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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}