  Aims: We aim to derive a stability condition for non-isothermal Bonnor-Ebert
spheres and compare the physical properties of critical non-isothermal and
isothermal gas spheres. These configurations can serve as models for prestellar
cores before gravitational collapse.
  Methods: A stability condition for non-isothermal spheres is derived by
constructing an expression for the derivative of boundary pressure with respect
to core volume. The temperature distribution is determined by means of
radiative transfer calculations. Based on the stability analysis, we derive the
physical parameters of critical cores for the mass range 0.1 - 5.0 M_sun. In
addition, the properties of roughly Jupiter-mass cores are briefly examined.
  Results: At the low-mass end the critical non-isothermal sphere has lower
central density and a slightly larger physical radius than the corresponding
isothermal sphere (i.e. one with the same mass and average temperature). The
temperature decrease towards the core centre becomes steeper towards smaller
masses as the central density becomes higher. The slope depends on the adopted
dust model. We find that the critical dimensionless radius increases above the
isothermal value xi_0 = 6.45 for very low-mass cores (< 0.2 M_sun). However, in
the mass-range studied here the changes are within 5% from the isothermal
value.
  Conclusions: The density structures of non-isothermal and isothermal
Bonnor-Ebert spheres for a given mass are fairly similar. However, the present
models predict clear differences in the average temperatures for the same
physical radius. Especially for low-mass cores, the temperature gradient
probably has implications on the chemistry and the observed line emission. We
also find that hydrostatic Jupiter-mass cores with radii less than 100 AU would
have very high boundary pressures compared with typical pressures in the
interstellar space.
