AC03 · Light through a stellar layer

Stellar Absorption Lines

Why does the same spectral line deepen, broaden or move? A line shifts when the gas moves along our view. Its depth depends on how much light the gas absorbs and emits, and its width reflects atomic motion and the instrument. Once the center saturates, extra absorbers mainly widen the line.

Drag the glowing atmosphere to change its motion. Warm the layer, add absorbing atoms and watch the same two lines emerge in a calibrated detector strip.

Radial velocity $12.0\,\mathrm{km\,s^{-1}}$

Total equivalent width $12.0\,\mathrm{pm}$

Layer / background brightness $0.201$

Strong-line center $500.020\,\mathrm{nm}$

Change the stellar layer

Layer temperature

4500

T\;[\mathrm K]

Absorber column scale

1

N/N_0

Radial velocity

12

v_r\;[\mathrm{km\,s^{-1}}]

Resolving power

60000

R=\lambda/\Delta\lambda_{\mathrm{FWHM}}

Drag the gold motion handle below the layer. Positive velocity moves both lines toward longer wavelengths.

What column scale means

Column scale counts this model’s fixed ion population per area, relative to a chosen reference. Temperature changes its four-level populations, net absorption and source brightness. Real elemental abundances also require ionisation and atmospheric structure.

Read the stellar-spectra course

Model assumptions

A uniform plane-parallel LTE slab lies in front of a 6000-kelvin blackbody, viewed along its normal. The two artificial transitions have vacuum rest wavelengths of 500 and 500.12 nanometres, an atomic mass of 56 atomic mass units, a four-level LTE reservoir with unit statistical weights. The common lower level lies two electronvolts above ground; each upper level is separated from it by the photon energy of its own transition. Net absorption includes stimulated emission. The ion stage is held fixed. Column scale multiplies a prescribed reference opacity; it is not an elemental abundance. The line source function is the Planck function at the slab temperature. Thermal and prescribed microturbulent Gaussian broadening are included, followed by a normalized Gaussian instrument response. Rotation, pressure wings, scattering, non-LTE populations, depth gradients and disk integration are omitted. Ray positions, colors, atmosphere thickness and motion are schematic; the spectrum intensity is calculated. The narrow wavelength band uses exaggerated display colors.

Intensity divided by the background continuum

I_\lambda/I_{\lambda,c}

Equivalent width of both lines; negative means emission

W_\lambda=\int(1-I_\lambda/I_{\lambda,c})\,d\lambda\quad[\mathrm{pm}]

Transfer law and fixed approximations

\frac{I_\lambda}{I_{\lambda,c}}=e^{-\tau_\lambda}+\frac{B_\lambda(T)}{B_\lambda(6000\,\mathrm K)}(1-e^{-\tau_\lambda})

The line opacity is the sum of two Gaussian transitions with strengths one and 0.42. Their fixed ion stage has a four-level LTE reservoir with upper-minus-lower energies matched to the photon wavelengths and net opacity including stimulated emission; the mass is 56 atomic mass units and microturbulent speed is two kilometres per second. No real atomic abundance is fitted. The first-order Doppler shift is used within sixty kilometres per second.

Krumholz, radiative transfer I: equations 24–28 · NRAO, transfer and LTE source function

Start with the essentials

Focus question: What happens when the absorbing layer becomes as hot as the background?
One-sentence intuition: A layer makes an absorption line only when its source brightness is lower than the background along the same ray.

Core mathematical model

Absorption and emission through one layer

I_\lambda=I_{\lambda,c}e^{-\tau_\lambda}+B_\lambda(T)(1-e^{-\tau_\lambda})

Optical depth is measured along the outward normal ray. The first term is transmitted background light; the second is emission by the uniform LTE layer.

Moving the line

\lambda_c\simeq\lambda_0(1+v_r/c)

Radial velocity is positive away from the observer. The model uses a first-order shift at speeds much smaller than light speed.

The missing area

W_\lambda=\int\left(1-\frac{I_\lambda}{I_{\lambda,c}}\right)d\lambda

The area is expressed as a width in wavelength. Emission gives a negative value under this convention.

Common difficulties

A deeper line and more atoms

Typical misconceptionDoubling the number of absorbers always doubles the line depth.

Better mental modelA saturated center already receives almost none of the background. Extra absorbers broaden the opaque part; the layer still emits its own light.

Run the experiment

01
Saturate the center
Compare Cool absorbing layer with The center saturates.
What to observe: The center stops deepening rapidly while the wings widen. The growth curve bends.
02
Move both lines together
Drag the gold handle below the layer, then choose The whole pattern shifts.
What to observe: Both centers shift by the same fractional wavelength; their fixed separation still identifies the pattern.
03
Replace absorption with emission
Warm the layer through six thousand kelvin or choose A hotter layer emits.
What to observe: The line first disappears when both source brightnesses match, then becomes bright.

Stellar Absorption Lines

Depth, width and motion leave different clues

What a dark line tells us

Core mathematical model

Absorption and emission through one layer

Moving the line

The missing area

Common difficulties

A deeper line and more atoms

Run the experiment

Saturate the center

Move both lines together

Replace absorption with emission

Related experiments and articles

Measuring the sky

Reading stellar absorption lines