The photosphere, chromosphere and corona

Atmospheric names describe physical regimes

A plasma contains mobile charged particles whose collective electromagnetic behaviour matters. Solar material can include ions, electrons and neutral particles in proportions that depend on its conditions. Calling the atmosphere a plasma does not assert that every atom is fully ionized everywhere.

The photosphere is the atmospheric region associated with much escaping visible continuum radiation. Above it lie the chromosphere, a transition region with a strong temperature change, and the more extended corona. Their conditions vary across structures and time; these are not rigid material shells with one fixed temperature and thickness.

The corona is dilute yet can be much hotter than the visible photosphere. Temperature describes a particle distribution under the adopted thermal description; density describes how much material occupies a volume. A hotter region need not contain more particles or emit more radiation in every instrumental band.

The preceding stellar-interior chapter supplies the background on the hidden energy-producing interior. Here the question is more specific: what do atmospheric observations constrain, and how do instruments and plasma models connect an arriving signal to physical conditions?

Wavelength and opacity change what contributes

Opacity measures how strongly material removes radiation from a beam by absorption or scattering. An optically thick signal can be weighted toward regions from which radiation can escape. An optically thin line of sight can instead combine emission from separated structures. The appropriate description depends on the wavelength, material and geometry.

Some coronal diagnostics use an optically thin thermal-plasma model. Their channel response can depend on temperature, ion populations, abundances and calibration. That conditional treatment should not be extended automatically to every chromospheric or photospheric signal.

A passband is a range of wavelengths accepted with a specified sensitivity. Its integrated brightness is not a label attached to one geometric height. Foreground and background material, multiple temperatures and unresolved structures can contribute to the same apparent pixel.

Line ratios and combinations of channels add constraints, but their interpretation still depends on response functions and physical assumptions. A spectral-line strength is not an abundance measurement alone: excitation, ionization, opacity and other atmospheric conditions can also matter.

Different mixtures can give the same first signal

A forward model starts with a physical description and predicts an observable. Construct an original noiseless two-component model for optically thin emission with fixed calibrated responses. In the adopted optically thin thermal-plasma description, emission measure is the integral of squared electron number density along the line of sight through the emitting material. A component can collect contributions assigned to a chosen temperature interval; its amount is not itself a temperature. Let a = X₁/E₀ and b = X₂/E₀ be nonnegative amounts of two selected emission-measure components, where E₀ is a chosen common emission-measure unit. They are component amounts, not temperatures.

Let s₁ = S₁/I₀ and s₂ = S₂/I₀ be two calibrated signals in a chosen signal unit I₀. Stipulate s₁ = a + 0.25b and s₂ = 0.2a + b. Before normalization, each response coefficient has units I₀/E₀, so adding the contributions gives compatible signal units.

Mixture A has (a,b) = (4,1), giving signals (4.25,1.8). Mixture B has (1,13), giving (4.25,13.2). Both produce exactly the same first-channel signal even though the component mixtures differ substantially.

The coefficients and values are invented for this calculation. They are not responses or observations from a named solar instrument. The example establishes a concrete information limit: one supplied channel equation does not determine these two component amounts.

An inverse answer depends on the model being solved

An inverse problem uses observables to infer the underlying description. In this exact two-unknown model, the second channel supplies independent information: the response-matrix determinant is 1 × 1 − 0.25 × 0.2 = 0.95, which is nonzero.

For signals s₁ = 4.25 and s₂ = 1.8, eliminate a by subtracting 0.2s₁ from s₂. This gives 0.95b = 0.95, so b = 1 and then a = 4. The exact model recovers mixture A from its two exact signals.

A real line of sight need not contain only two predefined components. In a differential emission-measure description, emission is distributed over temperature and the instrument samples response-weighted integrals of that distribution. Finite channels, uncertain responses and measurement noise can leave many plausible distributions.

Extra assumptions or regularization can stabilize an inference, but they also shape what is recovered. Successful inversion of the exact small teaching system does not prove that two real images uniquely determine a continuous atmospheric temperature structure.

A hot corona requires an energy explanation

Describing the temperature distribution and explaining its maintenance are related but different tasks. An atmospheric energy account includes input, transport, radiation, conduction and outflow as appropriate. The high coronal temperature cannot be explained solely by naming the regions in outward order.

Magnetic motions, waves and changes of magnetic connectivity are investigated as parts of coronal energy transfer and heating. Their relative contributions must be assessed for particular structures and conditions. A single bright channel image does not identify one universally established heating mechanism.

A defensible comparison records what was measured, the calibration relation and uncertainty, wavelength response, observing time, location and adopted plasma assumptions. Calibration connects indications with reference values under stated conditions; it does not remove physical model uncertainty.

The useful habit is to keep three questions explicit: which atmospheric material can contribute, what observable the instrument records, and what additional information is needed for the desired inference. The next lessons follow magnetic activity and outflow beyond this atmospheric starting point.

Worked examples

Try the reasoning

1. Does describing solar material as plasma require every atmospheric atom to be fully ionized?

   Show the answer and reasoning

   No.

   Ionization varies with conditions; charged and neutral components can coexist.

2. Does one passband brightness automatically identify one unique geometric height?

   Show the answer and reasoning

   No.

   Opacity, response, line-of-sight structure and formation conditions determine which material contributes.

3. What second-channel signal does mixture B produce in the stipulated model?

   Show the answer and reasoning

   13.2 in units I₀.

   s₂ = 0.2 × 1 + 13 = 13.2. This differs from A’s 1.8 despite their equal first-channel signal.

4. Does solving two exact toy equations prove that two real images uniquely determine every coronal temperature component?

   Show the answer and reasoning

   No.

   Real response uncertainty, noise and a much larger or continuous unknown distribution change the inverse problem.

What to carry forward

• Solar atmospheric regions organize changing plasma conditions, without rigid universal boundaries.
• An instrumental signal combines physical emission, geometry, opacity and calibrated response.
• A forward model and an inverse inference require explicit assumptions; more channels do not automatically remove every ambiguity.