EPoS Contribution

When and How Do Prestellar Cores Collapse? Critical Conditions and Collapse Dynamics from Analytic Modeling and Numerical Simulations Sanghyuk Moon PrincetonU, Princeton, US
Starless cores are observed to be centrally concentrated and have subsonic infall motions, indicating that they are gravitationally stratified and sometimes contracting. Their number count relative to T-Tauri stars suggests that their lifetime is no more than a factor of a few times the free-fall time. While it is evident that a fraction of these cores collapses to form a star/stellar system, two central questions regarding their dynamics have yet to be fully answered: which cores will ultimately collapse, and in what manner they do so? To answer these questions, we track the evolutionary histories of individual cores forming in a suite of numerical simulations of idealized molecular clouds and directly measure the angle-averaged physical quantities including the forces acting on the cores to assess their dynamical status. We also construct an analytical model of turbulent cores characterized by a power-law linewidth-size relation by solving the angle-averaged equations of hydrodynamics. The analytic model naturally generalizes the traditional Bonnor-Ebert sphere, yielding the critical density contrast, mass, and radius as a function of the average velocity dispersion and power-law index of the linewidth-size relation. We find that the simulated cores initiate runaway gravitational collapse when 1) their mass exceeds the critical mass and 2) the critical radius becomes smaller than the tidal radius, the latter of which is the maximum radius that any given core can be considered relatively isolated. At the critical time when both conditions are met, the measured net force is zero on average and the structure of simulated cores is similar to the analytic model. The difference between the gravity and pressure gradients slowly increases during the collapse, but the force imbalance does not exceed ~30% even at the end of the collapse. For the entire ensemble of simulated cores, the average force imbalance during the collapse is only 13%, indicating that the prestellar core collapse is more like a quasi-equilibrium process rather than a pressureless free-fall. Due to this small force imbalance, the duration of the collapse (up to the point when gas density blows up at the center) is a factor of 2-3 longer than the central free-fall time, although it is comparable to a free-fall time corresponding to the average core density. Infall motions within the simulated cores are inherited from the core-building converging flows and remain subsonic throughout most of the core lifetime, where the supersonic infall speeds only appear near the end of the collapse. The time taken for a core with a certain average density to collapse and form a sink particle is remarkably consistent with the observed trend of core lifetime versus average density, suggesting that a significant fraction of observed prestellar cores might be already undergoing a quasi-equilibrium collapse.

Caption: (a) The time evolution of the fractional force imbalance (the net force divided by the gravitational force) of the simulated cores. Time is normalized such that τ=0 at the critical time (see the abstract) and τ=1 at the end of the collapse. The background colors show the distribution of the entire ensemble of the simulated cores, while the thick red line show the median force imbalance at each time bin. (b) Radial profiles of the gas density averaged over a full solid angle, for a simulated core at the onset of collapse (blue solid line) and for our analytic equilibrium solution (red dashed line). The critical radius and the tidal radius are marked in vertical ticks with corresponding labels. (c) Observationally inferred lifetime of prestellar cores in Aquila cloud complex taken from Konyves et al. (2015) (orange line with circles) and the measured lifetime (i.e., time to sink formation) of our simulated cores (blue line with error bars) as a function of the average density. The observed lifetime is subject to systematic uncertainties arising from the uncertainties in the reference lifetime of T-Tauri stars as well as the star formation history, the latter of which is typically assumed to be steady. The red line with circles is identical to the orange line, but shifted down by a factor of ~3, which is appropriate if the star formation is accelerating and/or the lifetime of T-Tauri stars is smaller than 2 Myr.
Collaborators: E. Ostriker, PrincetonU, US	Relevant topic(s): Collapse Cores
Relevant Big Question: Which physical processes determine the onset of prestellar core collapse?