Filament Eruption: A Rope of Plasma Snapping Free

A cold rope in a million-degree sky

The corona is a near-vacuum at one to two million kelvin. A filament is a thread of chromospheric material sitting inside it — about 7,000-8,000 K and 10¹⁰-10¹¹ particles per cm³, roughly two orders of magnitude cooler and two orders denser than its surroundings. Pressure balance works because the two effects cancel: nT is comparable inside and outside.

Gravity is the real problem. Solar surface gravity is 274 m s^-2, and the filament is parked 10,000-100,000 km up. Nothing thermal holds it there — the pressure scale height of 8,000 K hydrogen is only ~250 km. The support is entirely magnetic. Field lines beneath the filament are bent into dips, and the upward curvature force — magnetic tension, the (B·∇)B/4π term of the Lorentz force — carries the weight.

The numbers check out. Balancing tension against gravity, B²/4πR_c ≈ ρg, with B = 10 G and n = 10¹¹ cm^-3 (ρ ≈ 1.7 × 10^-13 g cm^-3) demands dips with a radius of curvature of ≈ 1.7 × 10⁴ km — exactly the observed sag scale. The plasma beta inside is ~0.03-0.1, so the field is firmly in charge. This is the Kippenhahn-Schlüter picture (1957); Kuperus-Raadu (1974) is the inverse-polarity version, in which the dips belong to a true helical flux rope.

Filament and prominence are the same object. Against the bright disc in Hα (656.28 nm) the cool gas absorbs and looks like a dark snake — a filament. Off the limb against black sky it re-emits and looks like a bright arch — a prominence. The vocabulary is 19th-century geometry, not physics.

Building the flux rope: shear, cancellation and chirality

Every filament lies along a polarity inversion line (PIL), where the line-of-sight photospheric field changes sign. The corridor around it — the filament channel — is not a normal potential arcade: its field runs nearly parallel to the PIL rather than crossing it at right angles. That shear is the stored energy.

Two ingredients build it. Differential rotation and surface flows drag arcade footpoints past each other over days. Then flux cancellation at the PIL: opposite-polarity fragments driven together by supergranular flows submerge or reconnect, and the van Ballegooijen & Martens (1989) mechanism converts a sheared arcade into a helical rope, one reconnection at a time, lifting a new dipped field line into the channel each event.

Filling the rope with cool gas has two competing answers. In injection models, chromospheric material is squirted up by reconnection jets. In evaporation-condensation models, footpoint heating evaporates plasma into the loop, which becomes thermally unstable near its apex — radiative losses run away as the gas cools below ~10⁵ K — and condenses in the dips. The same thermal non-equilibrium produces coronal rain. High-resolution imaging shows the filament is a bundle of threads 100-600 km wide with lifetimes of ten to twenty minutes, carrying counterstreaming flows of 5-20 km s^-1 (Zirker, Engvold & Martin, 1998).

Filaments also have a handedness. Sara Martin's chirality rules (1998) find filaments predominantly dextral in the north and sinistral in the south, in about 75-80% of cases, matching the helicity injected by the dynamo. That handedness survives the eruption and reappears in the twist of the interplanetary magnetic cloud measured at L1.

Why the equilibrium fails

A filament can sit stably for weeks, so its loss of equilibrium needs a trigger. Four mechanisms compete, and real events often combine them.

• Kink instability. If the rope is wound too tightly the axis itself buckles into a helix. For a line-tied coronal loop the critical twist is around Φ_crit ≈ 2.5π-3.5π radians (Hood & Priest, 1979-81), between about one and two full turns. Kinking converts twist into writhe and can rotate an erupting filament by 90° or more within a few solar radii.
• Torus instability. A current ring feels an outward hoop force restrained by the overlying strapping field. Which wins depends on the decay index n = −d ln B_ext / d ln h. When n exceeds roughly 1.5 (Kliem & Török, 2006; observed thresholds scatter over ~1.1-2.0), the rope runs away. This is the most-used quantitative diagnostic: extrapolate the coronal field from an SDO/HMI vector magnetogram, plot n(h), read off the critical height.
• Magnetic breakout. In a multipolar configuration, reconnection above the rope at a coronal null peels away the strapping field before any internal instability occurs (Antiochos, DeVore & Klimchuk, 1999).
• Tether-cutting. Reconnection beneath the rope, between the two sheared elbows of the arcade, cuts the low-lying tethers while adding flux and twist to the rope (Moore et al., 2001).

Observationally the failure announces itself as a slow-rise phase: the filament creeps upward at 1-10 km s^-1 for tens of minutes to hours, often with mass draining down its legs. Past the critical height the rise turns exponential, then impulsive.

