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Protostellar disks in their natural habitat -- the formation of protostars and their accretion disks in the turbulent and magnetized interstellar medium

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Zoom-in simulations from a supernova-driven turbulent interstellar medium find that ideal magnetohydrodynamics prevents protostellar disks larger than about 10 au at stellar birth, while ambipolar diffusion restores such disks in only two…

desk verdict Impressive multi-scale zoom-in comparison, but the universal 'never-with-a-disk' statement outruns the six-core sample. read the letter →

arxiv 2506.14394 v3 pith:BD5U3U2G submitted 2025-06-17 astro-ph.GA astro-ph.SR

Alexander C. Mayer , Thorsten Naab , Paola Caselli , Alexei V. Ivlev , Tommaso Grassi , Oliver Zier , Rüdiger Pakmor , Stefanie Walch
show 1 more author
Volker Springel
This is my paper
classification astro-ph.GAastro-ph.SR PACS 95.30.Qd97.10.Bt
keywords protostellardisksambipolardiffusionmagneticbrakingcatastrophezoom-insimulationsturbulentinterstellarmediumLarsoncoresmagnetohydrodynamicsprotostarformation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks whether a protostar is actually born with an accretion disk when its gas arrives from a realistically turbulent and magnetized interstellar medium, rather than from an idealized isolated core. The authors grow six collapsing cores out of a $(256\,\mathrm{pc})^3$ cube of supernova-driven gas and follow each one down to $10^{-4}$ au, resolving both the first and second Larson cores under three magnetic treatments: none, ideal MHD, and ambipolar diffusion. They find that ideal MHD strips angular momentum so effectively, through magnetic braking and magneto-rotational outflows, that no rotationally supported disk larger than about 10 au exists at the moment of stellar birth in any of the six cores. Ambipolar diffusion changes the outcome in only a subset: two of the six cores grow large, gravitationally unstable disks with spiral arms and Toomre $Q < 1$. The paper's sharp conclusion is that if ideal MHD described reality, stars would never be born with a disk, which makes the treatment of non-ideal magnetic effects decisive for how planets get their starting environments.

What carries the argument

The machinery is a two-stage zoom-in simulation pipeline built on the moving-mesh code AREPO. A $(256\,\mathrm{pc})^3$ periodic box of supernova-driven turbulent interstellar medium is evolved with gravity until dense cores collapse; six well-separated cores are then re-simulated from identical initial conditions with pure hydrodynamics, ideal MHD, or ambipolar diffusion, with mass resolution down to $3.33\times10^{-7}\,\mathrm{M}_\odot$ and no sink particles, so the first and second Larson cores form explicitly. The decisive physics is the competition between magnetic braking, the removal of angular momentum by field tension and magneto-rotational outflows, and ambipolar diffusion, the slip of neutral gas past the magnetic field that resists that transport; the ambipolar diffusion coefficient comes from a chemical library table with a cosmic-ray ionization rate of $10^{-17}$ s$^{-1}$. Supporting apparatus includes an eccentricity-based disk definition (cells with orbital eccentricity $e < 0.3$ and density above $8\times10^{-14}$ g cm$^{-3}$, projected onto the rotation plane) and a Toomre $Q$ analysis with magnetic pressure added to the effective sound speed.

What would settle it

Decisive test one: re-simulate the six zoom-in cores with the physical, uncapped ambipolar diffusion coefficient, adding Ohmic dissipation and cosmic-ray attenuation; if three or more of the six cores then form disks larger than 10 au, the 'two of six' statistic and the claim that ambipolar diffusion does not guarantee a disk would need revision. Decisive test two: re-simulate any single core in ideal MHD from an earlier zoom-in start, without the volume limit, at higher resolution; a rotationally supported disk larger than 10 au already present at second-core formation would refute the claim that ideal MHD prevents disk birth, and the paper's own Appendix C tests currently find no such disk.

