Why do some cores remain starless ?
  Physical conditions that could render a core starless(in the local Universe)
is the subject of investigation in this work. To this end we studied the
evolution of four starless cores, B68, L694-2, L1517B, L1689, and L1521F, a
VeLLO. The density profile of a typical core extracted from an earlier
simulation developed to study core-formation in a molecular cloud was used for
the purpose. We demonstrate - (i) cores contracted in quasistatic manner over a
timescale on the order of $\sim 10^{5}$ years. Those that remained starless did
briefly acquire a centrally concentrated density configuration that mimicked
the density profile of a unstable Bonnor Ebert sphere before rebounding, (ii)
three of our test cores viz. L694-2, L1689-SMM16 and L1521F remained starless
despite becoming thermally super-critical. On the contrary B68 and L1517B
remained sub-critical; L1521F collapsed to become a VeLLO only when gas-cooling
was enhanced by increasing the size of dust-grains. This result is robust, for
other cores viz. B68, L694-2, L1517B and L1689 that previously remained
starless could also be similarly induced to collapse. Our principle conclusions
are : (a) acquiring the thermally super-critical state does not ensure that a
core will necessarily become protostellar, (b) potentially star-forming cores
(VeLLO L1521F here), could be experiencing coagulation of dust-grains that must
enhance the gas-dust coupling and in turn lower the gas temperature, thereby
assisting collapse. This hypothesis appears to have some observational support,
and (c) depending on its dynamic state at any given epoch, a core could appear
to be pressure-confined, gravitationally/virially bound, suggesting that
gravitational/virial boundedness of a core is insufficient to ensure it will
form stars, though it is crucial for gas in a contracting core to cool
efficiently so it can collapse further to become protostellar.
