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Ewan D. Barr edited scattering part4.tex
over 8 years ago
Commit id: 43d6a34eff742175418f01ef4b90d8dcead54031
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By rearranging equation \ref{eqn:best_case_scattering} we can determine the limiting DM (DM$_{\rm limit}$) above which it is no longer possible to achieve a given timing resolution ($t_{\rm res}$) due to scattering:
\begin{equation}
\label{eqn:limiting_dm}
\log_{10}{\rm DM_{\rm limit}}(\nu,t_{\rm res}) = \frac{1}{2.14}(-0.154 + \sqrt{0.0247 + 4.28(13.46+3.86\log_{10}{\nu}+\log_{10}{t_{\rm res}})}.
\end{equation}
Here $t_{\rm res}$ has units of seconds and $\nu$ has units of GHz. Figure \ref{fig:crossover_dm} shows the limiting DM for 200 ns timing resolution for all SKA observing frequencies.
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