Composite polytrope models of molecular clouds. I. Theory

We construct spherical, hydrostatic models of dense molecular cores and Bok globules consisting of two distinct, spatially separate gas components: a central, isothermal region surrounded by a negative-index, polytropic envelope. The clouds are supported against their own self-gravity by a combination of thermal, mean magnetic, and turbulent wave pressure. The latter two are included by allowing for locally adiabatic, nonisentropic pressure components. Such models are meant to represent, in a schematic manner, the velocity and density structure of cores and globules, as inferred from molecular line and dust continuum observations. In addition, our picture reflects the theoretical expectation that MI-ID wave motions, which are important at scales greater than or similar to 0.1 pc in typical low-mass star-forming regions, are damped at smaller scales, giving rise to a finite-sized, thermally dominated core region. We show that if the pressure components are isentropic, then the pressure drop from the center to the edge of the composite polytropes we consider is limited to 197, the square of the value for the Bonnor-Ebert sphere. If the pressure components are nonisentropic, it is possible to have arbitrarily large pressure drops, in agreement with the recent work of McKee & Holliman. However, we find that even for nonisentropic pressure components, the ratio of the mean to surface pressure in the composite polytropes we consider is less than 4. We show by explicit construction that it is possible to have dense cores comparable to the Jeans mass embedded in stable clouds of much larger mass. In a subsequent paper, we show that composite polytropes on the verge of gravitational instability can reproduce the observed velocity and density structure of cores and globules under a variety of physical conditions.