Non-ideal MHD and protostellar feedback effects on disc formation and evolution in numerical simulations of star cluster formation

Abstract: While recent surveys have resolved hundreds of nearby protostellar discs, numerical simulations assuming ideal magnetohydrodynamics (MHD) have historically struggled to achieve disc formation due to efficient angular momentum removal by magnetic torques. Non-ideal MHD effects, relevant at the low ionization fractions typical of molecular clouds, have been shown to reduce the effectiveness of magnetic braking and promote disc formation. In this work, we present the results from a suite of calculations following the gravitational collapse of 50 $M_{\odot}$ turbulent molecular cloud cores down to the formation and evolution of stellar systems and protostellar discs. We use the radiation-MHD code GIZMO including non-ideal MHD (Ohmic resistivity, ambipolar diffusion, and the Hall effect) and the STARFORGE numerical framework for modeling star formation and stellar feedback. We compare the effects of assuming ideal vs. non-ideal MHD and including sub-grid protostellar jet feedback on disc formation and evolution. Discs form in all of our models but are least massive in the model with ideal MHD and sub-grid jet feedback. Apart from the ideal MHD$+$jets model, we do not observe any significant differences in disc properties between the ideal and non-ideal MHD models; however, ideal MHD discs are embedded in smaller rotating envelopes. Disc sizes are in general agreement with those of observed discs. Jet feedback increases core fragmentation and reduces final stellar masses. Our results suggest that magnetic braking does not efficiently suppress disc formation, regardless of whether ideal or non-ideal MHD is assumed, under the dynamical conditions in which multiple stellar systems form.

• The paper compares simulations of ideal and non-ideal MHD models, showing that non-ideal effects do not efficiently suppress disk formation in star cluster simulations.
• Rotations envelopes, identified by lower density thresholds, are more dominant in their comparison include material effectively sustaining disk formation.
• Jet feedback was shown to increase fragmentation, reduce stellar masses by an order of magnitude and enable second-generation disk formation, which does not rely on disk fragmentation in this dynamic.

Overview and motivation

This paper by Filippova, Offner, Grudić, and Hopkins (2608.19518) presents a suite of six radiation-MHD simulations following the gravitational collapse of turbulent 50 $M_{\odot}$ molecular cloud cores through star cluster formation, protostellar disk birth, and disk evolution. The central question is whether non-ideal MHD effects—Ohmic resistivity, ambipolar diffusion, and the Hall effect—and sub-grid protostellar jet feedback alter disk formation outcomes relative to ideal MHD. The simulations use GIZMO's meshless finite-mass solver with $N_{\rm gas} = 5 \times 10^6$ cells at mass resolution $\Delta m = 10^{-5}\,M_{\odot}$, embedded in the STARFORGE framework with sink particles ($R_{\rm sink} = 0.5$ AU), five-band M1 radiative transfer, protostellar evolution tracks, and full thermochemistry. Initial conditions are generated with the TURBSPHERE setup of Lane et al., which combines localized density profiles and outflow boundaries with fully developed turbulence after three turbulent crossing times.

The paper's headline conclusion is stated plainly: magnetic braking does not efficiently suppress disk formation under these dynamical conditions, regardless of whether ideal or non-ideal MHD is assumed. This directly echoes Wurster et al.'s "no magnetic braking catastrophe" result for comparable 50 $M_{\odot}$ SPH calculations. The distinguishing contribution here is the inclusion of jet feedback, a self-consistent analysis of rotating envelopes at lower density thresholds, and an explicit treatment of the Hall effect in a turbulent, feedback-regulated environment.

Numerical method and microphysics

The non-ideal MHD implementation follows the single-fluid "strong coupling" approximation, solving the modified induction equation with Ohmic, Hall, and ambipolar resistivities computed dynamically from the local plasma state. The conductivity framework follows Wardle (2007), with collision rates from Pinto & Galli (2008) and a positive-definite formulation for $\eta_{\rm A}$ to avoid round-off errors. Charged species include electrons, Mg-dominated ions ($m_i = 24.3\,m_p$ at cold dense conditions), and singly-sized dust grains ($a_g = 0.1\,\mu$m, $\rho_g = 3\,{\rm g\,cm^{-3}}$) with cosmic-ray charging at a fixed rate $\zeta_{\rm CR} = 1.6 \times 10^{-17}\,{\rm s}^{-1}$. Grain charge is solved iteratively via charge neutrality. The authors verify the implementation against the oblique isothermal C-shock (maximum relative error of a few percent) and the whistler-wave dispersion relation (relative error $N_{\rm gas} = 5 \times 10^6$0 across nine values of $N_{\rm gas} = 5 \times 10^6$1). Notably, tests with $N_{\rm gas} = 5 \times 10^6$2 require a small stabilizing Ohmic resistivity ($N_{\rm gas} = 5 \times 10^6$3); they argue that in their production runs $N_{\rm gas} = 5 \times 10^6$4 throughout, placing the calculations in a numerically safe regime. This caveat bears directly on the interpretation of Hall-dominated results below.

