  Recent measurements of PeV energy neutrinos at IceCube and a 3.5 keV X-ray
line in the spectra of several galaxies are both tantalizing signatures of new
physics. This paper shows that one or both of these observations can be
explained within an extended supersymmetric neutrino sector. Obtaining light
active neutrino masses as well as phenomenologically interesting (keV-GeV)
sterile neutrino masses without any unnaturally small parameters hints at a new
symmetry in the neutrino sector that is broken at the PeV scale, presumably
tied to supersymmetry breaking. The same symmetry and structure can
sufficiently stabilize an additional PeV particle, produce its abundance
through the freeze-in mechanism, and lead to decays that can give the energetic
neutrinos observed by IceCube. The lightest sterile neutrino, if at 7 keV, is a
non-resonantly produced fraction of dark matter, and can account for the 3.5
keV X-ray line. The two signals could therefore be the first probes of an
extended supersymmetric neutrino sector.
