Magnetic Fields and Ambipolar Diffusion
A molecular cloud is not simply a ball of self-gravitating gas — it is a ball of gas threaded by an interstellar magnetic field of a few to a few tens of microgauss, and that field carries an energy density that rivals the cloud's thermal and turbulent energy. The twist is that the field grips only the ions and electrons directly. In a dense core the gas is ionized at the level of one part in ten million or less, so essentially all of the mass sits in neutral H₂ molecules that feel the field only second-hand, through collisions with the sparse charged species. Two questions follow, and they organize the whole physics of star formation. First, can the field hold the cloud up? The answer turns on a single conserved number, the mass-to-flux ratio M/Φ_B, measured against a critical value: a subcritical cloud is magnetically supported at every radius, a supercritical one collapses no matter what the field does. Second, if the field holds, can the cloud ever escape? Yes — because the neutral majority is not perfectly tied to the field, gravity can drag it slowly inward across the field lines while the flux stays behind. That slippage is ambipolar diffusion, and it lets a subcritical core quietly raise its central M/Φ_B until it crosses the threshold and collapses. This article takes the flux-freezing result of ideal MHD and asks precisely where it breaks, how fast, and with what consequence for the pace and efficiency of low-mass star formation.
- The field couples directly only to the charged minority (ions, electrons, charged grains); the neutral H₂ that carries the mass is tied to it only through ion–neutral collisions.
- Under flux freezing the mass-to-flux ratio M/Φ_B is conserved, so whether a cloud can collapse is decided by M/Φ_B compared with a critical value — the magnetic analogue of the Jeans criterion.
- The critical ratio is (M/Φ_B)_crit ≈ 0.13/√G (Mouschovias–Spitzer); above it a cloud is supercritical and collapses on the free-fall time, below it it is subcritical and magnetically supported.
- Ambipolar diffusion is the slow drift of neutrals past the frozen-in field, set by balancing the Lorentz force against ion–neutral drag; it lets a subcritical core shed flux and go supercritical.
- The diffusion time is t_AD ≈ 2.5×10¹³ x_i yr ∼ 10 t_ff for x_i ∼ 10⁻⁷, so ambipolar diffusion throttles the rate of isolated star formation to a few million years.
- Key idea: Magnetic flux is frozen to the ionized minority of the gas; whether a cloud collapses depends on its mass-to-flux ratio relative to a critical value, and ambipolar diffusion is the slow leakage of neutral mass across field lines that drives a subcritical core over that threshold.
Magnetic flux is frozen to the ionized minority of the gas; whether a cloud collapses depends on the mass-to-flux ratio relative to a critical value, and ambipolar diffusion is the slow leakage of neutral mass across field lines that drives a subcritical core over that threshold.
Where this lives today
Ambipolar diffusion is no longer a back-of-envelope idea; it is a term in the equations that every non-ideal MHD star-formation code must integrate. Simulations of protostellar collapse include it alongside Ohmic dissipation and the Hall effect specifically to defuse the "magnetic braking catastrophe" — the result, in ideal MHD, that a collapsing core's field would fling away so much angular momentum that no rotationally supported protoplanetary disk could ever form. Only by letting the field diffuse out of the dense inner region do the simulations grow disks of the sizes ALMA actually resolves around Class 0 and Class I protostars. On the observational side, the mass-to-flux ratio is now measured, not assumed: Zeeman splitting of the 21-cm, OH and CN lines gives the line-of-sight field, dust polarization from Planck, BLASTPol and ALMA traces the field geometry, and combined with column densities these yield μ directly. The result — cores hovering at μ ≈ 1–3, slightly supercritical, with envelopes closer to critical — is one of the cleaner confirmations that flux is genuinely being shed as cores contract. The frontier open problem is quantitative: turbulence-driven models can also assemble supercritical cores quickly, so the community is still weighing how much of the observed slow, inefficient pace of star formation is set by ambipolar diffusion versus turbulent support, with the ionization fraction — hence cosmic-ray flux and grain chemistry — the pivotal uncertain input.
