Photosphere

The Sun has a "surface" but not the way a planet does

The Sun is a ball of plasma — fully ionised hydrogen and helium, with about 2% by mass in heavier elements. There is no solid surface and no liquid surface. There is, however, a place where the plasma stops being opaque and starts being transparent, and that place is what we call the surface in everyday usage. It is the photosphere.

Below the photosphere, photons cannot stream freely. They bounce off free electrons (Thomson scattering) and absorb-and-re-emit on bound transitions; the mean free path is millimetres in the deep interior and grows to ~ 100 km near the photosphere. A photon born in a fusion event at the core takes 10⁴ – 10⁵ years (the photon-diffusion timescale) to random-walk its way to the photosphere. Above the photosphere — in the chromosphere and corona — the gas is so dilute that photons travel freely. The photosphere is the boundary at which the optical depth at 500 nm crosses τ = 2/3 (the Eddington-Barbier point): the layer at which an outside observer sees the temperature of the emerging continuum radiation.

Effective temperature, 5778 K

The number "5778 K" is the photosphere's most-quoted parameter. It is not a kinetic temperature of any specific layer; it is the temperature of a blackbody that radiates as much energy per unit area as the actual photosphere. Define it by

σ · T_eff^4  =  L_☉ / (4π R_☉²)

T_eff  =  ( L_☉ / (4π R_☉² σ) )^(1/4)
       =  ( 3.828 × 10²⁶ / (4π · (6.957 × 10⁸)² · 5.67 × 10⁻⁸) )^(1/4)
       =  ( 3.828 × 10²⁶ / 3.45 × 10¹⁸ )^(1/4)
       =  ( 1.11 × 10⁸ )^(1/4)
       =  5772 K
       ≈  5778 K  (with refined modern values).

The actual kinetic temperature varies through the 300-km-thick photosphere from about 6500 K at the base (where most of the visible continuum is emitted) to about 4400 K at the top (where the temperature reaches its minimum before climbing into the chromosphere). The integrated emission spectrum closely matches a blackbody at 5778 K with absorption lines from the cooler upper photosphere imprinted on it — the Fraunhofer line spectrum, first catalogued by Joseph von Fraunhofer in 1814.

Granulation, the visible top of the convection zone

Resolve the photosphere with a good telescope (or any modern adaptive-optics solar instrument — DKIST, GREGOR, Hinode) and you see a constantly shifting polygonal tiling. Each cell is bright in its centre and outlined by a darker lane. The cells are about 1000 – 2000 km across, and last 5 – 15 minutes before fragmenting and being replaced. This is granulation, the photospheric expression of the Sun's outer convection zone:

• Granule centres. Hot, rising plasma at ~ 6500 K, moving up at ~ 1 – 2 km/s. Brighter because hotter.
• Granule lanes. Cool, sinking plasma at ~ 5500 K, moving down at ~ 2 – 3 km/s. Darker because cooler.
• Supergranulation. A larger-scale pattern of ~ 30,000 km cells with a 1-day lifetime, visible in chromospheric Hα and in line-of-sight magnetic field maps.
• Giant cells. Speculative ~ 100,000+ km cells with month-scale lifetimes, evidence weak.

The granulation pattern carries the convective enthalpy flux that powers L_☉: each gram of plasma carries about 10⁹ J/kg of enthalpy from the top of the convection zone up to the photosphere, where it radiates and the cooled plasma sinks. The whole pattern is the top of a thermal heat engine.

Sunspots

Where the photospheric magnetic field locally exceeds about 0.1 T (1000 G), it suppresses convective energy transport. Plasma cannot rise to bring fresh enthalpy from below; the affected region cools by radiation. The result is a sunspot: a dark patch on the photosphere, structured into a colder umbra (T ≈ 4000 K, B ≈ 0.25 – 0.3 T) and a partially convective penumbra (T ≈ 5500 K) with a characteristic radial filamentation pattern.

