Definition

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The average energy of the neutrinos $\langle E \rangle$ emitted during a supernova explosion is of the order of 10MeV, and the neutrino luminosity at the early epoch of the explosion is approximately $10^{52}\mathrm{ergs\cdot s^{-1}}$. Therefore, the number density of the neutrinos at the radius $R$ is

$$ \begin{equation*} n \sim 10^{18} \mathrm{cm^{-3}} \left(\frac{100\mathrm{km}}{R}\right)^2 \left(\frac{10\mathrm{MeV}}{\langle E \rangle}\right). \end{equation*} $$