On the interaction of a Bonnor-Ebert sphere with a stellar wind
  The structure of protostellar cores can often be approximated by isothermal
Bonnor-Ebert spheres (BES) which are stabilized by an external pressure. For
the typical pressure of $10^4k_B\,\mathrm{K\,cm^{-3}}$ to
$10^5k_B\,\mathrm{K\,cm^{-3}}$ found in molecular clouds, cores with masses
below $1.5\,{\rm M_\odot}$ are stable against gravitational collapse. In this
paper, we analyze the efficiency of triggering a gravitational collapse by a
nearby stellar wind, which represents an interesting scenario for triggered
low-mass star formation. We derive analytically a new stability criterion for a
BES compressed by a stellar wind, which depends on its initial nondimensional
radius $\xi_{max}$. If the stability limit is violated the wind triggers a core
collapse. Otherwise, the core is destroyed by the wind. We estimate its
validity range to $2.5<\xi_{max}<4.2$ and confirm this in simulations with the
SPH Code GADGET-3. The efficiency to trigger a gravitational collapse strongly
decreases for $\xi_{max}<2.5$ since in this case destruction and acceleration
of the whole sphere begin to dominate. We were unable to trigger a collapse for
$\xi_{max}<2$, which leads to the conclusion that a stellar wind can move the
smallest unstable stellar mass to $0.5\,\mathrm{M_\odot}$ and destabilizing
even smaller cores would require an external pressure larger than
$10^5k_B\,\mathrm{K\,cm^{-3}}$. For $\xi_{max}>4.2$ the expected wind strength
according to our criterion is small enough so that the compression is slower
than the sound speed of the BES and sound waves can be triggered. In this case
our criterion underestimates somewhat the onset of collapse and detailed
numerical analyses are required.
