Solar Physics
Wilson Depression: Why Sunspots Are Dented Below the Solar Surface
Look at a large sunspot near the edge of the solar disk and something strange happens: the dark central umbra appears to sink, as if the spot were a shallow crater pressed into the Sun's surface. That optical dent is the Wilson depression, and it is real — the level at which we "see" the Sun inside a sunspot lies roughly 400 to 800 kilometers deeper than the surrounding photosphere. First noticed by the Scottish astronomer Alexander Wilson in 1769, it is one of the oldest quantitative clues to what sunspots actually are.
The Wilson depression is not a hole in the Sun. It is a geometric offset in the surface of unit optical depth: because a sunspot's interior gas is cooler, less dense, and less opaque than the hot photosphere around it, our line of sight penetrates farther down before the plasma becomes opaque. The strong magnetic field of the spot — typically 2,000 to 3,500 gauss — is what makes the gas cool and evacuated in the first place, so the depression is a direct fingerprint of magnetic pressure at work.
- TypeGeometric/optical depression of the visible surface
- RegimeSolar photosphere, strong-field sunspots
- DiscoveredAlexander Wilson, 1769 (Wilson effect)
- Typical depth400-800 km below quiet photosphere
- Key relationP_in + B²/8π = P_out (magnetohydrostatic balance)
- Observed inSunspot umbrae, esp. near solar limb
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What the Wilson Depression Actually Is
The visible "surface" of the Sun is not a solid boundary but the layer where the plasma becomes opaque to our line of sight — the surface of optical depth τ ≈ 1 at visible wavelengths. In the quiet photosphere this happens at a well-defined height. Inside a sunspot umbra, the gas is cooler (about 3,700-4,200 K versus 5,800 K outside) and strongly evacuated by its magnetic field, so it is far more transparent. Photons escape from deeper down, and the τ=1 surface is pushed 400-800 km lower.
This means a sunspot is genuinely a depression in the visible surface, even though the Sun has no solid crust. It is not caused by material being pushed away like a footprint; it is an opacity effect. The dip is what Alexander Wilson inferred in 1769 when he watched a large spot near the limb foreshorten asymmetrically — the near-side penumbra vanished before the far-side one, exactly as expected for a saucer-shaped cavity rotating over the horizon.
The Mechanism: Magnetic Pressure and Hydrostatic Balance
The physics is magnetohydrostatic equilibrium. Across the boundary between a sunspot and the surrounding plasma, total pressure must balance. Inside the spot, magnetic field contributes a magnetic pressure P_mag = B²/8π (Gaussian units). So the balance reads:
- P_gas,inside + B²/8π = P_gas,outside
Because the field adds pressure, the gas pressure inside must be lower than outside at the same geometric height — the spot is partially evacuated. Lower gas pressure and density mean lower opacity, so light escapes from deeper layers.
The cooling and the evacuation reinforce each other: the vertical magnetic field (2,000-3,500 G) suppresses the convective heat transport that normally keeps the photosphere hot, so the umbra chills, contracts, and becomes even more transparent. Integrating the reduced density down the line of sight gives the geometric offset of the τ=1 surface — the Wilson depression. The depth scales with field strength, which is why the darkest, most magnetized umbrae show the deepest depressions.
Characteristic Numbers and a Worked Estimate
Take a strong umbra with B ≈ 3,000 gauss. The magnetic pressure is P_mag = B²/8π = (3000)²/(8π) ≈ 3.6 × 10⁵ dyn/cm² (≈ 3.6 × 10⁴ Pa). The quiet photospheric gas pressure at τ=1 is roughly 1.2 × 10⁵ dyn/cm², so the field alone can support and even exceed the external gas pressure — the spot is strongly evacuated.
- Pressure scale height in the photosphere: H = kT/(μ m_H g) ≈ 150 km (cooler gas → smaller H).
- To let light escape from a level several scale heights deeper requires a geometric drop of order 500 km, matching observations.
Typical inferred values: quiet Sun = 0 km, penumbra ≈ 100-250 km, umbra ≈ 400-800 km, with the largest spots reaching ~1,000 km. For context, 500 km is only about 0.07% of the solar radius (R_sun ≈ 696,000 km) — a shallow saucer, not a canyon, but easily measurable.
How It Is Observed and Measured
There are two classic routes to the Wilson depression:
- The Wilson effect (geometric): track a sunspot as it rotates toward the limb. A depressed, saucer-shaped umbra foreshortens asymmetrically — the limbward penumbra narrows and disappears first. Wilson measured this by eye in 1769; modern imaging quantifies the offset from the projected geometry.
- Fourier / spectroscopic methods: using the pressure balance and magnetic field maps from the Zeeman effect, one solves the magnetohydrostatic equations to infer the depth. The Martínez Pillet & Vázquez (1993) analysis is a benchmark, giving depressions of a few hundred km.
