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4 Comments on individual sources

In the context, the apparent brightness temperature is given by Gopal-Krishna et al. (1984),


\begin{displaymath}T_{\rm app}\geq \frac{2c^{2}\bigtriangleup S}{\pi \kappa \nu^{2}\theta_{\rm app}^{2}}~{\rm K},
\end{displaymath} (1)

when transforming to the co-moving frame of the source it becomes,

\begin{displaymath}T'_{\rm app}\geq T_{\rm app}(1+z)^{3}\delta^{-3}~{\rm K},
\end{displaymath} (2)

where $\bigtriangleup S$ is the flux change during a period $\tau$, $\theta_{\rm app} \leq 2c\tau/D_{\rm a}$ the apparent diameter of the variable component based on the causality argument, $D_{\rm a}$ (Lang 1974) the angular distance of the source, and $\delta$ the Doppler factor.


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