The eruption: reconnection, acceleration, and the CME

As the rope accelerates, the field below it is stretched into a vertical current sheet. Reconnection there does three things at once, and is the heart of the CSHKP standard flare model (Carmichael 1964; Sturrock 1966; Hirayama 1974; Kopp & Pneuman 1976): it cuts the remaining tethers, adds poloidal flux to the rope from below, and dumps energy downward into the chromosphere.

The bookkeeping is straightforward. Magnetic energy density is B²/8π: at 100 G that is ~400 erg cm^-3, so 10²⁹ cm³ holds ~4 × 10³¹ erg, of which perhaps 10-50% is free. Against that, lifting 10¹² kg out of the Sun's gravity well costs GM_☉m/R_☉ ≈ 1.9 × 10³⁰ erg, and giving it 1,000 km s^-1 costs another 5 × 10³⁰ erg. One active region comfortably supplies the ~10³¹ erg needed; the largest events reach 10³²-10³³ erg. Emslie et al. (2012) found that in most large events the CME's kinetic energy equals or exceeds the total radiated flare energy — the flare is the by-product.

Gravity sets the scale: escape speed at the solar surface is 617.7 km s^-1, falling as r^−1/2 to ~437 km s^-1 at 2 R_☉. It is not a hard floor on catalogued speeds, though — a slow eruption launched high in the corona is dragged outward by the faster ambient solar wind and still escapes. Impulsive acceleration of 100-2,000 m s^-2 (a few km s^-2 in extreme cases) is delivered within about 2 solar radii; afterwards the CME coasts and is dragged toward the ambient wind speed.

Reconnection rate is the awkward part. Sweet-Parker theory gives M ≈ S^-1/2, and a coronal Lundquist number of 10¹²-10¹⁴ predicts M ~ 10^-6-10^-7 and flares lasting months. Observed rates are ~0.01-0.1, requiring Petschek-type geometry or a current sheet fragmenting via the plasmoid instability — blobs streaming up and down the sheet are seen directly in SDO/AIA 131 Å.

The aftermath is diagnostic. Particle beams and conduction fronts light up the footpoints of newly closed field as two flare ribbons that separate at 10-100 km s^-1. Between them grows the post-flare arcade, cooling through the AIA passbands in sequence — 131 Å (~10 MK), then 94, 335, 211, 193, 171 Å — over several hours. At the rope's footpoints, twin coronal dimmings mark the plasma that left, and their area and total brightness deficit are among the best proxies for CME mass in disc-centre events.

How we actually watch one

On the disc: Hα at 656.28 nm is the workhorse, with round-the-clock coverage from the GONG Hα network, Kanzelhöhe and Big Bear. Filaments are dark in EUV too, because cool hydrogen and helium absorb below the 912, 504 and 228 Å continuum edges — hence dark channels in SDO/AIA 193 Å while glowing in 304 Å He II, formed at ~50,000-80,000 K in the prominence-corona transition region. Those 304 Å movies from the Solar Dynamics Observatory (2010-) are the source of nearly every viral eruption clip.

Magnetic field: quiescent-filament fields are far too weak for straightforward Zeeman splitting, so they are measured with the Hanle effect — magnetic modification of resonance-scattering polarisation. Leroy, Bommier & Sahal-Bréchot (1984), using the Pic du Midi coronagraph, established the canonical result: a few to ~15 G, mostly horizontal, crossing the filament axis at a shallow ~20-25°. Active-region filaments are strong enough for Zeeman work in He I 10830 Å, giving hundreds of gauss. The 4-metre Daniel K. Inouye Solar Telescope (first light 2019) now resolves ~20-25 km on the Sun and is beginning to map thread-scale fields.

Off the limb: SOHO/LASCO (1995-) images from 2 to 30 solar radii and has catalogued more than 30,000 CMEs; STEREO (2006-) added stereoscopic triangulation of trajectories; Solar Orbiter (2020-) closes to 0.28 AU; Parker Solar Probe has flown through CME material inside 20 solar radii. Radio type II bursts track the CME-driven shock through drifting plasma-frequency emission, GOES soft X-rays set the flare's C/M/X class, and ACE, Wind and DSCOVR catch the shock, sheath and smoothly rotating magnetic cloud in situ at L1. The first unambiguous CME detection came on 14 December 1971 from the OSO-7 coronagraph (Richard Tousey), confirmed as routine by Skylab's Apollo Telescope Mount in 1973-74.

Famous eruptions and what they did to Earth

A CME matters geomagnetically only if its embedded field has a strong southward component, B_z < 0. Earth's dayside field points north, so a southward interplanetary field reconnects efficiently at the magnetopause and drives the ring current measured by the Dst index. A 2,000 km s^-1 CME with a steadily northward B_z drives little ring-current storm — though its shock and turbulent sheath still register — while a 600 km s^-1 one with sustained −30 nT does. This is the crux of a geomagnetic storm.

