  Observations of prestellar cores in star-forming filaments show two distinct
morphologies. While molecular line measurements often show broad cores,
submillimeter continuum observations predominantly display pinched cores
compared to the bulk of the filament gas. In order to explain how different
morphologies arise, we use the gravitational instability model where prestellar
cores form by growing density perturbations. The radial extent at each position
is set by the local line-mass. We show that the ratio of core radius to
filament radius is determined by the initial line-mass of the filament.
Additionally, the core morphology is independent of perturbation length scale
and inclination, which makes it an ideal diagnostic for observations. Filaments
with a line-mass of less than half its critical value should form broad cores,
whereas filaments with more than half its critical line-mass value should form
pinched cores. For filaments embedded in a constant background pressure, the
dominant perturbation growth times significantly differ for low and high
line-mass filaments. Therefore, we predict that only one population of cores is
present if all filaments within a region begin with similar initial
perturbations.
