Ewan D. Barr edited scattering part4.tex  over 8 years ago

Commit id: 82940a700360d9d3cdba1d2545bbcd57161f8646

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By rearranging equation \ref{eqn:best_case_scattering} we can determine the maximum DM (DM$_{\rm max}$) for which it is possible to achieve a given timing resolution ($t_{\rm res}$):  \begin{equation}  \log_{10}{\rm DM} = \frac{-0.154 \frac{1}{2.14}(-0.154  + \sqrt{0.0247 + 4.28(13.46+3.86\log_{10}{\nu}+\log_{10}{t_{\rm res}})}}{2.14}. 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 100 ns timing resolution for all SKA observing frequencies.