Polytropes: Implications for Molecular Clouds and Dark Matter

Molecular clouds are supported against their own self-gravity by several different sources of pressure: thermal pressure, mean magnetic pressure, and turbulent pressure. Multi-pressure polytropes, in which each of these pressures is proportional to a power of the density, can account for many of the observed properties of molecular clouds. The agreement with observation can be improved with composite polytropes, in which an isothermal core is embedded in a turbulent envelope. Observed molecular clouds generally have γp < 1, corresponding to a velocity dispersion that increases with scale. For such clouds the ratio of the mean pressure to the surface pressure must be less than 4. Small, very dense (n̄H ∼ 10 11 cm−3) molecular clouds have been proposed as models for both dark matter and for extreme scattering events. Insofar as the equation of state in these clouds can be represented by a single polytropic relation, such models conflict with observation. It is possible to contrive composite polytropes that do not conflict with observation, but whether the thermal properties of the clouds are consistent with such structures remains to be determined.