The Fermi $gamma$-ray space telescope reported the observation of several Galactic supernova remnants recently, with the $gamma$-ray spectra well described by hadronic $pp$ collisions. The possible neutrino emissions from these Fermi detected superno
va remnants are discussed in this work, assuming the hadronic origin of the $gamma$-ray emission. The muon event rates induced by the neutrinos from these supernova remnants on typical km$^3$ neutrino telescopes, such as the IceCube and the KM3NeT, are calculated. The results show that for most of these supernova remnants the neutrino signals are too weak to be detected by the on-going or up-coming neutrino experiment. Only for the TeV bright sources RX J1713.7-3946 and possibly W28 the neutrino signals can be comparable with the atmospheric background in the TeV region, if the protons can be accelerated to very high energies. The northern hemisphere based neutrino telescope might detect the neutrinos from these two sources.
The $gamma$-ray and neutrino emissions from dark matter (DM) annihilation in galaxy clusters are studied. After about one year operation of Fermi-LAT, several nearby clusters are reported with stringent upper limits of GeV $gamma$-ray emission. We us
e the Fermi-LAT upper limits of these clusters to constrain the DM model parameters. We find that the DM model distributed with substructures predicted in cold DM (CDM) scenario is strongly constrained by Fermi-LAT $gamma$-ray data. Especially for the leptonic annihilation scenario which may account for the $e^{pm}$ excesses discovered by PAMELA/Fermi-LAT/HESS, the constraint on the minimum mass of substructures is of the level $10^2-10^3$ M$_{odot}$, which is much larger than that expected in CDM picture, but is consistent with a warm DM scenario. We further investigate the sensitivity of neutrino detections of the clusters by IceCube. It is found that neutrino detection is much more difficult than $gamma$-rays. Only for very heavy DM ($sim 10$ TeV) together with a considerable branching ratio to line neutrinos the neutrino sensitivity is comparable with that of $gamma$-rays.
Recently PAMELA released their first results on the positron and antiproton ratios. Stimulated by the new data, we studied the cosmic ray propagation models and calculated the secondary positron and antiproton spectra. The low energy positron ratio c
an be consistent with data in the convection propagation model. Above $sim 10$ GeV PAMELA data shows a clear excess on the positron ratio. However, the secondary antiproton is roughly consistent with data. The positron excess may be a direct evidence of dark matter annihilation or decay. We compare the positron and anti-proton spectra with data by assuming dark matter annihilates or decays into different final states. The PAMELA data actually excludes quark pairs being the main final states, disfavors gauge boson final states. Only in the case of leptonic final states the positron and anti-proton spectra can be explained simultaneously. We also compare the decaying and annihilating dark matter scenarios to account for the PAMELA results and prefer to the decaying dark matter. Finally we consider a decaying neutralino dark matter model in the frame of supersymmetry with R-parity violation. The PAMELA data is well fitted with neutralino mass $600sim 2000$ GeV and life time $sim 10^{26}$ seconds. We also demonstrate that neutralino with mass around 2TeV can fit PAMELA and ATIC data simultaneously.
