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

Commit id: 0497cc9e5e262d12450e963bea0f5fbcad68a38b

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By rearranging the \citet{Bhat_2004} scattering relation 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{-b + \sqrt{b^2 - 4ac}}{2a}\\  where,\\  a = 1.07\\  b = 0.154\\  c = -13.46-3.86\log_{10}{\nu} - \log_{10}{\tau_s}\\  \log_{10}{\rm DM} = \frac{-0.154 + \sqrt{0.0247 - 4.28(-13.46-3.86\log_{10}{\nu} - \log_{10}{\tau_s})}}{2.14}  \end{equation}