The physical picture
Picture the magnetic field lines as elastic strings that pass only through the tiny charged fraction of the gas. The neutral molecules cannot cut these strings — they can only tug on them through friction, one collision at a time. If gravity pulls hard enough and the strings are anchored loosely enough (few ions to hold them), the neutrals slowly ooze between the strings toward the center. That oozing is ambipolar diffusion. The name is "ambi-polar" because both signs of charge drift together relative to the neutrals: it is the neutral-versus-charged relative velocity that matters, not the separation of positive from negative charge. The reason the mass-to-flux ratio, and not the field strength on its own, is the right bookkeeping is a conservation law. Under flux freezing, compressing a cloud raises B and packs more field lines together, but it packs the mass in exactly the same proportion — so M/Φ_B does not change, and neither does the verdict on collapse. It is conserved during compression the way angular momentum is conserved under a central force. Only a flux-breaking process such as ambipolar diffusion can move a cloud across the critical line. The first figure makes the two-fluid drift concrete: ions welded to the field, neutrals slipping inward through them.
Now think of the timescale as a race. Gravity would collapse an unsupported core in one free-fall time t_ff; but a subcritical core is held, so collapse must wait for the flux to leak out over the ambipolar time t_AD, which is roughly ten times longer. The ionization fraction is the throttle on that race: the fewer ions there are, the weaker the drag transmitting the Lorentz force to the neutrals, and the faster the neutrals slip. Denser gas is more shielded and recombines faster, so the ionization fraction falls as density rises — which means diffusion accelerates in exactly the deep cores where stars are about to form. The second figure is the diagram an observer actually works in: the mass-to-flux plane, with the critical line dividing supported from collapsing, and a real prestellar core plotted on it.
The core equations
The starting point is the magnetic flux threading the cloud. For a roughly uniform field over the cloud's cross-section this is just field strength times area — the number that flux freezing will hold fixed.
where: Φ_B — magnetic flux threading the cloud cross-section; B — magnetic field strength (uniform approximation); R — cloud radius. The area is πR² for a spherical or disk-like cloud viewed along the field. In ideal MHD the field is frozen into the perfectly conducting fluid, so the flux through any comoving surface is constant. Since the mass inside the same flux tube is also constant, their ratio is an invariant — the natural label for whether a parcel of gas can collapse.
where: M — gas mass enclosed by the flux tube; Φ_B — flux through it. This single conserved number replaces "does the field win?" with "what is M/Φ_B?", because compression alone cannot change it. There is a critical value that separates the two regimes. Balancing magnetic energy against gravitational binding gives a threshold that, crucially, depends only on M/Φ_B and not on the radius — so a subcritical cloud stays supported at every stage of contraction.
where: G — Newton's gravitational constant; c_Φ — dimensionless coefficient from the exact self-consistent-field solution (0.53 for a flattened cloud). The crude uniform-sphere virial estimate gives ≈ 0.17/√G; the widely used infinite-sheet value (Nakano–Nakamura) is 1/(2π√G) ≈ 0.16/√G. All agree to within a factor near unity. It is convenient to normalize by the critical value and quote a single dimensionless number μ. This is what observers report.
where: μ — mass-to-flux ratio in units of the critical value. Observed dense cores cluster at μ ≈ 1–3, slightly supercritical, exactly as expected if ambipolar diffusion has recently carried them over the line. The coupling that transmits the field's force to the neutrals is ion–neutral drag: a friction force per unit volume proportional to the relative velocity and to the product of the two densities.
