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 envel ope. The clouds are supported against their own self-gravity by a combinati on of thermal, mean magnetic, and turbulent wave pressure. The latter two a re included by allowing for locally adiabatic, nonisentropic pressure compo nents. Such models are meant to represent, in a schematic manner, the veloc ity and density structure of cores and globules, as inferred from molecular line and dust continuum observations. In addition, our picture reflects th e theoretical expectation that MI-ID wave motions, which are important at s cales greater than or similar to 0.1 pc in typical low-mass star-forming re gions, are damped at smaller scales, giving rise to a finite-sized, thermal ly dominated core region. We show that if the pressure components are isent ropic, 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 B onnor-Ebert sphere. If the pressure components are nonisentropic, it is pos sible to have arbitrarily large pressure drops, in agreement with the recen t work of McKee & Holliman. However, we find that even for nonisentropic pr essure components, the ratio of the mean to surface pressure in the composi te 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 embedd ed in stable clouds of much larger mass. In a subsequent paper, we show tha t composite polytropes on the verge of gravitational instability can reprod uce the observed velocity and density structure of cores and globules under a variety of physical conditions.