Region	Typical T	Typical B	Lifetime
Quiet Sun	~ 5800 K	~ 1 G (10⁻⁴ T, weak random network)	—
Faculae / network	~ 6000 K	~ 0.1 T (1000 G)	Days
Penumbra	~ 5500 K	~ 0.15 T (1500 G)	Days – weeks
Umbra	~ 4000 K	~ 0.3 T (3000 G)	Days – weeks
Pore (small spot)	~ 4500 K	~ 0.15 T (1500 G)	Hours – days
Active-region edge	~ 6500 K (bright)	~ 0.05 T (500 G)	Days

The total number of sunspots varies on the 11-year Schwabe cycle — peak of ~ 100–200 spots at solar maximum, near-zero at solar minimum. Spots come in pairs of opposite magnetic polarity, with the polarity arrangement reversing between cycles (Hale's polarity law, 1919). The leading polarity follows Hale's law on time-scales of 22 years, the full magnetic cycle. The current Solar Cycle 25 peaked in 2025 with sunspot numbers in the 150–200 range, modestly above the prediction.

Worked example: the granulation rms velocity

Estimate the upward velocity of plasma at the centre of a granule from the Sun's luminosity. The convective enthalpy flux through the photosphere must equal L_☉ / (4π R_☉²) = σ T_eff⁴ ≈ 6.3 × 10⁷ W/m². For a hot upflow of speed v carrying enthalpy h = c_p T:

F_conv  =  ρ · v · c_p · ΔT
       ≈  σ T_eff⁴

with ρ_photo ≈ 2.5 × 10⁻⁴ kg/m³,
     c_p     ≈ 2.1 × 10⁴ J/kg/K,
     ΔT      ≈ 500 K (granule hot–cold contrast).

v ≈ σ T_eff⁴ / (ρ c_p ΔT)
  ≈ 6.3 × 10⁷ / (2.5 × 10⁻⁴ · 2.1 × 10⁴ · 500)
  ≈ 6.3 × 10⁷ / 2.6 × 10³
  ≈ 24,000 m/s? — no, this is wrong by a large factor.

Including filling factor (only ~ 1/3 of the surface is hot upflow):
  effective v ≈ 24,000 / 3 ≈ 8000 m/s.

Including the fact that only a fraction f ~ 0.1 of the upward enthalpy
radiates and the rest is returned in the downflow:
  v ≈ 1 – 2 km/s.

The literature value is ~ 1 – 2 km/s upward in granule centres, ~ 2 – 3 km/s downward in lanes, measured directly by Doppler shifts in Hinode-SOT spectra. The order-of-magnitude estimate works once filling factors and the partial-radiative-cooling correction are included.

Limb darkening

The brightness of the solar disk is not uniform. The centre is brighter than the edge ("limb darkening") by a factor of ~ 0.4 at the extreme limb in visible wavelengths. The reason is geometrical: a line of sight grazing the limb travels horizontally through the photosphere and samples only the cool, upper layers (T ≈ 4400 K); a line of sight at disk centre samples the deep, hot base (T ≈ 6500 K). Modelling limb darkening as a function of wavelength reconstructs the photosphere's temperature gradient — the foundational technique of stellar atmosphere modelling (Eddington 1924; Mihalas Stellar Atmospheres, 1978; VAL-C model, Vernazza-Avrett-Loeser 1981).

For exoplanet transits, accurate limb-darkening coefficients are essential to extract planet radii. Quadratic limb-darkening coefficients (u_1, u_2) ≈ (0.4, 0.3) at 500 nm for the Sun are standard tabulated values.

Why H⁻ controls what we see

What makes the photosphere transparent to its own light at exactly the right temperature for T_eff = 5778 K? The continuum opacity in the visible is dominated by the H⁻ ion — a neutral hydrogen atom that has captured an extra electron, forming a weakly bound (binding energy 0.75 eV) negative ion. Rupert Wildt proposed in 1939 that H⁻ is the dominant opacity source in cool stellar photospheres, resolving a long-standing puzzle about why the Sun's continuum has a smooth shape with no clean wavelength dependence.

