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ϵ(θobs)=ϵ0e−θobs22σgau2\epsilon(\theta_{obs})=\epsilon_0e^{\frac{-\theta_{obs}^2}{2\sigma_{gau}^2}}

ϵ(θobs)={ϵ0θobs≤θjetϵ0θobsθjet−sθobs>θjet\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}

ϵ0\epsilon_0

Ψ(θj)=Aθ2πσθexp[−(logθj−logθc)22σθ2]\Psi(\theta_{j})=\frac{A_{\theta}}{\sqrt{2\pi}\sigma_{\theta}}exp[{-\frac{(log\theta_{j}-log\theta_{c})^2}{2\sigma^2_{\theta}}}]

Scrown=2πR(1−cosθobs)S_{crown}=2\pi R(1-cos\theta_{obs})

P(θobs)=1−cosθobsP(\theta_{obs})=1-cos\theta_{obs}

∫0θobsΨ(θobs)dθobs=P(θobs)=1−cosθobs\int_0^{\theta_{obs}} \Psi(\theta_{obs})d\theta_{obs}=P(\theta_{obs})=1-cos\theta_{obs}

Ψ(θobs)=sinθobs\Psi(\theta_{obs})=sin\theta_{obs}

peak=Eiso4πDL(z)2T90kpeak=\frac{E_{iso}}{4\pi D_{L}(z)^2T_{90}k}

Ψ(ϵ0)=Aϵ02πσϵ0exp[−(logϵ0−logϵ0c)22σϵ02]\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}}}]

σϵ0logϵ0cσgaus\sigma_{\epsilon_0} \quad log\epsilon_{0c} \quad \sigma_{gau} \quad s

E=mc2E=mc^2