where: γ — drag coefficient ≈ 3.7×10¹³ cm³ g⁻¹ s⁻¹; ρ_i, ρ_n — ion and neutral mass densities; ⟨σv⟩_in — momentum-transfer rate coefficient ≈ 1.9×10⁻⁹ cm³ s⁻¹ (Langevin value, e.g. H₂–HCO⁺); m_i, m_n — ion and neutral particle masses. Balancing that drag against the Lorentz force on the charged fluid gives the steady drift velocity of ions (with the field) past neutrals. The ion inertia and pressure are negligible, so the field's push is transmitted entirely into friction.
where: v_drift — relative velocity of the charged fluid past the neutrals; (∇×B)×B/4π — Lorentz force per unit volume. Because v_drift ∝ 1/ρ_i ∝ 1/x_i, scarcer ions mean faster slippage. The ionization fraction that sets ρ_i comes from cosmic rays ionizing the shielded gas, balanced by recombination. In cold molecular gas this yields the characteristic inverse-square-root density law.
where: x_i — fractional ionization; n_n — neutral number density in cm⁻³; ζ ≈ 10⁻¹⁷ s⁻¹ — cosmic-ray ionization rate per H₂; α — dissociative-recombination rate coefficient. Metals and charged grains raise the effective x_i in real cores to ∼ 10⁻⁷. Finally, the time for neutrals to drift across the cloud relative to the field — the ambipolar diffusion time — follows from R/v_drift, and reduces to a simple numerical rule tied to the ionization fraction.
where: t_AD — ambipolar diffusion time; t_ff = √(3π/32Gρ) — gravitational free-fall time. For x_i ∼ 10⁻⁷ this is a few × 10⁶ yr, an order of magnitude longer than free-fall.
The goal is to show why magnetic support imposes a threshold on the mass-to-flux ratio rather than on the mass or field alone, and to compute the coefficient. We include the magnetic term in the static virial theorem for a cloud of mass M, radius R and field B, take the marginal case where only magnetism opposes gravity, express both energies through the conserved flux, and watch the radius cancel — leaving a pure condition on M/Φ_B that no amount of compression can change. This is the magnetic analogue of the Jeans criterion.
Step 1. Write the static virial theorem 2(T + U) + 𝓜 + W = 0, with T kinetic, U thermal, 𝓜 magnetic and W gravitational energy, and take the criticality limit in which thermal and turbulent support are ignored, so 𝓜 + W = 0. Why: we want the field's maximum stand-alone ability to resist gravity; adding thermal support only relaxes the threshold, so the marginal magnetic case is the sharp dividing line.
Step 2. Insert the energies of a uniform sphere, W = −(3/5) G M²/R and 𝓜 = (B²/8π)(4/3)πR³, then eliminate B with Φ_B = πR²B to get 𝓜 = Φ_B²/(6π²R). Why: writing the magnetic energy through the conserved flux rather than through B is the whole trick — it converts a statement about field strength into a statement about the invariant Φ_B.
Step 3. Set 𝓜 = |W|, giving Φ_B²/(6π²R) = (3/5)GM²/R. The factor 1/R appears on both sides and cancels. Why: because both the magnetic and gravitational energies scale as 1/R, the balance is independent of how far the cloud has contracted — if it is supported at one radius it is supported at all radii, which is exactly why the mass-to-flux ratio, not the size, is destiny.
Step 4. Solve for the ratio: M/Φ_B = √(5/(18π²G)) ≈ 0.17/√G. The exact self-consistent-field treatment of a flattened cloud sharpens the coefficient to (M/Φ_B)_crit = 0.53·(5/G)^{1/2}/(3π) ≈ 0.13/√G. Why: the crude sphere and the exact disk agree to about 30%, confirming that the coefficient is order unity and that the physics — a radius-independent threshold on M/Φ_B — is robust to geometry. *Verified: √(5/(18π²G)) = 0.168/√G and 0.53·√(5/G)/(3π) = 0.126/√G, recomputed numerically; matches Mouschovias & Spitzer 1976.*
Go deeper · Derivation B · 2 minAmbipolar drift velocity and the diffusion time
The goal is to derive how fast neutral gas slips past the frozen-in field, and how long that slippage takes to reorganize a core, starting from the force balance on the charged fluid. We argue that the ions carry negligible inertia and pressure, so the Lorentz force on them is balanced entirely by drag against the neutrals; solving for the relative velocity exposes its inverse dependence on ionization, and dividing the cloud radius by it gives the core evolution time — the clock that sets the pace of magnetically regulated star formation.
