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| - Global collapses and expansions in star-forming clouds
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| - Spectral observations of star-forming molecular clouds sometimes reveal distinct red asymmetric double-peaked molecular line profiles with weaker blue peaks and stronger red peaks. For some star-forming molecular clouds, molecular line transitions with red asymmetric line profiles coexist with those with blue asymmetric line profiles (i.e. blue asymmetric double-peaked molecular line profiles with weaker red peaks and stronger blue peaks) in spatially resolved spectral observations from different lines of sight, whereas for others molecular transitions with red asymmetric line profiles dominate. Blue asymmetric line profiles are usually interpreted as signals of central core collapses, whereas 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 (EECCs) 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 observation of red asymmetric line profiles in molecular cloud cores indicates that EECC processes are probably essential hydrodynamic processes in star formation. Using spatial distributions, we explore various profiles of molecular lines for several tracer molecules in various settings of EECC dynamic models with and without shocks.
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