Watch

Extended reading notes

Core claim

The central claim is that the magnetic field treatment, not the initial core properties, decides whether a protostar has a disk at birth. In all six zoom-in cores the purely hydrodynamical runs form rotationally supported disks of roughly 10-100 au before the second core appears, while every ideal MHD run ends with a nearly spherical hydrostatic core and no disk above about 10 au, even though these cores are irregular, shock-shaped, and carry magnetic fields misaligned with their rotation, conditions previously thought to bypass the magnetic braking catastrophe. With ambipolar diffusion the outcome splits: cores n1 and n6 form large disks with rotation speeds above 1 km s$^{-1}$ extending past 100 au, spiral substructure, and Toomre $Q < 1$, while the other four cores remain diskless. The mechanism the authors identify is the magneto-rotational outflow: wherever outflows carry away sufficient angular momentum, disk formation is shut off, and ambipolar diffusion enables disks precisely by weakening those outflows and letting the magnetic flux diffuse outward in the inner few au. The paper extends this to a stark statement: if ideal MHD were a good description of reality, stars would never be born with a disk, although disks might still assemble later, beyond the simulated epoch.

Load-bearing premise

The paper caps the ambipolar diffusion coefficient so that the non-ideal magnetic effect is weaker than the real physical effect, and if that cap were removed, more than two of the six cores might form large disks and the central 'two out of six' statistic would change.

Editorial extensions

If this is right

  • The magnetic braking catastrophe survives realistic turbulence: ideal MHD suppresses disks above about 10 au at stellar birth in all six cores, so the suppression is not an artifact of idealized aligned rotators.
  • Non-ideal MHD does not guarantee a disk; the two-of-six outcome means disk presence at birth depends on core geometry interacting with ambipolar diffusion.
  • Magneto-rotational outflows are the angular-momentum valve: where they are strong they prevent rotationally supported disks, and ambipolar diffusion's main disk-enabling effect is to weaken them.
  • Disks that do form early are large and gravitationally unstable, with $Q < 1$ in spiral arms, so fragmentation and complex substructure can begin at birth.
  • The diversity among six cores, from diskless births to 100 au grand-design disks with nested second disks around the stellar core, implies observations of the youngest protostars should find a wide range of disk sizes and morphologies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the code caps the ambipolar diffusion coefficient at a fraction of the ideal-MHD timestep, making the non-ideal effect weaker than the modeled physics, the two-in-six figure is best read as a lower bound on how often ambipolar diffusion enables early disks; including Ohmic dissipation, the Hall effect, and cosmic-ray attenuation could push the count higher.
  • The paper switches ambipolar diffusion on only at the zoom-in stage; evolving the driving and tracing phases with non-ideal MHD as well could change which cores are selected and how their fields are oriented, possibly shifting the disk statistics from the outset.
  • A direct observational consequence, implicit but untested here, is a population of genuinely diskless births: very young Class 0 protostars in strongly magnetized clouds with no detectable rotationally supported structure would be the signature of the ideal-MHD-like outcome the paper predicts for a subset of cores.
  • If early disks are required for subsequent planet formation, the paper's result implies that the planet-forming potential of a star is partly set by the magnetic microphysics (ionization, grain properties) of its natal core, not just by core mass and angular momentum.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents zoom-in simulations that start from a (256 pc)^3 supernova-driven turbulent ISM and follow six prestellar cores down to the formation of the second Larson core, comparing pure hydrodynamics, ideal MHD, and ambipolar diffusion. The main qualitative findings are that the hydro runs form rotationally supported disks of roughly 10-100 au, that ideal MHD suppresses such disks by the time of second-core formation, and that ambipolar diffusion allows large disks in two of the six cores while generally weakening outflows. The paper also reports magnetically driven outflows, strong magnetic field growth to >10 G in the first cores, Toomre Q<1 spiral structure in the disks that do form, and streamer-like anisotropic accretion. The authors conclude that non-ideal MHD is required for early disk formation in realistic turbulent environments and, in the final paragraph, state that if ideal MHD were a good description of reality, 'stars would never be born with a disk'.