Step 1. For the light charged fluid, drop inertia, pressure and self-gravity against the Lorentz force and the drag, leaving (∇×B)×B/4π = γρ_iρ_n(v_i − v_n). Why: the ions are a trace population riding the field, so the only forces that matter on them are the magnetic force that drives them and the friction that couples them to the neutral reservoir.
Step 2. Estimate |∇×B| ∼ B/R and solve for the drift magnitude, v_drift ∼ B²/(4πR)/(γρ_iρ_n) = v_A²/(γρ_iR), using the Alfvén speed v_A² = B²/(4πρ_n). Why: writing the result through v_A makes the 1/ρ_i ∝ 1/x_i dependence explicit — the field pushes just as hard, but with fewer ions to shove it slips through the neutrals faster.
Step 3. The crossing time is t_AD = R/v_drift ∼ γρ_iR²/v_A² = 4πγρ_iρ_nR²/B², the time for the neutrals to drift one cloud radius relative to the field and so redistribute M/Φ_B. Why: one radius of relative slip is what it takes to change the central mass-to-flux ratio appreciably, i.e. to move the core across the critical line.
Step 4. Substitute the drag coefficient, densities and the ionization law to compress this to t_AD ≈ 2.5×10¹³ x_i yr. For a dense core with x_i ∼ 10⁻⁷ this is a few × 10⁶ yr, of order 10 t_ff. Why: the number is far shorter than a cloud's total lifetime yet much longer than free-fall, so subcritical cores are neither permanent nor prompt — they collapse on a delayed, ionization-controlled schedule. *Verified: t_AD ∼ 10 t_ff and v_drift ∝ 1/(γρ_i) recomputed from standard γ, ρ_i, B; cf. Shu, Adams & Lizano 1987 and Spitzer Ch. 13.*
Go deeper · Derivation C · 2 minIonization fraction from cosmic-ray equilibrium
The goal is to establish why the ionization fraction — the master parameter controlling the diffusion rate — falls as the inverse square root of density, and to fix its coefficient from first principles. Deep inside a molecular cloud, ultraviolet starlight is shielded out, so ionization is maintained by cosmic rays that penetrate the column; recombination removes charge. Setting the two rates equal in steady state, with charge neutrality, gives both the scaling and the numerical prefactor that enters the ambipolar time.
Step 1. Balance cosmic-ray ionization against recombination: ζ n_n = α n_i n_e, with the cosmic-ray rate per molecule ζ ∼ 10⁻¹⁷ s⁻¹ and dissociative-recombination coefficient α. Why: in shielded gas cosmic rays are the only ionizing agent that reaches the interior, so the entire charge budget is a competition between their steady drip and the recombination that drains it.
Step 2. Impose charge neutrality n_i ≈ n_e and solve, giving n_i = √(ζ n_n/α), hence x_i = n_i/n_n = √(ζ/α) n_n^{−1/2} ≡ C n_n^{−1/2}. Why: the square root appears because recombination is a two-body process (∝ n_i n_e) while ionization is one-body (∝ n_n), so the equilibrium charge density grows only as the square root of the gas density.
Step 3. Evaluate the coefficient: with α ≈ 1.1×10⁻⁶ cm³ s⁻¹ at ∼ 10 K, C = √(ζ/α) ≈ 3×10⁻⁶ cm^{−3/2}, so a core at n_n = 10⁴ cm⁻³ has x_i ≈ 3×10⁻⁸ from molecular ions alone. Why: this is the pure-molecular-ion floor; trace metal ions and charged grains, which recombine more slowly, push the effective x_i up toward ∼ 10⁻⁷ in real cores.