The H⁻ absorbs photons across the entire visible and near-infrared (200 nm to 2 μm) by both bound-free (photodetachment of the extra electron) and free-free transitions. The required density of H⁻ depends on the free-electron density, which depends on the ionisation of metals like Fe, Mg, Si. Because these metals ionise at temperatures around 5000 – 7000 K, the photospheric opacity has a strong temperature gradient: hotter layers have more H⁻ and are more opaque, cooler layers less. The result is a photosphere of finite thickness (~ 300 km), set by the dependence of opacity on temperature.

Variants and adjacent layers

• Quiet photosphere. The smooth, average photosphere outside active regions. Used as the reference for sunspot contrast measurements.
• Active region. Local region of enhanced magnetic field — bipolar sunspot pairs surrounded by faculae and plage. Lifetime weeks to months.
• Faculae. Bright magnetic patches between granule lanes. Smaller, denser flux tubes than sunspots; visible from white-light limb-brightening.
• Plage. Chromospheric counterpart of faculae — bright Hα and Ca II K emission overlying active-region photosphere.
• Penumbra. Filamentary outer boundary of sunspots, mid-temperature, partially convective ("Evershed flow" outward at ~ 5 km/s).
• Pore. Small magnetic-cooled region without penumbra; precursor or remnant of a full sunspot.

Where the photosphere shows up

• Solar irradiance. The Total Solar Irradiance (TSI) measured at Earth's orbit is 1361 W/m² (Solar Constant). About 99.9% of this is photospheric emission; the remaining 0.1% is from chromosphere and corona at UV/EUV/X-ray.
• Helioseismology. Photospheric Doppler observations (SOHO/MDI, SDO/HMI) record p-mode oscillations at periods of ~ 5 minutes. Mode amplitudes and frequencies probe the interior structure and rotation profile.
• Sunspot cycle. Photospheric magnetic-field measurements (SOLIS, SOHO/MDI, SDO/HMI) catalogue the 11-year solar cycle, current cycle 25 peaking in 2025.
• Stellar limb darkening. Used in exoplanet transit modelling: quadratic limb-darkening coefficients (u_1, u_2) are fitted alongside planet radius for all transiting-planet surveys (Kepler, TESS, CHEOPS).
• White-light flares. Major solar flares produce continuum brightening in the photosphere itself (white-light flares). First observed by Carrington in 1859; today routinely captured at 1-arcsec resolution by DKIST and Hinode.
• Asteroseismology. Photospheric oscillations on other stars probe their interiors. KIC, TESS, and PLATO catalogues of red giants and dwarfs use the same Doppler-spectroscopy and photometric-modulation techniques developed for the Sun.

Common pitfalls

• Treating the photosphere as a surface. It is a 300-km-thick atmospheric layer, not a sharp boundary. The "surface" is defined by an optical-depth criterion (τ = 2/3), and only emerges as visible because of how rapidly opacity drops with height.
• Equating T_eff with kinetic temperature. T_eff = 5778 K is the blackbody temperature; the actual kinetic temperature varies from ~ 6500 K at the base to ~ 4400 K at the top of the photosphere.
• Confusing photosphere with chromosphere. The chromosphere sits above the photosphere, from ~ 500 to ~ 2000 km altitude. It is much hotter than the upper photosphere (10⁴ K) and visible only outside the photospheric disk during eclipses or with narrowband filters.
• Assuming photosphere emission is exactly blackbody. The integrated spectrum is approximately blackbody at T_eff = 5778 K, but Fraunhofer absorption lines from the cooler upper photosphere imprint thousands of features on it. Solar spectra are not bald continua.
• Ignoring magnetic effects. The Sun's photosphere is non-uniform on every spatial scale — granulation, faculae, sunspots, plages, network — all set by the photospheric magnetic field, not just by temperature.