  The flavor composition of astrophysical neutrinos observed in neutrino
telescopes is a powerful discriminator between different astrophysical neutrino
production mechanisms and can also teach us about the particle physics
properties of neutrinos. In this paper, we investigate how the possible
existence of light sterile neutrinos can affect these flavor ratios. We
consider two scenarios: (i) neutrino production in conventional astrophysical
sources, followed by partial oscillation into sterile states; (ii) neutrinos
from dark matter decay with a primary flavor composition enhanced in tau
neutrinos or sterile neutrinos. Throughout the paper, we constrain the sterile
neutrino mixing parameters from a full global fit to short and long baseline
data. We present our results in the form of flavor triangles and, for scenario
(ii), as exclusion limits on the dark matter mass and lifetime, derived from a
fit to IceCube high energy starting events and through-going muons. We argue
that identifying a possible flux of neutrinos from dark matter decay may
require analyzing the flavor composition as a function of neutrino energy.