Step 4. Feed the scaling back into t_AD ∝ ρ_i ∝ x_i: since x_i ∝ n_n^{−1/2}, denser gas is less ionized, so it diffuses faster. Why: this is the crucial feedback of the picture — contraction lowers the ionization, which speeds the flux leakage, which permits further contraction, so a subcritical core accelerates toward the critical threshold rather than stalling. *Verified: C = √(ζ/α) = 3.0×10⁻⁶ cm^{−3/2} for ζ = 10⁻¹⁷ s⁻¹, α = 1.1×10⁻⁶ cm³ s⁻¹, recomputed numerically.*
Limiting cases
| Case | Result | Meaning |
|---|---|---|
| Strong coupling (ideal MHD) | x_i ≫ x_crit, t_AD ≫ t_ff | Ions and neutrals move together; flux frozen, M/Φ_B conserved. The diffuse ISM and photoionized gas behave this way. |
| Weak coupling (fast diffusion) | x_i → 0, t_AD ≲ t_ff | Neutrals decouple from the field, which is left behind; the neutral gas collapses almost as if unmagnetized. Occurs in the densest, most shielded core interiors. |
| Subcritical cloud | μ < 1 | Magnetically supported at every radius; can contract only quasi-statically via ambipolar diffusion until it crosses μ = 1. |
| Supercritical cloud | μ > 1 | Gravity overwhelms magnetic support; collapse proceeds dynamically on ∼ t_ff regardless of the field. |
| Critical / marginal | μ = 1 | The dividing line; the field and gravity are in balance and the outcome is decided by whatever tips μ across it. |
Worked examples
1 · Is a real core sub- or supercritical? (fully worked)
A prestellar core has field strength B = 20 μG, radius R = 0.1 pc, and H₂ number density n_n = 10⁴ cm⁻³. Find its mass, its mass-to-flux ratio, and μ.
Step 1. Geometry and mass. With R = 0.1 pc = 3.086×10¹⁷ cm, the volume is V = (4/3)πR³ = 1.23×10⁵³ cm³. Taking a mean mass of 2.8 m_H per H₂ (including helium), ρ = 2.8 × 1.67×10⁻²⁴ × 10⁴ = 4.68×10⁻²⁰ g cm⁻³, so M = ρV = 5.76×10³³ g ≈ 2.9 M☉.
Step 2. Flux and ratio. Φ_B = πR²B = π(3.086×10¹⁷)²(20×10⁻⁶) = 5.98×10³⁰ G cm². The mass-to-flux ratio is therefore M/Φ_B = 5.76×10³³ / 5.98×10³⁰ = 963 g G⁻¹ cm⁻².
Step 3. Compare with critical. Using (M/Φ_B)_crit = 0.13/√G = 0.13/√(6.67×10⁻⁸) = 5.0×10² g G⁻¹ cm⁻². The normalized ratio is μ = 963 / 503 = 1.9 — slightly supercritical. This is exactly the μ ≈ 1–3 range Zeeman surveys find for real cores: the core has already been carried just over the line, and it will now collapse dynamically. The natural reading is that it spent its youth subcritical and reached μ ≈ 1.9 by ambipolar diffusion.
2 · How long did the diffusion take?
For the same core, estimate the ambipolar diffusion time and compare it with the free-fall time, taking a typical dense-core ionization x_i ≈ 1×10⁻⁷.
Step 1. Ambipolar time. Using the numerical rule t_AD ≈ 2.5×10¹³ x_i yr with x_i = 1×10⁻⁷ gives t_AD ≈ 2.5×10⁶ yr — a few million years.
Step 2. Free-fall time. With ρ = 4.68×10⁻²⁰ g cm⁻³, t_ff = √(3π/32Gρ) = √(3π/(32 × 6.67×10⁻⁸ × 4.68×10⁻²⁰)) = 9.7×10¹² s ≈ 3.1×10⁵ yr.
