Tracking the evolutionary stage of protostars by the abundances of
  astrophysical ices
  The physical evolution of Young Stellar Objects (YSOs) is accompanied by an
enrichment of the molecular complexity, mainly triggered by the heating and
energetic processing of the astrophysical ices. In this paper, a study of how
the ice column density varies across the protostellar evolution has been
performed. Tabulated data of H$_2$O, CO$_2$, CH$_3$OH, HCOOH observed by
ground- and space-based telescopes toward 27 early-stage YSOs were taken from
the literature. The observational data shows that ice column density and
spectral index ($\alpha$), used to classify the evolutionary stage, are well
correlated. A 2D continuum radiative transfer simulation containing bare and
grains covered by ices at different levels of cosmic-ray processing were used
to calculate the Spectral Energy Distributions (SEDs) in different angle
inclinations between face-on and edge-on configuration. The H$_2$O:CO$_2$ ice
mixture was used to address the H$_2$O and CO$_2$ column density variation
whereas the CH$_3$OH and HCOOH are a byproduct of the virgin ice after the
energetic processing. The simulated spectra were used to calculate the ice
column densities of YSOs in an evolutionary sequence. As a result, the models
show that the ice column density variation of HCOOH with $\alpha$ can be
justified by the envelope dissipation and ice energetic processing. On the
other hand, the ice column densities are mostly overestimated in the cases of
H$_2$O, CO$_2$ and CH$_3$OH, even though the physical and cosmic-ray processing
effects are taken into account.
