Feedback and Star Formation Efficiency in High-Mass Star-Forming Regions

TL;DR

This study uses FLASH-based AMR simulations to follow the gravitational collapse of 1000 $M_\odot$ parsec-scale cores and to quantify how ionizing radiation, radiation pressure, and non-ionizing heating regulate star formation efficiency (SFE). By modeling sink particles with self-consistent radiative feedback and chemistry, the authors show that ionizing radiation ultimately halts mass accretion while radiation pressure accelerates ultra-compact HII region expansion; non-ionizing heating suppresses fragmentation and raises the Jeans mass. A parameter study varying initial density profiles, virial parameter, and metallicity demonstrates SFEs in the range $35\%-57\%$, with flatter density profiles, higher virial parameters, and higher metallicities tending to promote fragmentation and modestly increase SFE. Higher spatial resolution increases sink formation and delays feedback trapping, yielding higher final SFEs and more massive sink particles. Overall, stellar feedback governs the final SFE and the evolution of the massive-star-forming core, providing a physically motivated framework for comparison with ALMAGAL observations in follow-up work.

Abstract

To advance our understanding of massive star formation, it is essential to perform a comprehensive suite of simulations that explore the relevant parameter space and include enough physics to enable a comparison with observational data. We simulate the gravitational collapse of isolated, parsec-scale turbulent cores using the FLASH code, modelling stars as sink particles. Our simulations incorporate ionizing radiation and the associated radiation pressure from stellar sources, and non-ionizing radiation and its dust heating, along with self-consistent chemistry, to capture the properties of emerging ultra-compact HII regions. Dust, gas, and radiation temperature are computed independently. The initial conditions are informed by ALMAGAL observations. We assess stellar feedback, comparing ionizing radiation and radiation pressure. Ionizing radiation ultimately halts mass accretion on to sink particles, while direct radiation pressure enhances the expansion of HII regions. Heating from non-ionizing radiation suppresses fragmentation. We examine the effect of spatial resolution, finding that higher resolution leads to more sink particles which are situated in environments with higher densities. As a result, ionizing radiation remains trapped longer, allowing continued accretion and yielding a higher overall star formation efficiency (SFE). We explore the impact of varying initial conditions, including the core density profile, virial parameter, and metallicity. Our parameter study reveals that a flatter density profile, higher virial parameter, and increased metallicity promote fragmentation, potentially enhancing the SFE by slowing the growth of the most massive stars and delaying the onset of stellar feedback. Overall, we find SFEs between 35% and 57%. Stellar feedback dictates the final SFE.

Figures (24)

• Figure 1: Looking into the heart of a massive star-forming core. Volume rendering of our run RFL10 shown at $0.78 \, t_{\rm ff}$. We render molecular hydrogen, H$_2$, showing the cold gas distribution within the core. In addition, we show atomic hydrogen, H, and ionized hydrogen, H$^{+}$ in blue and red, respectively. The alpha channels are proportional to the logarithmic density. The volume rendering reveals a violent outflow accompanied by an expanding ultra-compact HII region with an asymmetric shape, supported by radiation pressure. The atomic gas (blue) surrounds the ionized gas (red), which fills the bubble.
• Figure 2: Time evolution of the fiducial run (from top to bottom). From left to right we show the projection in $z$-direction of the column density $\Sigma$ and the mass-weighted temperatures of gas $T_\mathrm{gas}$, dust $T_\mathrm{dust}$, and radiation $T_\mathrm{rad}$. Small circles represent sink particles. A green colour scheme represents lower-mass stars, while a blue colour scheme shows more massive sinks ($>8 \mathrm{M}_\odot$). After $\sim 0.4 t_\mathrm{ff}$ (where $t_\mathrm{ff}=0.526$ Myr; see Table \ref{['tab_parameter']}) massive sink particles are formed and drive an UC-HII region.
• Figure 3: Properties of sink particles in time in the fiducial run. Top Left: Sink mass. Top Right: Luminosity (smoothed). Bottom Left: Accretion rate (smoothed). Bottom Right: Rate of emitted ionizing (Lyman Continuum) photons (smoothed). In total 20 sink particles are formed. The sink particle that ends up being most massive (MMS) is coloured in black.
• Figure 4: Time evolution of the column density of the Fiducial run. The circles show the current position of the sink particles, similar to Fig. \ref{['fig:fiducialrun']}. The lines show the track of each sink particle, coloured as in Fig. \ref{['fig:sinkprop']}. The geometric centre and the centre of mass are marked with black and red crosses, respectively. Sink particles that are formed in the outer region fall towards the central region and immediately escape the potential well due high velocities.
• Figure 5: Evolution of the radial distribution of sink particles with respect to the geometric centre of the simulation box. The colour code shows the mass of the sink particles, while diamonds indicate when the sink particle has accreted $95\%$ of its final mass. The black dashed line shows the half-mass-radius, which is the radius of the sphere in which half of the initial mass (here $500 \, \mathrm{M}_\odot$) is located. The dotted lines indicate the radii used in Fig. \ref{['fig:massoutflow']}. Sink particles that are formed near the geometric centre stay near the centre, while particles that are formed outside perform a V-shaped movement in terms of radius. The MMS is formed near the centre, while sinks with very low final masses are formed at larger distances. However, for intermediate final masses, sink particles can form near the centre or in the outer parts.