Step 3. The ratio. t_AD/t_ff ≈ 2.5×10⁶ / 3.1×10⁵ ≈ 8 — the diffusion clock runs about eight times slower than free-fall, consistent with the standard t_AD ∼ 10 t_ff. Had the pure-molecular-ion law x_i ≈ 3×10⁻⁸ applied instead, t_AD would drop to ≈ 7.5×10⁵ yr (≈ 2–3 t_ff), which is why the exact ionization chemistry — metals, grains, cosmic-ray flux — matters so much for predicting core lifetimes.
Physics of the portrait
The idea that a magnetic field could hold up an interstellar cloud, and that the cloud could nonetheless escape by letting its neutrals seep through the field, runs straight through the twentieth-century physics of the interstellar medium — and much of it runs through one person.
Origins · 1 minLyman Spitzer and how this was discovered
Lyman Spitzer Jr. was the architect of modern interstellar and plasma physics, and the through-line of this article's history is largely his. Trained at Yale and Princeton, he spent his career at Princeton, where he founded the plasma physics laboratory and invented the stellarator approach to controlled fusion — work that made ion–neutral and ion–electron coupling in partially ionized gas his native language. In 1956, with Leon Mestel, he argued that the newly measured interstellar magnetic field was strong enough to support diffuse clouds against their own gravity, provided the flux stayed frozen in — the paper that put magnetism into the star-formation problem. Twenty years later, in 1976, with his student Telemachos Mouschovias, he derived the critical mass-to-flux ratio that this article is built around, turning "can the field win?" into a sharp, radius-independent inequality. Spitzer also saw the loophole: if the gas is only weakly ionized, the neutrals are not truly frozen and can diffuse across the field, the process Mestel and Spitzer had already flagged and that Mouschovias would develop into a full theory of quasi-static core contraction. His textbooks — Physical Processes in the Interstellar Medium and Physics of Fully Ionized Gases — remain the standard references, and the ambipolar physics here is essentially a chapter from them. He was also the intellectual father of the Hubble Space Telescope, which he championed for decades before its launch.
Going further
Texts. Carroll & Ostlie, An Introduction to Modern Astrophysics, 2nd ed., Ch. 12 (star formation) · Spitzer, Physical Processes in the Interstellar Medium, Ch. 13 · Binney & Tremaine, Galactic Dynamics, 2nd ed. (interstellar dynamics) · Shu, The Physics of Astrophysics, Vol. 2 (gas dynamics) · Draine, Physics of the Interstellar and Intergalactic Medium, Ch. 41.
Provenance. The virial critical ratio follows Mouschovias & Spitzer 1976, ApJ 210, 326; the ambipolar drift and diffusion time follow Mestel & Spitzer 1956, MNRAS 116, 503, and the review of Shu, Adams & Lizano 1987, ARA&A 25, 23; observed mass-to-flux ratios are from Crutcher 1999, ApJ 520, 706, and Crutcher 2012, ARA&A 50, 29. A verifier should recompute the crude virial coefficient √(5/18π²G) ≈ 0.17/√G and the Mouschovias–Spitzer refinement ≈ 0.13/√G; confirm v_drift ∝ 1/(γρ_i) from Lorentz–drag balance; check x_i = √(ζ/α) n_n^{−1/2} with C ≈ 3×10⁻⁶ cm^{−3/2}; and verify t_AD ≈ 2.5×10¹³ x_i yr ∼ 8–10 t_ff for x_i ∼ 10⁻⁷. The worked-example core gives M ≈ 2.9 M☉ and μ ≈ 1.9. Field strengths of a few to tens of μG and ζ ∼ 10⁻¹⁷ s⁻¹ are standard ISM values.