Significance. If the qualitative result holds, this is a valuable demonstration that ideal-MHD magnetic braking suppresses early disk formation in a realistic multi-scale ISM context, beyond the idealized aligned-collapse setups that motivated the 'magnetic braking catastrophe' debate. The study's strengths are its dynamic range (256 pc to ~10^-4 au), the matched six-core comparison across three magnetic treatments, the resolved first and second Larson cores without sink particles in the zoom-in, and the additional robustness runs in Appendix C. The morphology and outflow diagnostics, the Toomre analysis of the two AD disks, and the streamer rendering in n6 are concrete, falsifiable contributions. The main weakness is that the paper's headline universal claim is not supported by its own stated sample-size caveat and by the acknowledged existence of later-time disks in ideal MHD from previous work; the global claim should therefore be separated from the sample-level result.

major comments (4)
  1. [Section 8; Section 7] The concluding statement that 'stars would never be born with a disk' under ideal MHD is a universal negative that is not supported by the simulation sample. Section 7 explicitly says the six-core sample is not statistically significant and 'precluding us from drawing very general conclusions', and it acknowledges that longer-term ideal-MHD studies (Kuffmeier et al. 2017; Yang & Federrath 2025) find disks forming later. Since the paper also says it cannot follow evolution beyond second-core formation, the final conclusion should be reworded to a statement about early disk formation in this sample, or the authors must supply evidence that the six cores are representative of all protostellar collapse geometries.
  2. [Abstract; Table 3] The abstract's claim that there are 'no disks larger than 10 au with ideal MHD' is quantitatively contradicted by Table 3, where simulation i1 has R_eff = 11 au, and Section 5.3 similarly notes that region 1 is the exception with disk material in the ideal-MHD run. The abstract should say 'about 10 au' or the i1 disk-size measurement must be re-examined, since this threshold is the paper's central quantitative result.
  3. [Section 2.3, Eq. (6); Appendix C] The cap on the ambipolar diffusion coefficient, eta_AD < (1/f_ni) c_s r with f_ni = 0.125, makes the non-ideal scheme weaker than the physical effect, as the paper states, and the lack of cosmic-ray attenuation further weakens AD. The conclusion that AD 'does not guarantee' a disk rests on the 2/6 statistic, and the only uncapped test is described inconsistently: Section 5.4 says 'in the case of n5', while the Appendix C text and Figure C1 caption refer to 'n6'. This test is the key evidence that the cap is not decisive, so the run identity must be corrected and the dependence of the 2/6 statistic on the cap should be discussed or tested more broadly.
  4. [Section 2.2, Eq. (5)] The barotropic equation of state is a fit to the densest fluid element in Wurster et al. (2018a) and, as the paper itself states, 'systematically underestimates the temperature of any material that collapses later, which includes the entire protostellar disk'. Because the disk temperature enters the pressure support and the Toomre Q analysis, the quantitative disk sizes, spiral-structure, and gravitational-instability claims are affected. The paper should either quantify the effect of this EOS choice or temper the quantitative conclusions that depend on it.
minor comments (5)
  1. [Section 5.4] The sentence 'it can then no longer amplify effectively ans is even diffused' contains a typo; it should read 'and is even diffused'.
  2. [Figure C1; Appendix C] The bottom-left panel is labeled 'n6' in the figure caption but is called 'n5_nolim' in the main text and in the Appendix text; the naming should be made consistent.
  3. [Section 2.2; Eq. (5)] The cooling prescription uses a mean molecular weight of mu = 1.4, while Eq. (5) uses mu ≈ 2.381; the paper should state explicitly that the two values correspond to different physical regimes.
  4. [Section 3.3] The text says the runs are continued 'until the formation of the second core', but n6 is stopped before that; this is explained later in the same paragraph, so the sentence should be adjusted for internal consistency.
  5. [Figure 19] The lower panels of Figure 19 repeat '(as y-axis)' in the axis labels, which is confusing; these should be replaced with proper distance labels.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the disk statistics emerge from self-contained MHD simulations; cited prior work is methodological, and the universal 'never' phrasing is an acknowledged generalization overreach, not a by-construction reduction.

