Shells and bubbles around compact clusters of massive stars: 3D MHD simulations

We present the results of three-dimensional magnetohydrodynamic (3D MHD) simulations of the plasma flow structure in the vicinity of a compact cluster of young massive stars. The cluster is considered at the evolutionary stage dominated by Wolf-Rayet stars. This stage occurs in clusters with ages of several million years, close to the onset of supernova explosions; the well-known objects Westerlund 1 and 2 are the prototypes. The collisions of powerful winds from massive stars in the cluster core, calculated as interactions of individual outflows, are accompanied by their partial thermalization and produce a collective cluster wind. The MHD dynamics of the cluster wind bubble expansion into the interstellar medium is considered, depending on the density of the surrounding medium with a uniform magnetic field. We show that when expanding into a cold neutral medium, the cluster wind is able to reshape its surrounding environment over the Wolf-Rayet star lifetime, sweeping up more than $10^4$ $M_{\odot}$ of gas in $\sim 2 \times 10^5$ yr and producing extended, thin and dense shells with an amplified magnetic field. In a cold neutral medium with a density of $\sim 20$ cm$^{-3}$ and a magnetic field of $\sim 3.5$ $μ$G, a thin shell forms around the cluster wind bubble, characterized by a cellular structure in its density and magnetic field distributions. The cellular magnetic field structure appears in parts of the shell expanding transversely to the orientation of the external magnetic field. Magnetic fields in the shell are amplified to strengths $\gtrsim 50$ $μ$G. The formation of the cellular structure is associated with the development of instabilities. The expansion of the bubble into a warm neutral interstellar medium also leads to the formation of a shell with an amplified magnetic field.

💡 Research Summary

This paper presents three‑dimensional magnetohydrodynamic (3‑D MHD) simulations of the plasma flow around a compact young massive star cluster (YMSC) during the Wolf‑Rayet (WR) dominated phase, i.e., a few Myr before the first core‑collapse supernovae explode. The authors model a cluster containing 60 massive stars (55 O‑type, 5 WR) randomly distributed within a 2 pc radius sphere. Each star injects a fast stellar wind (O‑type: v≈2400 km s⁻¹, Ṁ≈10⁻⁶ M⊙ yr⁻¹; WR: v≈2000 km s⁻¹, Ṁ≈10⁻⁵ M⊙ yr⁻¹) via a small spherical boundary condition. The winds collide, partially thermalise, and generate a collective cluster wind with a total mechanical luminosity ≥10³⁸ erg s⁻¹.

The MHD equations are solved with the PLUTO code using a Godunov‑type HLLD Riemann solver, second‑order TVD reconstruction, and a second‑order Runge‑Kutta time integrator on a uniform 3‑D grid (≈0.05 pc resolution). Non‑ideal effects include anisotropic thermal conduction (classical Braginskii plus saturated Cowie‑McKee flux) and optically thin radiative cooling/heating. Cooling is assembled from low‑temperature (Koyama & Inutsuka 2002), intermediate (Schure et al. 2009), and high‑temperature bremsstrahlung prescriptions; heating follows collisional ionisation equilibrium (CIE) for neutral gas and photo‑ionisation equilibrium (PIE) for ionised bubble material, using the Meyer et al. (2014) recipe.

Two ambient interstellar medium (ISM) environments are examined: (1) a cold neutral medium (CNM) with n≈20 cm⁻³, T≈160 K, and a uniform magnetic field B₀≈3.5 µG aligned with the x‑axis; (2) a warm neutral medium (WNM) with n≈0.5 cm⁻³, T≈6400 K, B₀≈5 µG. Open (outflow) boundary conditions are applied at the domain edges.

In the CNM case, the collective wind inflates a bubble that expands to a radius of ~30 pc within ~2 × 10⁵ yr, sweeping up >10⁴ M⊙ of ambient gas. A thin, dense shell forms at the bubble’s outer edge, with an average density ≈10 times the ambient value and a thickness of 0.2–0.5 pc. Where the expansion is transverse to the ambient magnetic field, the shell exhibits a cellular (filamentary) pattern caused by the combined action of Rayleigh‑Taylor, Kelvin‑Helmholtz, and magnetic shear instabilities. In these cellular regions the magnetic field is amplified to ≥50 µG, i.e., a factor of ≳15 over the initial field. The shell’s temperature stays in the 10⁶–10⁷ K range due to efficient thermal conduction, which smooths the temperature gradient between the hot interior wind and the cold external medium.

In the WNM case the bubble also forms a shell, but the lower ambient pressure and higher sound speed reduce the compression factor to ≈3–4, the shell thickness increases to 0.5–1 pc, and magnetic amplification reaches only 20–30 µG. Nonetheless, a coherent thin shell still develops, implying observable signatures in HI 21 cm and CO line emission.

Key insights from the simulations are: (i) individual stellar wind collisions efficiently convert kinetic energy into a collective wind that drives large‑scale feedback before supernovae occur; (ii) the orientation of the ambient magnetic field strongly influences shell morphology, with transverse expansion fostering magnetic shear instabilities that generate cellular structures and strong field amplification; (iii) amplified magnetic fields (≥50 µG) provide conditions conducive to cosmic‑ray confinement and acceleration, offering a natural explanation for the extended γ‑ray emission observed around clusters such as Westerlund 1; (iv) even in warm media, wind‑driven shells form, though with weaker compression and amplification, highlighting the sensitivity of feedback to the surrounding ISM phase.

The authors conclude that modeling the pre‑supernova phase of compact massive clusters is essential for a complete picture of star‑forming region feedback, superbubble formation, and high‑energy particle production. They suggest future work to incorporate realistic, clumpy molecular cloud structures, couple particle acceleration and non‑thermal radiation modules directly to the MHD simulations, and perform quantitative comparisons with multi‑wavelength observations (HI, CO, X‑ray, γ‑ray). Such extensions will refine our understanding of how YMSCs shape galactic ecosystems on both local (∼10 pc) and global (∼kpc) scales.