Synthetic Spectral Signatures from Isothermal Collapsing Gas and the
  Interpretation of Infall Profiles
  We revisit the interpretation of blue-excess molecular lines from dense
collapsing cores, considering recent numerical results that suggest prestellar
core collapse occurs from the outside-in, and not inside-out. We thus create
synthetic molecular-line observations of simulated collapsing,
spherically-symmetric, density fluctuations of low initial amplitude, embedded
in a uniform, globally gravitationally unstable background, without a turbulent
component. The collapsing core develops a flattened, Bonnor-Ebert-like density
profile, but with an outside-in radial velocity profile, where the peak infall
speeds 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 3-2
rotational lines, we consider several "typical" beamwidths and use a simple
line-fitting model to infer infall speeds from the synthetic profiles similarly
to what is done in standard line modeling. We find that the inferred infall
speeds are ~ 25-30% of the actual peak infall speed as the largest speeds are
downweighted by the low density gas in which they occur, due to the outside-in
nature 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 the
asymmetry parameter, $\delta v\equiv(V_{thick}-V_{thin})/\Delta v_{thin}$,
during the collapse, finding good agreement with observed values. Finally, the
HCO$^+$ J=3-2 lines exhibit extreme $T_b$/$T_r$-ratios like those for evolved
cores, for larger beams late in the collapse. Our results suggest that standard
dynamical infall reproduces several observed features, but that low-mass core
infall speeds are generally undervalued, often interpreted as being subsonic
although the actual speeds are supersonic, due to incorrectly assuming an
inside-out infall radial velocity profile with a static outer envelope.