full rationale

The paper's central result—that ideal MHD suppresses disks larger than ~10 au at second-core formation while ambipolar diffusion allows such disks in two of six cores—is an emergent outcome of solving the ideal/non-ideal MHD equations (Eq. 1) with standard subgrid physics, not a quantity fitted to or defined by the input parameters. The ambipolar diffusion coefficient cap (Eq. 6, f_ni = 0.125) is a numerical timestep restriction, explicitly stated to make the non-ideal scheme weaker than physical, and the paper does not tune it to produce the disk statistics; Appendix C's n5_nolim runs remove the cap and add Ohmic diffusion yet still find no disk, so the non-disk outcome is not forced by the cap. The self-citations (Mayer et al. 2025 for the barotropic EOS of Eq. 5 and the NICIL chemistry table; Zier et al. 2024a,b for the AREPO non-ideal MHD implementation) are code and method references, not load-bearing evidence for the disk-size conclusion, and the EOS itself is a fit to external radiative calculations of Wurster et al. (2018a). The only concern the manuscript itself raises is statistical and logical generality: Section 7 states the sample is 'not statistically significant... precluding us from drawing very general conclusions,' and the final paragraph qualifies the 'never born with a disk' statement with 'even though they might still form later, which is beyond the scope of our study.' These are inference-strength and sample-representativeness caveats, not circularity by construction. No equation or parameter in the paper reduces to the target disk statistics, so no circular step is present.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claims rest on the numerical fidelity of the MHD scheme, the barotropic EOS, the AD coefficient cap, and the choice of six cores. These are inputs chosen from prior literature or numerical convenience, not fitted to the target result, so they do not create circularity, but they do determine the quantitative outcomes.

free parameters (3)
  • Barotropic EOS parameters = c_s0 = 0.22 km/s, n1 = 2e10 cm^-3, n2 = 2.5e14 cm^-3, n3 = 1e20 cm^-3, mu = 2.381
    Equation (5) is a fit to the temperature evolution of the densest fluid element in Wurster et al. (2018a); the paper states it 'systematically underestimates the temperature of any material that collapses later, which includes the entire protostellar disk'. This affects disk temperature, pressure support, and the Toomre Q analysis.
  • Ambipolar diffusion timestep cap f_ni = 0.125
    Section 2.3, Eq. (6): the code caps the ambipolar diffusion coefficient so the AD timestep never falls below 12.5% of the ideal MHD timestep. The authors note this makes the non-ideal MHD scheme weaker than the physical effect, which could bias the 'two of six' disk statistic.
  • Density thresholds for core and disk definitions = rho_core = 5e-18 g/cm^3, rho_fhc = 1e-11 g/cm^3, rho_disk = 8e-14 g/cm^3
    These thresholds define what counts as a prestellar core, a first hydrostatic core, and a disk (Sections 3.3 and 5.3). Disk sizes and masses in Table 3 depend directly on these choices.
assumptions (6)
  • standard math Ideal MHD equations with Powell divergence cleaning provide a valid description of the magnetic field evolution.
    Used throughout the simulation; the paper relies on the code's MHD implementation (Pakmor et al. 2011; Pakmor & Springel 2013).
  • domain assumption The barotropic equation of state (Eq. 5) captures the essential thermal physics of collapse.
    Section 2.2: pressure is a function of density alone; replaces full radiative transfer. The authors acknowledge it underestimates temperatures in the disk.
  • domain assumption Ambipolar diffusion is the dominant non-ideal MHD effect; Ohmic and Hall terms are negligible at the scales studied.
    Section 2.1: 'we only include ambipolar diffusion in this study as it is the dominant effect early in the collapse.' Section 7 notes Ohmic and Hall effects are future work; this assumption affects the non-ideal MHD results.
  • domain assumption The supernova-driving prescription and the absence of galactic shear and a galactic potential produce a representative ISM.
    Section 3.1: random thermal injections at f_SN = 6.0 Myr^-1; no shear. The authors note limitations in Section 7: no vertical stratification and no mixed driving.
  • domain assumption The six selected cores are isolated and representative of star-forming cores in the ISM.
    Section 3.3: cores are chosen as the first isolated protostellar cores, with one excluded for similarity. Section 7 acknowledges the 'lack of a statistically significant sample.'
  • domain assumption Sink particles in the tracing phase correctly identify collapsing regions without feedback.
    Section 3.2: sinks accrete material but do not inject energy; the authors state that feedback would affect the later evolution of the box.

