  The progress of neutrino astronomy makes the precise measurement of the
flavor ratio of high energy astronomical neutrinos (HANs) possible in the near
future. Then matter effects and new physics effects on the flavor transition of
HANs could be tested by the next-generation neutrino telescopes. In this paper
we study matter effects in gas around the sources of HANs. The matter effects
are dependent on both the decoherence schemes and the sources of neutrinos. We
examine the predictions on the flavor ratio at Earth for typical sources with
five decoherence schemes. For the adiabatic schemes, the matter effect is
notable and may be identified in the special range of the electron density,
irrespective of the production sources of HANs. Hence, the precise measurement
of the flavor ratio would provide constrains on the propagation schemes and the
matter parameter.
