would have unnecessary cost implications for pulsar timing with the SKA. We therefore suggest that for SKA1\_Low, the maximum DM required to be supported for each coarse frequency channel should be defined by equations \ref{eqn:limiting_dm} and \ref{eqn:limiting_dm_p} with the value of $\nu$ set by the centre frequency of the coarse channel. For SKA1\_Mid we suggest that the maximum DM to be supported by each frequency band is given by equations \ref{eqn:limiting_dm} and \ref{eqn:limiting_dm_p} with the value of $\nu$ set by the highest frequency in the band. For both SKA1\_Low and SKA1\_Mid, the value of $n_{\rm bins}$ will be user defined on a per-observation basis. This leads to two new requirements for pulsar timing with SKA1:
\begin{itemize}
\item \textbf{SKA1-SYS\_REQ-XXXX:} \textit{\bf SKA1\_Mid Pulsar Timing DM limits.} The SKA1\_Mid when in pulsar timing mode shall time pulsars
out up to a dispersion measure defined by:\\
$\log_{10}{\rm DM}= \frac{1}{2.14}(-0.154 + \sqrt{0.0247 + 4.28(13.46+3.86\log_{10}{\nu}+\log_{10}{t_{\rm res}})}$,\\ where the frequency ($\nu$) is defined as the top of the current observing band and the time resolution ($t_{\rm res}$) is defined by SKA1-SYS\_REQ-2961.
\item \textbf{SKA1-SYS\_REQ-XXXX:} \textit{\bf SKA1\_Low Pulsar Timing DM limits.} The SKA1\_Mid when in pulsar timing mode shall time pulsars
out up to a dispersion measure defined by:\\
$\log_{10}{\rm DM}= \frac{1}{2.14}(-0.154 + \sqrt{0.0247 + 4.28(13.46+3.86\log_{10}{\nu}+\log_{10}{t_{\rm res}})}$,\\
where the frequency ($\nu$) is defined as the centre of the given coarse frequency channel and the time resolution ($t_{\rm res}$) is defined by SKA1-SYS\_REQ-2962.
\end{itemize}
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