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We revisit the interpretation of blue-excess molecular lines from densecollapsing cores, considering recent numerical results that suggest prestellarcore collapse occurs from the outside-in, and not inside-out. We thus createsynthetic molecular-line observations of simulated collapsing,spherically-symmetric, density fluctuations of low initial amplitude, embeddedin a uniform, globally gravitationally unstable background, without a turbulentcomponent. The collapsing core develops a flattened, Bonnor-Ebert-like densityprofile, but with an outside-in radial velocity profile, where the peak infallspeeds are at large radii, in lower density gas, with cloud-to-core accretion,and no hydrostatic outer envelope. Using optically thick HCO$^+$ J=1-0 and 3-2rotational lines, we consider several "typical" beamwidths and use a simpleline-fitting model to infer infall speeds from the synthetic profiles similarlyto what is done in standard line modeling. We find that the inferred infallspeeds are ~ 25-30% of the actual peak infall speed as the largest speeds aredownweighted by the low density gas in which they occur, due to the outside-innature of the actual radial collapse profile. Also, with the N$_2$H$^+$$J_{F_1F}=1_{01}-0_{12}$ hyperfine line, we investigate the change in theasymmetry parameter, $\delta v\equiv(V_{thick}-V_{thin})/\Delta v_{thin}$,during the collapse, finding good agreement with observed values. Finally, theHCO$^+$ J=3-2 lines exhibit extreme $T_b$/$T_r$-ratios like those for evolvedcores, for larger beams late in the collapse. Our results suggest that standarddynamical infall reproduces several observed features, but that low-mass coreinfall speeds are generally undervalued, often interpreted as being subsonicalthough the actual speeds are supersonic, due to incorrectly assuming aninside-out infall radial velocity profile with a static outer envelope.

Synthetic Spectral Signatures from Isothermal Collapsing Gas and the Interpretation of Infall Profiles