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Pith. "Pith review of Protostellar disks in their natural habitat -- the formation of protostars and their accretion disks in the turbulent and magnetized interstellar medium." pith.science (2026). https://pith.science/paper/BD5U3U2G

@misc{pith2026250614394,
  author       = {Pith},
  title        = {Pith review of: Protostellar disks in their natural habitat -- the formation of protostars and their accretion disks in the turbulent and magnetized interstellar medium},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BD5U3U2G}},
  note         = {Machine review of arXiv:2506.14394}
}
abstract

We present simulations of the supernova-driven turbulent interstellar medium (ISM) in a simulation domain of volume $(256\,{\rm pc})^3$ within which we resolve the formation of protostellar accretion disks and their stellar cores to spatial scales of $\sim 10^{-4}$ au, using the moving-mesh code {\small AREPO}. We perform simulations with no magnetic fields, ideal magnetohydrodynamics (MHD) and ambipolar diffusion, and compare the resulting first Larson cores and their associated structures, including the accretion disks, their location within the larger-scale structure and the streamers connecting these. We find that disks of sizes $10-100\,{\rm au}$ form early in the simulations without magnetic fields, while there are no disks larger than 10 au with ideal MHD. Ambipolar diffusion causes large disks to form in a subset of cases (two out of six cores), and generally reduces the strength of outflows, which are seen to play a central role. When they are able to carry away significant angular momentum, they prevent the formation of a rotationally supported disk. Magnetic fields strengths grow from $0.1 - 1$ mG in the protostellar core to more than 10 G in the first Larson core in all simulations with ideal MHD. The rotationally supported disks which form can have rotation speeds $> 1$ km s$^{-1}$ even out to further than 100 au from the centre, become gravitationally unstable and form complex spiral substructures with Toomre $Q < 1$. We conclude that the impact of magnetic fields and non-ideal MHD on the formation of protostellar disks is substantial in realistic formation scenarios from the turbulent ISM.

Figures

Figures reproduced from arXiv: 2506.14394 by the authors.

