these two regions we assume a transition coefficient $D_\mathrm{tran} = D_B(R/3 pc)^2$, where $R$ is the distance from the core. We assume a mean cloud density $\sim 25$[cm$^{-3}$]{}, cloud radius $\sim 30$pc, and have set, at 1 PeV, $D_B = D_\mathrm{ISM}$ at $R = $ 30 pc. A cloud of radius 30 pc with mean density 25 $\cmc$ would have a mass $\sim 10^5 M_{\odot}$. Outside the cloud we assumed an ISM density of $\sim 1$[cm$^{-3}$]{}. We note that the densities we assume for the clouds match available [$\gamma$-ray]{} observations of  [@hessWd1; @ohmea13].

The IceCube data points in Fig. \[fig:NeuOnly\] show the neutrino energy flux consistent with the position of  considering the angular resolution of the instrument. The CSF model applied to  with reasonable parameters can explain a subset of the observed Ice Cube neutrinos.

![Gamma-ray emission from inelastic [$p\!-\!p$]{}-interactions in the CSF source at $\sim 10^4$yr after the SN explosion when CR protons produced in the short-lived accelerator have propagated into a nearby cloud of $\sim 30$pc size. The magnetic field amplified by the CR-driven instabilities in the vicinity of the fast shock in the CSF accelerator were parameterized as 0.8 mG (c), 0.9 mG (b), and 1 mG 