  Following an approach initially outlined by McKee & Holliman, we investigate
the structure and stability of dense, starless molecular cloud cores. We model
those as spherical clouds in hydrostatic equilibrium and supported against
gravity by thermal, turbulent, and magnetic pressure. We determine the gas
pressure by solving for thermal equilibrium between heating and cooling, while
the turbulent and magnetic pressures are assumed to obey polytropic equations
of state. In comparing the models to observed cloud cores we find that the
observed peak column densities often exceed the limit for stable equilibria
supported by thermal pressure alone, suggesting significant non-thermal
pressure if the cores are to be stable. Non-thermal support is also needed to
stabilize cores embedded in molecular clouds with high average pressures. Since
the observed molecular linewidths of cores suggest that the turbulent pressure
is lower than the thermal pressure, magnetic field are likely a dominant
pressure component in many such cores.