Spacecraft such as Hinode (2006), the Solar Dynamics Observatory, and the ground-based Daniel K. Inouye Solar Telescope (DKIST) now resolve umbral structure to under 30 km, letting researchers combine geometric and spectropolarimetric estimates. Helioseismology and local wave-travel-time measurements provide an independent, purely dynamical handle on the subsurface geometry.
How It Differs From Related Phenomena
It is easy to confuse the Wilson depression with several cousins:
- Granulation dips: ordinary convective granules have τ=1 corrugations of only a few tens of km — an order of magnitude shallower and constantly changing.
- Sunspot darkness: the umbra looks black because it is cooler (Stefan-Boltzmann: emission ∝ T⁴, so ~4,000 K vs 5,800 K radiates only ~22% as much). Darkness is a temperature effect; the depression is an opacity/geometry effect. They share a cause (the magnetic field) but are distinct observables.
- Faculae and plage: bright magnetic features where thin flux tubes create small "hot walls" — the opposite brightness sign, with only tiny depressions.
The unifying thread is that magnetic pressure reshapes the τ=1 surface. Strong, concentrated fields (umbrae) evacuate and depress; weak or thin fields barely dent it. The Wilson depression is simply the extreme, most measurable case.
Significance, Famous Cases, and Open Questions
The Wilson depression is historically pivotal: it was among the first evidence that sunspots are cavities of altered physical state, not clouds floating above the surface or holes to a dark interior (an 18th-19th century idea championed by William Herschel). Today it anchors models of sunspot structure and is a key input for inverting magnetic and thermal profiles.
Landmark work includes Wilson's original 1769 limb observations, Bray & Loughhead's mid-20th-century monograph Sunspots, and Martínez Pillet & Vázquez's quantitative 1993 inversions. Large, long-lived spots such as those of solar-maximum active regions show the deepest, cleanest depressions.
- Open questions: the exact depth of the darkest umbrae remains uncertain because opacity, temperature, and field are coupled and hard to disentangle.
- Whether the depression connects smoothly to a deep subsurface "magnetic root" (the monolithic vs. cluster/spaghetti sunspot models) is still debated.
- DKIST-era high-resolution spectropolarimetry aims to pin depths to ±50 km and test these competing models directly.
| Region | Magnetic field (gauss) | Temperature at τ=1 (K) | Depression below quiet Sun |
|---|---|---|---|
| Quiet photosphere | ~1-10 | ~5,800 | 0 km (reference) |
| Sunspot penumbra | ~700-1,500 | ~5,000-5,500 | ~100-250 km |
| Sunspot umbra | ~2,000-3,500 | ~3,700-4,200 | ~400-800 km |
| Large/dark umbra | up to ~4,000 | ~3,500 | up to ~1,000 km |
| Pore (spot without penumbra) | ~1,500-2,000 | ~5,200 | ~150-300 km |
Frequently asked questions
What is the Wilson depression?
It is the geometric dip in the visible surface of the Sun inside a sunspot. Because the cool, magnetically evacuated umbral gas is more transparent than the surrounding photosphere, our line of sight reaches the τ=1 (unit optical depth) surface about 400-800 km deeper than in the quiet Sun. It is an opacity effect, not a physical hole.
Who discovered the Wilson depression and when?
The Scottish astronomer Alexander Wilson noticed it in 1769 by watching a large sunspot rotate toward the Sun's limb. He saw the umbra and penumbra foreshorten asymmetrically, which is only explained if the spot is a saucer-shaped cavity. This is now called the Wilson effect, and the inferred depth is the Wilson depression.
Why does the sunspot surface sink below the photosphere?
A sunspot's magnetic field (2,000-3,500 gauss) adds magnetic pressure B²/8π. To keep total pressure balanced, the internal gas pressure and density drop, and the field suppresses convection so the gas cools. Lower density and lower temperature make the plasma more transparent, so light escapes from deeper down — producing the depression.
How deep is a typical Wilson depression?
About 400-800 km for a normal sunspot umbra, with the largest, darkest umbrae reaching roughly 1,000 km. The penumbra is shallower, around 100-250 km. Even 500 km is only about 0.07% of the solar radius, so it is a shallow saucer rather than a deep canyon, but it is readily measurable.
Is the Wilson depression the same as why sunspots look dark?
No. Sunspots look dark because the umbra is cooler (~4,000 K versus 5,800 K), and by the Stefan-Boltzmann law (emission ∝ T⁴) it radiates only about a fifth as much light. The Wilson depression is a separate geometric/opacity effect. Both ultimately stem from the same strong magnetic field, but they are distinct observables.
How is the Wilson depression measured today?
Two main ways: geometrically, by tracking the asymmetric foreshortening of a spot as it nears the limb (the Wilson effect); and spectroscopically, by solving magnetohydrostatic pressure balance using Zeeman-derived field maps. Instruments like Hinode, SDO, and DKIST, plus helioseismic wave-travel-time methods, refine these estimates to tens of kilometers.