The initial cloud has $N_{\rm gas} = 5 \times 10^6$5 (supercritical), but turbulent dynamo amplification raises magnetization to $N_{\rm gas} = 5 \times 10^6$6 in gas above $N_{\rm gas} = 5 \times 10^6$7 before collapse. Each run costs roughly 240,000–320,000 CPU hours on Frontera; including all three non-ideal terms slows execution by about 20%.

Cloud structure: ambipolar diffusion smooths shocks

A robust pre-collapse finding is that ambipolar diffusion modifies the turbulent density structure. In TURBSPHERE stirring runs, non-ideal models develop fewer small-scale ($N_{\rm gas} = 5 \times 10^6$8 pc) features than the ideal model, consistent with C-type shock formation: the ion Alfvén speed exceeds the gas speed by orders of magnitude everywhere, satisfying the condition for continuous shock fronts. The degree of smoothing correlates strongly with assumed dust grain size—the turnover wavenumber of the density power spectrum shifts systematically between $N_{\rm gas} = 5 \times 10^6$9 and $\Delta m = 10^{-5}\,M_{\odot}$0m, and $\Delta m = 10^{-5}\,M_{\odot}$1 differs by more than two orders of magnitude at $\Delta m = 10^{-5}\,M_{\odot}$2. Because the fiducial grain size likely overestimates grain sizes in diffuse cloud regions (where an MRN-like distribution applies), the authors caution that the fiducial smoothing may be overestimated. Observations of NGC 1333 showing no ion-neutral dissipation down to $\Delta m = 10^{-5}\,M_{\odot}$34000 AU support this concern. Once self-gravity is enabled, magnetic field strength follows $\Delta m = 10^{-5}\,M_{\odot}$4 over eight decades in density in all three physics variants, with no significant difference between ideal and non-ideal medians—an extension of the universal $\Delta m = 10^{-5}\,M_{\odot}$5–$\Delta m = 10^{-5}\,M_{\odot}$6 relation found by He & Ricotti to the non-ideal regime at these densities.

Star formation and fragmentation

Star counts vary widely: 3 (ideal), 4 (ideal+jets), 1 (non-ideal OA), 5 (non-ideal OA+jets), 4 (non-ideal OAH), and 10 (non-ideal OAH+jets). Two trends emerge consistently when jets are included:

• Jet feedback increases fragmentation, producing more stars per cloud.
• Jet feedback reduces final stellar masses by roughly an order of magnitude, by ejecting accreted material ($\Delta m = 10^{-5}\,M_{\odot}$7, launched at $\Delta m = 10^{-5}\,M_{\odot}$8 of escape speed along the angular momentum axis) and disrupting accretion flows.

Multiple systems form exclusively via core and filament fragmentation at wide separations, never via disk fragmentation—a point with observational implications discussed below. A notable structure is a $\Delta m = 10^{-5}\,M_{\odot}$92000 AU gravitationally unstable rotating envelope in the non-ideal OA+jets model that fragments into three additional stars; this object would be classified as a "disk" if the density threshold were lowered to $R_{\rm sink} = 0.5$0, blurring the conventional disk/envelope boundary.

Disk formation and bulk properties

Disks form in every model, identified by density ($R_{\rm sink} = 0.5$1), dominance of azimuthal over radial/vertical velocities, and rotational support exceeding thermal support. Disk lifetimes range from $R_{\rm sink} = 0.5$2 to $R_{\rm sink} = 0.5$3 kyr, broadly matching Class 0/I durations. Disk masses span $R_{\rm sink} = 0.5$4–$R_{\rm sink} = 0.5$5 and radii tens to hundreds of AU, in general agreement with VANDAM survey statistics given the large uncertainties in dust-based mass conversion. Disk-to-stellar mass ratios exceed 0.1 early on, then fall by orders of magnitude; no disk ever fragments, with Toomre $R_{\rm sink} = 0.5$6 throughout except marginal $R_{\rm sink} = 0.5$7 regions in some non-ideal disks during the first 50–100 kyr.

