THE EQUILIBRIA AND EVOLUTIONS OF MAGNETIZED, ROTATING, ISOTHERMAL CLOUDS .4. QUASI-STATIC EVOLUTION

The evolution of a magnetized, rotating, isothermal cloud is studied assuming quasi-static evolution. The evolution is driven by the plasma drift (ambipolar diffusion) and magnetic braking. Mass and angular momentum are transferred inwardly across the magnetic flux tube due to the plasma drift. Since the rotating cloud winds the magnetic field, torsional Alfvén waves transport angular momentum away from the cloud. We consider the cloud rotating with an angular momentum parallel to the magnetic field, which is immersed in a static external pressure and is threaded by a uniform magnetic field at infinity. The problem is characterized by four parameters which determine the initial equilibrium structure (cloud mass, magnetic flux, ratio of thermal pressure to magnetic pressure, and total angular momentum) and a parameter which expresses the efficiency of magnetic braking, i.e., density of the ambient medium ρa. Due to the plasma drift, the mass-to-magnetic flux ratio at the center increases and, accordingly, the central density ρc increases. After the epoch when the mass-to-flux ratio exceeds a critical value, there exist no equilibrium solutions and the cloud begins to collapse dynamically. This occurs in τP ≃ 16(Gρc)1/2 ∼ several Myr for molecular cores with density 2 × 104 cm-3. The angular momentum is lost by magnetic braking in a time τ∥ ≃ σ/(2ρa VA) ∼ several Myr, where σ and VA denote, respectively, column density of the cloud and Alfvén speed in the ambient medium, in agreement with the analytical result by Mouschovias and Paleologou. Depending on the relative magnitude of τP and τ∥, the final angular momentum kept in the cloud varies. In the final phase of the quasi-static evolution, as long as the magnetic flux decreases by ∼1/2 to the critical value, the cloud central density increases by a factor of more than 100.