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$\epsilon(\theta_{obs})=\epsilon_0e^{\frac{-\theta_{obs}^2}{2\sigma_{gau}^2}}$

$\epsilon(\theta_{obs})= \begin{cases} \epsilon_0 & \theta_{obs}\leq \theta_{jet} \\ \epsilon_0\frac{\theta_{obs}}{\theta_{jet}}^{-s} & \theta_{obs}> \theta_{jet} \\\end{cases}$

$\epsilon_0$

$\Psi(\theta_{j})=\frac{A_{\theta}}{\sqrt{2\pi}\sigma_{\theta}}exp[{-\frac{(log\theta_{j}-log\theta_{c})^2}{2\sigma^2_{\theta}}}]$

$S_{crown}=2\pi R(1-cos\theta_{obs})$

$P(\theta_{obs})=1-cos\theta_{obs}$

$\int_0^{\theta_{obs}} \Psi(\theta_{obs})d\theta_{obs}=P(\theta_{obs})=1-cos\theta_{obs}$

$\Psi(\theta_{obs})=sin\theta_{obs}$

$peak=\frac{E_{iso}}{4\pi D_{L}(z)^2T_{90}k}$

$\Psi(\epsilon_0)=\frac{A_{\epsilon_0}}{\sqrt{2\pi}\sigma_{\epsilon_0}}exp[{-\frac{(log\epsilon_0-log\epsilon_{0c})^2}{2\sigma^2_{\epsilon_0}}}]$

$\sigma_{\epsilon_0} \quad log\epsilon_{0c} \quad \sigma_{gau} \quad s$

$E=mc^2$