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

Commit id: 9788b7a9fd08f232066d7a84e482037c323738fc

deletions | additions      

       

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}  \log_{10}{\rm DM_{\rm limit}} = \frac{1}{2.14}(-0.154 + \sqrt{0.0247 + 4.28(13.46+3.86\log_{10}{\nu}+\log_{10}{\tau_{s_{\rm best}}})}. 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.