Figure 1
Figure 1. Schematic of the zoom-in simulation approach labeled by the respective size bars. The background image (20 pc) shows the turbulent gas distribution in the 256 pc supernova-driven box at the time (13.9 Myr) when the first six dense regions we investigate formed sinks (circles, see Sec. 3.2). The panels with scale-bars of 4 pc show the larger scale gas distribution and structure around the six individual cores (panels… view at source ↗
Figure 2
Figure 2. Density profiles of the six cores (solid lines) and fitted Bonnor￾Ebert spheres (dashed lines) at the start of the zoom-in simulations (see also the panels with a scale-bar of 0.5 pc in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Slices (zero width) through the initial cores 1 to 6 from top left to bottom right (see 0.5 pc panels in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (15 more)
Figure 4
Figure 4. Figure 4: Density projections at the end of each zoom simulation of the collapse of cores 1 to 6 (left to right), in face-on (three top rows) and edge-on directions (three bottom rows), as defined by the angular momentum of the first core. For each projection, we show the hydrod…
Figure 5
Figure 5. Figure 5: Masses in the hydrostatic cores for all 6 zoom-targets as a function of time from first to second core formation for the hydrodynamical (h, left), ideal MHD (i, middle), and non-ideal MHD (n, right) zoom simulations. There is a large variation in the time it takes for …
Figure 6
Figure 6. Figure 6: Specific angular momentum in the first cores as a function of time since their formation (similar to [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Instantaneous net flow-rates through the surface of a sphere with radius 200 au centred on cores 1 to 6. The 𝑥-axis measures time from the formation of the first hydrostatic core (same ordering as in Figs. 5 and 6). All cores have comparable mass-accretion rates of the…
Figure 8
Figure 8. Figure 8: Final Keplerian (black) and tangential velocity (blue) as a function of radius for the six simulations (left to right) for the hydrodynamical (h, top), ideal MHD (i, middle), and non-ideal MHD (n, bottom) simulations. The Keplerian velocity is calculated assuming all m…
Figure 9
Figure 9. Figure 9: Absolute value of the magnetic field as a function of radius on a logarithmic scale for the final cores 1 to 6 from left to right for the ideal MHD (i,top) and non-ideal MHD (n, bottom) zoom simulations. The dotted vertical lines show the disc sizes as in [PITH_FULL_I…
Figure 10
Figure 10. Figure 10: Plasma beta (𝛽 = 𝑃therm/𝑃mag) at the end of each ideal (i) and non-ideal (n) MHD simulation, in face-on (top panels) and edge-on views (bottom) for cores 1 to 6. In contrast to the hydrostatic cores and discs (i.e., n1 and n6) themselves, their low-density surrounding…
Figure 11
Figure 11. Figure 11: Radial velocity on a 50 au spherical surface around the core in the frame of the first hydrostatic core. 𝜃 = 0, 𝜋 correspond to the poles, while 𝜃 = 𝜋 2 is the plane of rotation. In the hydro cases, material moving outwards (red) is, if present at all, part of the dis…
Figure 12
Figure 12. Figure 12: Line-of-sight velocity (left), radial velocity (middle), and absolute value of the magnetic field (right) of the outflow formed in simulation i3 before the launching of the outflow, approximately at the time of formation of the first hydrostatic core (top). The frame …
Figure 13
Figure 13. Figure 13: Mass-flux per area on the surface of a sphere with radius 200 au around the first hydrostatic core in rectilinear projections, in the same frame as [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]
Figure 14
Figure 14. Figure 14: Face-on projection of the Toomre 𝑄 parameter of core 1 (top) and core 6 (bottom) with hydrodynamics (left) and non-ideal MHD (middle). The right panels show the magnetic 𝑄 including the Alf Alfvé in the sound speed. Unstable regions with 𝑄 < 1, indicating that the dis…
Figure 15
Figure 15. Figure 15: Density slices (face-on on the left, edge-on on the right) of the disk resulting from regions 1 (top) and 6 (bottom) with ambipolar diffusion. Note the different diameters of the upper and lower panels. The in-plane velocity is shown as red arrows in the left panels, …
Figure 16
Figure 16. Figure 16: Density distribution and magnetic field lines of the non-ideal MHD disks in regions 1 and 6. Shown 16×16 field lines that intersect a spherical surface of radius 20 au. In both cases, the magnetic field near the disk is largely toroidal, but the imprint of the large-s…
Figure 17
Figure 17. Figure 17: A 3D volume rendering showing all material with 𝜌 > 10−15 g cm−3 up to approximately 1000 au from the centre of the disk in the non-ideal MHD simulation n6 (on the bottom right). There is one large structure connecting to the disk (the ‘streamer’) as well as multiple …
Figure 19
Figure 19. Figure 19: Visual zoom sequence of the final cores of region 1 for the hydrodynamic (h, left), ideal-MHD (i, middle), and non-ideal MHD (n, right) simulations. The systems are shown from scales of the protostellar (∼ 103 au, top) down to the stellar core (∼ 10−2 au, bottom). Dif…

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Cited by 1 Pith paper

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.