DAWN. I. Simulating the formation and early evolution of stellar clusters with Phantom N-Body

TL;DR

This work tackles the challenge of simulating the formation and early evolution of stellar clusters embedded in molecular clouds by introducing a fast, statistically robust Phantom N-Body framework that couples hydrodynamics with direct N-body dynamics. It integrates a fourth-order Forward Symplectic Integrator (FSI) and Slow Down Algorithmic Regularisation (SDAR) to efficiently handle close encounters and multiple systems, plus a novel sink-based star-formation prescription and a simplified HII region feedback model. The authors demonstrate the approach with fiducial cloud-collapse simulations, revealing that massive stars and their ionising feedback can both dismantle gas and trigger secondary star formation, but also that the resulting star-formation efficiencies are still high, indicating missing physics such as jets and magnetic fields. These results underscore the stochastic nature of embedded cluster formation and motivate large ensembles to build robust dynamical models, with Paper II planned to explore the star-formation outcomes across broader parameter space.

Abstract

Context. Simulating stellar dynamics in a molecular cloud environment is numerically challenging due to the strong coupling between young stars and their surrounding gas, and the large range of length and time scales. Aims. This paper is the first of a suite aimed at investigating the complex early stellar dynamics in star-forming regions. We present a new simulation framework which is the key to generating a larger set of simulations, enabling statistical analysis. Methods. Methods originating from the stellar dynamics community, including regularisation and slowdown methods (SDAR), have been added to the hydrodynamical code Phantom to produce simulations of embedded cluster early dynamics. This is completed by a novel prescription of star formation to initialise stars with a low numerical cost, but in a way that is consistent with the gas distribution. Finally, a prescription for H ii region expansion has been added to model the gas removal. Results. We have run testcase simulations following the dynamical evolution of stellar clusters from the cloud collapse to a few Myr. Our new numerical methods fulfil their function by speeding up the calculation. The N-body dynamics with our novel implementation never appear as a bottleneck. Our first simulations show that massive stars largely impact the star formation process and shape the dynamics of the resulting cluster. Depending on the position of these massive stars and the strength of their feedback, they can prematurely dismantle part of the cloud or trigger a second event of cloud collapse, preferentially forming low-mass stars. This stochastic behaviour confirms the need for statistical studies. Conclusions. Our new Phantom N-Body framework enables efficient simulation of the formation and evolution of star clusters. It enables the statistical analysis needed to build models of the dynamical evolution of embedded star clusters.

Figures (11)

• Figure 1: The star formation process described by our new prescription, from the clump transformation into sink particles to stars release inside the simulation domain. This process is subdivided into three parts. First, a collapsing clump of gas passes tests to be transformed into a sink particle. The sink particle can accrete during $t_\mathrm{acc}$. After reaching this time, the sink is dissolved and its mass is shared to produce newborn stars at its last location.
• Figure 2: Snapshots showing the evolution of three fiducial clouds computed at multiple time steps. Each column corresponds to a specific run (top: ECF1, middle: ECF2, bottom: ECF3) and rows give different epochs in each of them. The colour map gives the $z$ integrated column density of the gas in $M_\odot\, \mathrm{pc}^{-2}$, while red circles correspond to sink positions and stars are coloured using realistic black body temperature extrapolated from a luminosity-mass relation. ECF1 presents a protostellar cluster under the influence of HII regions distributed in various parts of the molecular cloud, like for instance Aquila. ECF2 presents a more centrally concentrated protostellar cluster, which develops a cluster of HII regions, like the region W43. ECF3 is more difficult to link with an existing star-forming region. As all the gas has been removed very rapidly, the resulting group of stars looks like a more evolved association or cluster like NGC 6611.
• Figure 3: Evolution over time of multiple key parameters linked to the gas-to-star mass conversion. The top panel shows the time evolution of the mass of gas converted in sinks and stars in ECF1. The formation of massive stars is represented by vertical lines, with their colour indicating the mass of the massive object. The bottom panels show the temporal evolution of the accretion rate (left), mass median (centre) and the number of stars and sinks formed in the simulation (right). For the first two panels, the quartile range (grey zone) and the maximum value (dashed line) are also shown. It allows us to see that the sharp transition at $4 {\mathrm{Myr}}$ occurs on the majority of sinks. However, even after the change of regime, the cloud is still capable of producing some massive sinks with a high accretion rate.
• Figure 4: Same as previous figure applied on ECF2 simulation
• Figure 5: Same as previous figure applied on ECF3 simulation