The most consequential comparison concerns not the disks themselves but their rotating envelopes, identified by lowering the density threshold to $R_{\rm sink} = 0.5$8. Ideal-MHD envelopes are one to two orders of magnitude less massive and far more compact (average radii $R_{\rm sink} = 0.5$9200–300 AU versus 500–1000 AU for non-ideal) and shorter-lived (193 kyr without jets, versus 320–602 kyr for non-ideal). Jet feedback extends and stabilizes envelope masses, likely by replenishing the accretable reservoir. The implication drawn is that while magnetic braking does not prevent disks in ideal MHD, it does strip the surrounding envelope that feeds long-term disk growth and survival—so non-ideal effects matter primarily for late-time disk evolution rather than for the existence of a disk.

Alignment, orientation, and the Hall signature

Disk and stellar angular momentum axes remain well aligned ($M_{\odot}$0) for most of disk evolution, with initial misalignments of 60–80° relaxing over time and sharp excursions caused by dynamical interactions. Relative to the local magnetic field (averaged within 1000 AU), disks in models without the Hall effect tend toward perpendicular alignment (the configuration where braking is weakest), while disks in Hall-included models become progressively anti-aligned, reaching angles $M_{\odot}$1. The latter is qualitatively consistent with the Hall polarity selection found in axisymmetric collapse studies by Zhao et al. However, the disk sample here consists of effectively one ideal disk and nine non-ideal disks differing in type and included physics, so the authors explicitly refrain from claiming statistical significance for any orientation trend.

Self-consistent outflows

Only the ideal MHD model produces a self-consistently launched bipolar outflow, and it is loosely collimated with $M_{\odot}$2—more than an order of magnitude slower than the $M_{\odot}$3 sub-grid jets. No high-velocity collimated jets arise in any model without the sub-grid prescription, which the authors attribute to insufficient resolution near the star-disk boundary, rapidly varying disk orientations from close encounters, and turbulent disruption of coherent field structure. This justifies retaining the sub-grid jet model even though it may be somewhat disruptive to nearby nascent disks.

Limitations and open questions

Several caveats constrain the strength of the conclusions. First, the disk sample is small and heterogeneous; differences in disk properties between ideal and non-ideal models are not statistically significant, and larger clouds forming more disks are needed. Second, the resistivities depend on poorly constrained microphysics: a single grain size, fixed cosmic-ray rate, and perfect gas-dust coupling are assumed, whereas grain growth, coagulation, settling, and drift can shift the balance among Ohmic, ambipolar, and Hall regimes substantially. Third, recent theoretical work by Hopkins et al. (2024) argues that superthermal charged-species drifts generate anomalous resistivity and plasma instabilities that would suppress the Hall-dominated regime entirely—if correct, the anti-alignment trend attributed to the Hall effect here could be an artifact of the standard resistivity model. Fourth, the resolution ($M_{\odot}$4, $M_{\odot}$5 AU) cannot resolve the star-disk interface, coupled episodic accretion-outflow dynamics, or the magnetic diffusion plateau expected at densities above $M_{\odot}$6. Finally, the ionization model neglects photoionized species, though the authors show HII regions do not affect any disk prior to its disappearance.

Conclusion

These simulations demonstrate that protostellar disks form robustly in turbulent, magnetized cluster-forming environments regardless of whether ideal or non-ideal MHD is assumed, resolving the classical magnetic braking catastrophe in favor of the view held by comparable SPH studies. Non-ideal MHD leaves its imprint not on whether disks exist but on the extended rotating envelopes that sustain them: ideal-MHD envelopes are smaller, less massive, and shorter-lived. Sub-grid jet feedback increases fragmentation, reduces stellar masses by an order of magnitude, extends envelope lifetimes, and enables second-generation disk formation from feedback-displaced gas. All companions form outside disk scales via core and filament fragmentation, supporting caution against interpreting close companions within observed marginally unstable disks as definitive evidence of disk fragmentation. The open questions the work leaves—whether the Hall-driven anti-alignment survives more realistic microphysics, and how disk populations differ statistically between ideal and non-ideal physics—require both larger samples and evolving treatments of dust and anomalous resistivity.