Dynamical Collapse of Nonrotating Magnetic Molecular Cloud Cores: Evolution through Point‐Mass Formation

Abstract

We present a numerical simulation of the dynamical collapse of a nonrotating, magnetic molecular cloud core and follow the core's evolution through the formation of a central point mass and its subsequent growth to a 1 M ⊙ protostar. The epoch of point-mass formation (PMF) is investigated by a self-consistent extension of previously presented models of core formation and contraction in axisymmetric, self-gravitating, isothermal, magnetically supported interstellar molecular clouds. Prior to PMF, the core is dynamically contracting and is not well approximated by a quasistatic equilibrium model. Ambipolar diffusion, which plays a key role in the early evolution of the core, is unimportant during the dynamical pre-PMF collapse phase. However, the appearance of a central mass, through its effect on the gravitational field in the inner core regions, leads to a "revitalization" of ambipolar diffusion in the weakly ionized gas surrounding the central protostar. This process is so efficient that it leads to a decoupling of the field from the matter and results in an outward-propagating hydromagnetic C-type shock. The existence of an ambipolar diffusion-mediated shock of this type was predicted by Li & McKee (1996), and we find that the basic shock structure given by their analytic model is well reproduced by our more accurate numerical results. Our calculation also demonstrates that ambipolar diffusion, rather than Ohmic diffusivity operating in the innermost core region, is the main field decoupling mechanism responsible for driving the shock after PMF.The passage of the shock leads to a substantial redistribution, by ambipolar diffusion but possibly also by magnetic interchange, of the mass contained within the magnetic flux tubes in the inner core. In particular, ambipolar diffusion reduces the flux initially threading a collapsing ∼ 1 M ⊙ core by a factor ∼ > 10 3 by the time this mass accumulates within the inner radius (≃ 7.3 AU) of our computational grid. This reduction, which occurs primarily during the post-PMF phase of the collapse, represents a significant step towards the resolution of the protostellar magnetic flux problem.Our calculations indicate that a 1 M ⊙ protostar forms in ∼ 1.5 × 10 5 yr for typical cloud parameters. The mass accretion rate is time dependent, in part because of the C-shock that decelerates the infalling matter as it propagates outward: the accretion rate rises to ≃ 9.4 M ⊙ Myr −1 early on and decreases to ≃ 5.6 M ⊙ Myr −1 by the time a solar-mass protostar is formed. The infalling gas disk surrounding the protostar has a mass ∼ 10 −2 M ⊙ at radii r ∼ > 500 AU. A distinguishing prediction of our model is that the rapid ambipolar diffusion after the formation of a protostar should give rise to large ( ∼ > 1 km s −1 ), and potentially measurable, ion-neutral drift speeds on scales r ∼ < 200 AU.The main features of our simulation, including the C-shock formation after PMF, are captured by a similarity solution that incorporates the effects of ambipolar diffusion (Contopoulos, Ciolek, & ...

Fragmentation Instability of Molecular Clouds: Numerical Simulations

“…There is considerable scatter, but the linear theory is a good guide to the average fragment mass. The clump masses are similar to the masses of the supercritical cores formed in some previous simulations (Fiedler & Mouschovias 1993 ;Basu & Mouschovias 1994 ;Ciolek & Mouschovias 1994 ;Ciolek & 1998). Ko nigl At sufficiently large T , the spatial mode with the largest linear growth rate is the fundamental mode in the simulation domain (j \ L ), and fragments larger than this cannot form in a periodic simulation.…”

“…The magnetic Ðeld is redistributed within the cloud so that the inner parts become supercritical. The cloud is then di †erentiated into a dynamically collapsing core with a magnetically supported envelope (Ciolek & Mouschovias 1993 ;Fiedler & Mouschovias 1993 ;Basu & Mouschovias 1994 ;Ciolek & Mouschovias 1994 ;SaÐer, McKee, & Stahler 1997 ;Ciolek & 1998). Much progress has been made in following Ko nigl this type of evolution through 6 or more orders of magnitude of increase in central density, including the e †ects of rotation as well as detailed chemistry and grain physics.…”

The origin of molecular protostellar outflows

“…This first stage of the cloud's evolution lasts for about 10 6 −10 7 years (Ciolek & Basu 2000;Ciolek & Basu 2001). When an inner magnetically supercritical core forms, it begins to collapse more and more dynamically, forming an inward increasing density profile with an ever decreasing (in size and mass) inner region of higher and higher density, and a similar highly centrally concentrated distribution of magnetic field.…”

Gravitational Collapse and Fragmentation of Molecular Cloud Cores

“…The collapse of nonrotating magnetic cloud cores through point mass formation was recently investigated numerically by Ciolek and Königl. 225 Ambipolar diffusion, which plays a key role in the early core evolution, becomes unimportant during the phase leading to point mass formation (t = 0). However, the appearance of a central mass, through its effect on the gravitational field in the inner core regions, leads to a revitalization of ambipolar diffusion in the weakly ionized gas surrounding the central protostar.…”