• 1-2 September 1859, the Carrington Event. Richard Carrington and Richard Hodgson independently saw a white-light flare; a magnetic crochet registered at Kew within minutes and the ejecta arrived in an extraordinary 17.6 hours. Reconstructed Dst estimates cluster near −900 nT (published values span roughly −850 to −1,700 nT). Telegraph lines sparked; aurorae reached Cuba and Hawaii.
• 4 June 1946, the "Grand Daddy" prominence, filmed at the High Altitude Observatory station in Climax, Colorado — an erupting arch reaching a few hundred thousand kilometres above the limb, and the textbook image of the phenomenon ever since.
• 13 March 1989. Dst ≈ −589 nT. Geomagnetically induced currents tripped the Hydro-Québec grid, blacking out six million people for about nine hours.
• Halloween storms, October-November 2003. X-class flares and fast CMEs from active regions 10486 and 10488, including the saturated ≈X28 event of 4 November, the largest ever recorded in GOES X-rays.
• 23 July 2012. Merged eruptions crossed STEREO-A at ~2,250 km s^-1 with B_z near −50 nT. Had it hit Earth — it missed by about a week of solar rotation — modelling suggests a Carrington-class storm (Baker et al., 2013).
• 10-11 May 2024, the Gannon storm. Successive eruptions from AR 13664 produced the first G5 event since 2003, minimum Dst ≈ −412 nT, aurorae over Mexico and southern Europe, GPS-guided farm equipment down across the US Midwest, and measurable satellite drag in low Earth orbit.

Transit time follows from the speed: 1 AU is 1.5 × 10⁸ km, so 1,000 km s^-1 means ~42 hours and 2,500 km s^-1 under 17. Operational forecasts (WSA-ENLIL and drag-based models at NOAA SWPC and ESA) still carry a mean arrival-time error near ±10 hours, and cannot predict B_z at all until the cloud reaches L1 — 15 to 60 minutes of real warning.

Look-alikes, failures, and what is still unsolved

A flare is not a CME. The flare is electromagnetic radiation from the reconnection site and the heated footpoints; its photons reach Earth in 8 minutes 20 seconds and cause radio blackouts. The CME is the mass. They usually accompany each other in large events, but only about a third of CMEs have an identifiable flare — most slow, narrow ones have none — and most small flares eject nothing. Headlines about a flare "hitting Earth tomorrow" conflate the two. Compare solar flare and coronal mass ejection.

Not every disappearance is an eruption. The old French term disparition brusque covers any sudden vanishing of a filament in Hα. Some are purely thermal: the plasma is heated above Hα visibility or the ionisation balance shifts, and the filament reappears in the same channel hours later, intact. A genuine eruption is confirmed by coronal dimming, arcade formation and a coronagraph signature.

Failed (confined) eruptions are common and instructive. The rope goes kink-unstable, rises tens of megametres, rotates dramatically — then stalls and falls back, because the overlying strapping field decays too slowly with height and n never exceeds ~1.5. The well-studied event of 27 May 2002 is the standard reference. Failed eruptions are the direct evidence that the torus criterion, not internal twist alone, decides whether material escapes.

Other look-alikes: a coronal hole high-speed stream produces recurrent, 27-day-periodic storms with no filament involved; surges and sprays are smaller jet-like chromospheric ejections; coronal rain is condensed material falling down the same field lines.

Open questions remain substantial. Does the flux rope exist before the eruption or form during it? What sets the filament's mass, and how much is injected versus condensed in situ? Why do near-identical configurations sometimes erupt and sometimes not, leaving CME forecasts barely better than climatology? And most practically: can the B_z of an approaching cloud be predicted from the observed chirality and orientation of the filament that made it, days rather than minutes ahead? That last is the central unsolved problem of operational space weather.

Three families of solar filament, and how differently they erupt

Property	Quiescent filament	Active-region filament	Polar-crown filament
Where it sits	Quiet Sun, between decayed active regions	Inside a sunspot group, along the sheared core of the neutral line	High-latitude boundary of the polar field
Axial field strength	~3-15 G (Hanle-effect measurements)	~100-800 G (He I 10830 A, Zeeman)	~3-10 G
Height and length	10-50 Mm high, 60-600 Mm long	5-30 Mm high, 10-100 Mm long	Up to ~50 Mm high, can wrap a large arc of latitude
Lifetime	Days to a few solar rotations	Hours to days	Weeks to months; drifts poleward with the cycle
Typical eruption speed	Slow, 200-600 km/s, often gradual	Fast, 800-3,000 km/s, impulsive	Slow, 200-500 km/s, very large angular width
Associated flare	Often weak or none (Hyder flare)	Usually M- or X-class two-ribbon flare	Usually weak; big, slow CME