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Ewan D. Barr added scattering part2.tex
over 8 years ago
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The scattering time scale is roughly related to the observing frequency, $\nu$, and distance between pulsar and observer, $D$, by
\begin{equation}
\tau_s \propto \frac{D^2}{\nu^\alpha}
\end{equation}
where $\alpha$ depends on the structure of turbulance in the ISM and is approximated as $\alpha \sim 4$.
The scattering timescale can also be expressed in terms of dispersion measure (DM). Here we will use the empirical model of \citet{Bhat_2004}, that relates $\tau_s$ to DM via
\begin{equation}
\log \tau_s = -6.46 + 0.154 \log{\rm DM} + 1.07 (\log{\rm DM})^2 - 3.86 \log{\nu}.
\end{equation}
In Table \ref{tab:mid_bands} we list the post-rebaselining observing bands of SKA1\_MID. Considering only the lowest frequency of each band (i.e. the frequency at which scattering will have the largest effect), we may determine DM-dependent minimum timing resolutions.
\begin{table}
\label{tab:mid_bands}
\caption{The post-rebaselining observing bands of SKA1\_MID}
\begin{tabular}{ c c }
Band 1 & 350 - 1050 (MHz) \\
Band 2 & 950 - 1760 (MHz)\\
Band 5 & 4600 - 13,800 (MHz)\\
\end{tabular}
\end{table}