Production of high-energy cosmic neutrinos inpγandnγscattering. I. Neutrino yields for power-law spectra of protons and neutrons

For the purpose of high-energy neutrino astronomy, the rates of neutrino production through decay of pions and kaons born in $p\gamma$ and $n\gamma$ scattering in cosmic sources are calculated. A source is assumed to be filled with low-energy photons and high-energy protons (neutrons). The photons are assumed to be isotropically distributed, while the distribution of protons might be anisotropic. The production rate of neutrinos per unit volume of the source is given by $Q_{{\nu }_i}(E_{\nu }, \theta )=Y_{{\nu }_i}\left({\epsilon }_{\nu }\right){\sigma }_0{n}_{0}c{n}_p(E_{\nu }, \theta )$, where $Y_{{\nu }_i}$ are neutrino yields, ${\sigma }_0=100\mathrm{}$ μb is a normalizing value of the $p\gamma$ cross section, $n_0$ (in ${\mathrm{cm}}^{-3\mathrm{}}$) is a spatial density of photons, and $n_p(E_{\nu }, \theta )$ (in ${\mathrm{cm}}^{-3\mathrm{}}$ ${\mathrm{sr}}^{-1\mathrm{}}$ Ge${\mathrm{V}}^{-1\mathrm{}}$) is the density of protons (neutrons) with momenta in some direction $\theta$. The neutrino yield is shown to be a function of the product ${\epsilon }_{\nu }=\frac{E_{\nu }{\omega }_0}{m_p^2}$, with ${\omega }_0$ being a photon energy where the spectrum $n_{\gamma }\left(\omega \right)$ has a maximum. Neutrino yields are calculated for the power-law spectra of protons, $n_p\mathrm{}\left(E\right)\mathrm{}\sim E^{-(\gamma +1)}$, and for several spectra of photons (namely, for the diluted Planckian spectrum with temperature $T$ and for the power-law spectra both with and without a highenergy cutoff).