  Spectral molecular line profile observations of star-forming molecular clouds
sometimes show distinct red asymmetric double-peaked molecular line profiles
with weaker blue peaks and stronger red peaks. For some star-forming molecular
clouds, such molecular transitions with red asymmetric line profiles and blue
asymmetric line profiles (i.e. blue asymmetric double-peaked molecular line
profiles with weaker red peaks and stronger blue peaks) may coexist in
spatially resolved spectral observations, while for others, such molecular
transitions with red asymmetric line profiles may completely dominate in
spatially resolved spectral observations. Blue asymmetric line profiles are
usually interpreted as signals of central core collapses, while red asymmetric
line profiles remain unexplained. In this paper, we advance a spherically
symmetric self-similar hydrodynamic model framework for envelope expansions
with core collapses (EECC) of a general polytropic molecular gas cloud under
self-gravity. Based on such EECC hydrodynamic cloud models, we perform tracer
molecular line profile calculations using the publicly available RATRAN code
for star-forming clouds with spectroscopic signatures of red asymmetric line
profiles. The presence of red asymmetric line profiles from molecular cloud
cores indicates that EECC processes are most likely an essential hydrodynamic
process of star formation. With spatial distributions, we explore various
profiles of molecular lines for several tracer molecules in different settings
of EECC dynamic models with and without shocks.
