The Zeeman Effect in Sunspots

Why the Zeeman effect matters

Magnetism runs the Sun's weather. Sunspots, flares, prominences, coronal loops, the 11-year activity cycle, and the coronal mass ejections that batter Earth's magnetosphere are all magnetic phenomena. But magnetic fields emit no light of their own — they are invisible. The Zeeman effect is the workaround: it imprints the field onto ordinary spectral lines that atoms are already emitting, converting an invisible vector field into a measurable wavelength split and a polarization signature. It is, quite literally, how we read the Sun's magnetism.

• First magnetism beyond Earth. Hale's 1908 measurement made the Sun the first astronomical body with a directly measured magnetic field.
• The engine of space weather. The fields Zeeman diagnostics reveal store the energy that erupts as flares and CMEs, so magnetograms underpin space-weather forecasting.
• A remote magnetometer. No probe need touch the plasma; the field strength arrives encoded in the starlight itself.
• The bridge to stellar physics. The identical signal measures magnetic fields on stars light-years away, from active M dwarfs to megagauss white dwarfs.
• A test of atomic and plasma physics. The line splitting depends on quantum mechanics (Landé factors) and the polarization on radiative transfer in a magnetized atmosphere.

How it works, step by step

The Zeeman effect is fundamentally a quantum-mechanical splitting of atomic energy levels by a magnetic field. Here is the chain from atom to magnetogram.

1. Degenerate levels split. An atomic level with total angular momentum J normally has 2J+1 magnetic sublevels (m_J = −J … +J) at the same energy. A magnetic field B breaks this degeneracy: each sublevel shifts by ΔE = g m_J μ_B B, where μ_B is the Bohr magneton and g is the Landé g-factor.
2. One line becomes several. A transition between two split levels no longer occurs at a single wavelength. Selection rules (Δm_J = 0, ±1) sort the components into an unshifted π component (Δm = 0) and two shifted σ components (Δm = ±1) — the classic normal Zeeman triplet.
3. The split scales with B. The σ components sit symmetrically about line center by Δλ = 4.67×10⁻¹³ · g · λ² · B (λ in ångströms, B in gauss). Measure Δλ, and you have B.
4. The components are polarized. Viewed along the field (longitudinal), the two σ components are oppositely circularly polarized and the π component vanishes. Viewed across the field (transverse), all three are linearly polarized. Polarization therefore encodes field direction, not just strength.
5. Sunspots supply the strong field. A sunspot umbra carries a near-vertical field of thousands of gauss — strong enough to split iron lines such as Fe I 630.25 nm by tens of milliångströms, comfortably resolvable with a good spectrograph.
6. Scan to build a magnetogram. Sweep the spectrograph slit (or use a filtergraph) across the disk, measuring the circular-polarization split at every pixel. The result is a longitudinal magnetogram — a black-and-white map where brightness encodes the strength and sign of the line-of-sight field.

Key numbers: fields, splits, and temperatures

Quantity	Value	Note
Earth's surface field	~0.25–0.65 G	Reference for scale
Quiet-Sun general field	~1–10 G	Large-scale poloidal field
Sunspot penumbra	~700–1500 G	Inclined, more horizontal field
Sunspot umbra	~2000–3500 G	Strong, near-vertical field
Strongest spots measured	~4000–6000 G	Rare, largest active regions
Umbra temperature	~3500–4000 K	vs ~5800 K photosphere
Zeeman split, Fe I 630.25 nm at 3000 G	~0.14 Å per σ (~0.28 Å full)	g = 2.5, easily resolved

The governing equation

For the normal Zeeman triplet, the wavelength separation between line center and each shifted σ component is:

Δλ = 4.67 × 10⁻¹³ · g · λ² · B

• Δλ — wavelength shift of a σ component from line center, in ångströms (Å).
• g — effective Landé g-factor of the transition (dimensionless), a quantum-mechanical number that sets the line's magnetic sensitivity. Fe I 630.25 nm has g = 2.5; a line with g = 0 does not split at all.
• λ — the rest wavelength of the line, in ångströms.
• B — the magnetic field strength, in gauss (1 G = 10⁻⁴ tesla).
• 4.67 × 10⁻¹³ — the constant e/(4πm_ec²) expressed for these units; it bundles the electron charge, mass, and the speed of light.

Worked example. For Fe I 630.25 nm (λ = 6302.5 Å, g = 2.5) in a 3000 G umbra, Δλ = 4.67×10⁻¹³ × 2.5 × (6302.5)² × 3000 ≈ 0.14 Å for each σ component from line center, so the two σ lines sit ≈0.28 Å apart. Note the crucial λ² scaling: an infrared line at 1.565 µm splits about six times more than a green line for the same field, which is exactly why weak-field work migrated to the near-infrared. Hale worked at Mount Wilson in 1908, saw both the split and its circular polarization, and read off ~2600–2900 G — the first magnetic field measured beyond Earth.

A note on Hale, 1908

Pieter Zeeman had split a sodium line in the lab in 1896, and Hendrik Lorentz's electron theory explained it — work that earned the pair the 1902 Nobel Prize. George Ellery Hale then asked whether the same signature might appear in sunspot spectra. Using the Snow telescope and later the 60-foot tower at Mount Wilson, he found that lines in sunspots were both split and circularly polarized, and that the polarity of the split flipped between spot pairs. His 1908 papers established that sunspots are seats of intense magnetism, and by 1919 Hale, Ellerman, Nicholson, and Joy had formulated Hale's polarity laws — the observation that a solar hemisphere's leading spots share one polarity, trailing spots the opposite, and the whole pattern reverses each ~11-year cycle (a 22-year magnetic cycle). All of it flows from reading the Zeeman effect.

Common misconceptions

• "Sunspots are dark because they are cold holes." They are cooler (~3500–4000 K) but still incandescent; they look dark only against the hotter surroundings. And they are cool because the strong field throttles convection, not the other way around.
• "The Zeeman effect changes the atom's chemistry." It only shifts and splits energy sublevels; the element and its transitions are unchanged. A line with Landé g = 0 shows no split at all.
• "A magnetogram is a photograph of magnetic field lines." It is a map of one field component (usually line-of-sight) inferred from polarization; the field lines themselves are reconstructed, not seen.
• "Bigger splitting always means a bigger field." Only for a given line — splitting also scales with g and with λ², so comparisons must hold the line fixed.
• "You need to resolve the star to measure its field." No — for distant stars the disk-integrated line still broadens and polarizes in proportion to the field, which is how stellar magnetism is measured.
• "Zeeman splitting and Doppler broadening are the same." Doppler broadening smears a line symmetrically with no polarization; Zeeman splitting produces polarized components whose separation tracks B.