Formation and collapse of magnetized spherical molecular cloud cores

We idealize the molecular clouds (from which dense cores are formed), as magnetized spheres, following a recent study by Safier, McKee, & Stabler. This idealization is motivated in part by analytical convenience and in part by the observation that isolated low-mass star-forming molecular cloud cores have typical elongations of a factor of about 2. The evolution of such clouds due to ambipolar diffusion is followed numerically. The simplified geometry allows us to study not only the gradual enhancement of the central cloud density leading to core formation, but also the dynamic collapse that builds up a central protostellar object. It is during this latter accretion process that hydromagnetic shocks are predicted to occur by Li & McKee. The spherical model enables us to explore their properties further. During the core formation phase, we find that the evolution of our model (in a new parameter region of comparable thermal and magnetic support against self-gravity) is qualitatively similar to those found previously: a relatively long quasi-static adjustment period is followed by a short period of "runaway" contraction. and a more or less power-law distribution of cloud density is established in a finite amount of time since the initiation of ambibolar diffusion. Interesting features appear in the core-collapse phase. The most prominent among them are the following: (1) the mass accretion rate onto the central object has a large initial peak, followed by a steady decline toward a more conventional value; (2) for a many solar mass cloud, accretion continues onto the central object well beyond a solar mass. In order to form a low-mass star, some additional process(es), such as a powerful wind, must intervene to terminate the accretion before too much mass is assembled; (3) a magnetically driven accretion shock appears in the infalling envelope, as predicted previously The shock significantly modifies the distribution of magnetic flux, the how dynamics, and to a lesser extent, the mass accretion rate onto the central object. Observational ramifications of these findings are discussed.