The non-oscillated fluence spectrum of neutrinos of a given species $({\nu }_{\mathrm{e}},{\bar{\nu }}_{\mathrm{e}},{\nu }_x)$ arriving at Earth from a core-collapse supernova is estimated by (M.T. Keil, G.G. Raffelt, and H.T. Janka (2003), Monte Carlo Study of Supernova Neutrino Spectra Formation, Astrophys. J. 590, 971) $${\mathrm{\Phi }}_{{\nu }_{\alpha }}^0(E)=\frac{1}{4\pi D^2}\frac{E_{{\nu }_{\alpha }}^{\mathrm{tot}}}{⟨E_{{\nu }_{\alpha }}{⟩}^2}\frac{{\beta }^{\beta }}{\mathrm{\Gamma }(\beta )}[\frac{E}{⟨E_{{\nu }_{\alpha }}⟩}{]}^{\beta -1}\exp [-\beta \frac{E}{⟨E_{{\nu }_{\alpha }}⟩}],$$ where $D$ is the distance to the SN, $E_{{\nu }_{\alpha }}^{\mathrm{tot}}$ is the total energy of the neutrino species, $⟨E_{{\nu }_{\alpha }}⟩$ is the average energy of the neutrino species, $\beta$ is a spectrum shape parameter, and $\mathrm{\Gamma }$ is the gamma function.

While distance D = 10 kpc is fixed, the default values for $\beta$, $E_{{\nu }_{\alpha }}^{\mathrm{tot}}$, and $⟨E_{{\nu }_{\alpha }}⟩$, are user-settable for exploring signals from different models.

Oscillation effects depend on the neutrino mass ordering (A.S. Dighe and A.Y. Smirnov (2000), Identifying the neutrino mass spectrum from a supernova neutrino burst, Phys. Rev. D 62, 033007).
For normal ordering (NO) with $m_3>m_2>m_1$ $$\begin{array}{rl}& {\mathrm{\Phi }}_{{\nu }_{\mathrm{e}}}={\mathrm{\Phi }}_{{\nu }_e}^0{\sin }^2{\theta }_{13}+{\mathrm{\Phi }}_{{\nu }_x}^0(1-{\sin }^2{\theta }_{13})\\ & {\mathrm{\Phi }}_{{\bar{\nu }}_{\mathrm{e}}}={\mathrm{\Phi }}_{{\bar{\nu }}_{\mathrm{e}}}^0{\cos }^2{\theta }_{12}{\cos }^2{\theta }_{13}+{\mathrm{\Phi }}_{{\nu }_x}^0(1-{\cos }^2{\theta }_{12}{\cos }^2{\theta }_{13})\\ & {\mathrm{\Phi }}_{{\nu }_x}=\frac{1}{2}({\mathrm{\Phi }}_{{\nu }_{\mathrm{e}}}^0(1-{\sin }^2{\theta }_{13})+{\mathrm{\Phi }}_{{\nu }_x}^0(1+{\sin }^2{\theta }_{13}))\\ & {\mathrm{\Phi }}_{{\bar{\nu }}_x}=\frac{1}{2}({\mathrm{\Phi }}_{{\bar{\nu }}_{\mathrm{e}}}^0(1-{\cos }^2{\theta }_{12}{\cos }^2{\theta }_{13})+{\mathrm{\Phi }}_{{\nu }_x}^0(1+{\cos }^2{\theta }_{12}{\cos }^2{\theta }_{13}))\end{array}$$

For inverted ordering (IO) with $m_2>m_1>m_3$ $$\begin{array}{rl}& {\mathrm{\Phi }}_{{\nu }_{\mathrm{e}}}={\mathrm{\Phi }}_{{\nu }_e}^0{\sin }^2{\theta }_{12}{\cos }^2{\theta }_{13}+{\mathrm{\Phi }}_{{\nu }_x}^0(1-{\sin }^2{\theta }_{12}{\cos }^2{\theta }_{13})\\ & {\mathrm{\Phi }}_{{\bar{\nu }}_{\mathrm{e}}}={\mathrm{\Phi }}_{{\bar{\nu }}_{\mathrm{e}}}^0{\sin }^2{\theta }_{13}+{\mathrm{\Phi }}_{{\nu }_x}^0(1-{\sin }^2{\theta }_{13})\\ & {\mathrm{\Phi }}_{{\nu }_x}=\frac{1}{2}({\mathrm{\Phi }}_{{\nu }_{\mathrm{e}}}^0(1-{\sin }^2{\theta }_{12}{\cos }^2{\theta }_{13})+{\mathrm{\Phi }}_{{\nu }_x}^0(1+{\sin }^2{\theta }_{12}{\cos }^2{\theta }_{13}))\\ & {\mathrm{\Phi }}_{{\bar{\nu }}_x}=\frac{1}{2}({\mathrm{\Phi }}_{{\bar{\nu }}_{\mathrm{e}}}^0(1-{\sin }^2{\theta }_{13})+{\mathrm{\Phi }}_{{\nu }_x}^0(1+{\sin }^2{\theta }_{13}))\end{array}$$

The relatively high energy, large fluence, and short duration of the CCSN neutrinos allows consideration of several reactions not presented elsewhere on this site. On this tab, in addition to pIBD and eES, we present cross section plots and event totals for pES, ¹⁶O IBD, ¹²C IBD, and CEvNS. While the cross sections for CEvNS and pES are calculated internally using the estabished code for two-body elastic scattering (e.g. eES), the calculations of the cross sections for ¹⁶O IBD and ¹²C IBD are not conducive to online execution. For the ¹⁶O IBD cross sections we use parameterized fits (with threshold energies slightly larger than the excitation energies of each of four excitation groups- from K. Nakazato, T. Suzuki and M. Sakuda (2018), Charged-current scattering off the ¹⁶O nucleus as a detection channel for supernova neutrinos, Prog. Theor. Exp. Phys., 123E02). For the ¹²C IBD cross sections we use the fits to calculated values (E. Kolbe, K. Langanke and P. Vogel (1999), Weak reactions on ¹²C within the continuum random phase approximation with partial occupancies, Nucl. Phys. A 652, 91-100) as found on the SNOwGLoBES site.

Parameterized depth spectra of the total cosmic-ray muon flux and the associated neutron flux on the Earth are presented following equations given in D.-M. Mei and A. Hime (2006), Muon-induced background study for underground laboratories, Phys. Rev. D 73, 053004. The calculator and the plot below give the total muon flux (Eq. 4) and the neutron flux emerging from the rock into the underground cavern (Eq. 13) as a function of the equivalent flat overburden.