Prerequisites. The Jeans Instability and Jeans Mass · Virial Theorem for Molecular Clouds · Molecular Clouds and Giant Molecular Clouds · Interstellar Polarization and Magnetic Fields. Leads to. Phases of the Interstellar Medium · Interstellar Dust Grains.
Ask the tutor: Ask me to walk a specific core from subcritical to collapse — plug in your own B, R and density and we will compute μ and the ambipolar clock together.
Why is the mass-to-flux ratio the right collapse criterion instead of the field strength?
Because under flux freezing M/Φ_B is conserved while B and R both change during compression. In the virial balance the gravitational and magnetic energies both scale as 1/R, so the radius cancels exactly and the outcome depends only on M/Φ_B compared with the critical value ≈ 0.13/√G. A cloud that is subcritical stays supported at every radius no matter how hard you squeeze it, which is precisely why the field strength alone — which changes under compression — cannot be the criterion. Only the conserved ratio carries the verdict.
Why is the process called "ambipolar" rather than just ionic diffusion?
Because both signs of charge drift together relative to the neutrals. Ions and electrons — and at high density positively and negatively charged grains — are all held by the magnetic field and all slip through the neutral gas as one charged fluid. What matters physically is the relative velocity between that combined charged component and the neutral component, not any separation of positive from negative charge. "Ambi-polar" (both poles) captures that the whole charged population moves as a unit against the neutrals, so the name emphasizes the two-fluid neutral-versus-charged slip that defines the effect.
How does the ambipolar time depend on ionization, and why does that matter?
The diffusion time scales as t_AD ∝ ρ_i ∝ x_i: fewer ions mean weaker ion–neutral drag, so the neutrals slip past the field faster and the core evolves more quickly. Because the ionization fraction itself falls with density, x_i ∝ n_n^{−1/2}, a contracting core becomes steadily less ionized and therefore diffuses faster as it gets denser. This positive feedback is the engine of the picture: rather than stalling, a subcritical core accelerates toward the critical threshold. It is also why predicting core lifetimes hinges on getting the ionization chemistry — cosmic-ray flux, metal ions, grain charging — right.
If the field is frozen to the ions, how do the neutrals ever cross it?
Through friction, not by breaking the field. Gravity pulls on the neutral H₂, which carries the mass; the neutrals collide with the sparse ions and drag on them; the ions are held back by the Lorentz force. The result is a steady-state relative drift in which the neutrals seep inward across the field lines while the flux, anchored to the ions, stays behind. No field line is ever cut — the flux is simply left in the envelope as the neutral mass flows through it to the center. Over one ambipolar time the central mass-to-flux ratio rises enough to tip the core supercritical.
Is ambipolar diffusion still relevant now that turbulence-driven star formation is popular?
Yes. Turbulence certainly helps assemble dense, sometimes already-supercritical cores quickly, and the pendulum of fashion has swung toward it. But ambipolar diffusion remains the dominant non-ideal MHD process across the densities where prestellar cores actually form, and it is essential in simulations for shedding magnetic flux, enabling protoplanetary disks, and setting the field young stars inherit. Even in turbulence-dominated models, how flux leaves the densest gas is still governed by ion–neutral drift. The two pictures are not exclusive: the open question is the quantitative division of labor, not whether ambipolar diffusion operates.
What is the "magnetic braking catastrophe" and how does diffusion resolve it?
In ideal MHD, a collapsing rotating core stays perfectly coupled to its field, which acts like a stiff lever transmitting angular momentum outward to the envelope extremely efficiently — so efficiently that the inner core loses essentially all its spin and cannot form a rotationally supported disk. Simulations that assume flux freezing therefore produce protostars with no disks, contradicting the disks ALMA routinely images. Allowing the field to diffuse out of the dense inner region — ambipolar diffusion, plus Ohmic and Hall terms — decouples the collapsing gas from the braking field, letting angular momentum be retained and disks of realistic size form. It is one of the clearest places where non-ideal MHD is not a refinement but a necessity.