AC30 · Light scattered by an expanding wind

Stellar Wind P Cygni Lines

Why does a stellar wind remove blue light and add scattered emission? Gas moving toward us removes blue-shifted light from the stellar disk. Scattering sends photons into our sight from the wider wind, adding emission on both sides of the line. The star and observing aperture intercept part of that light.

Drag the wind-speed marker and the collecting aperture. Watch the same expanding gas absorb and scatter light into a saved P Cygni spectrum.

Actual speed at the wind boundary $v_{\rm out}=176\,\mathrm{km\,s^{-1}}$

Saved spectrum’s absorption-positive area $W_v=14.8\,\mathrm{km\,s^{-1}}$

Model scattered photons captured $f_{\rm cap}=79.7\%$

Model scattered photons returned to the star $f_{\rm back}=20.3\%$

Change the flow and its spectrum

Asymptotic terminal speed

200

v_\infty,/,\mathrm{km\,s^{-1}}

Shape of the acceleration zone

1.00

\beta_{\rm w}

Mass-flow scale at fixed reference opacity

1.00

\dot M/\dot M_{\rm ref}

Collecting aperture radius

8.00

p_{\rm ap}/R_\star

Drag the wind-speed arrow or the collecting aperture. The spectrum below comes from the saved photon observation.

The default photon observation is already saved.

Opacity assumptions and numerical scope

Relative ion / opacity multiplier

1.00

\begin{aligned}\rho&=\frac{\dot M}{4\pi r^2v}\\[4pt]\tau&=\frac{\kappa_V\rho}{\mu^2v^\prime+(1-\mu^2)v/r}\end{aligned}

The speed law is prescribed. The one-line force is checked separately, and does not sustain this flow. Intrinsic line width is zero; the fixed 8 km/s Gaussian belongs to the detector.

Read and replay the original IUE observations

Model assumptions

A stationary spherical monotonic beta velocity law is prescribed; density follows mass continuity. A single isolated zero-intrinsic-width resonance line uses isotropic conservative Sobolev scattering, finite-star illumination and local multiple-interaction escape probabilities. The opaque photosphere intercepts returning photons; an aperture containing the full stellar disk can lose halo emission. This is a line-formation calculation, not a hydrodynamic or self-consistent radiation-driven wind. The computed one-line force remains far below the force required by this prescribed flow for the illustrative continuum and opacity. Instrumental Gaussian sigma is fixed at 8 km/s; it is not wind thermal/turbulent width. Photon intensity is convolved and binned before synthetic Poisson counting. Actual IUE observations are separately fixed, vacuum/heliocentric and masked by native quality flags; their FN noise is not a physical-flux error vector. Reference opacity and ion fraction are assumptions, so no true mass-loss posterior is inferred. Nonmonotonic velocities, overlapping doublets, realistic phase functions, polarization, non-LTE populations, clumps/velocity gaps, continuum opacity and thermal photon creation are omitted. The finite wind is a bounded line-forming volume; its outer speed differs from asymptotic terminal speed. Particle weights, velocity arrows and playback time are schematic.

The same flow leaves a saved photon spectrum

Blue points are saved synthetic counts. The pale curve is the separate zero-width wind profile; orange includes the fixed instrumental response.

Saved observation and declared detector expectation

Where the scattered photons go

Fixed original IUE spectra; native orders stay separate

Blue: order 83. Orange: order 82. Dashed markers: MgII laboratory vacuum wavelengths.

Vertical scale unit: $10^{-11}\,\mathrm{erg\,cm^{-2}\,s^{-1}\,\mathring A^{-1}}$

The default observation is saved and analyzed.

Force mismatch, quality flags and sources

The one-line force is compared with the acceleration and gravity required by this prescribed flow. It is far too small to sustain the wind; no hydrodynamic solution is inferred.

Conditional line force divided by required force

LWP15586 · 24 May 1989 · 239.493 s. Orders 83/82 retain vacuum heliocentric wavelengths, independent overlap and QUALITY==0 gaps. FN noise is not a calibrated physical-flux uncertainty.

The real observations stay fixed when wind controls move. MgII is a doublet with stellar/interstellar structure; SiIV is strongly blended. The toy singlet is a mechanism comparison, with no fitted true mass loss.

Read the original observations and offline reproduction

Start with the essentials

Focus question: Which photons disappear behind the star, and which miss a small aperture?
One-sentence intuition: The front wind can absorb the stellar disk, while a wider volume scatters photons into our sight. Star occultation and aperture loss affect those paths differently.

Core mathematical model

Density from steady mass flow

\rho(r)=\frac{\dot M}{4\pi r^2v(r)}

The same mass crosses every spherical shell per unit time. Faster flow spends less time in a shell, reducing its density at fixed mass flow.

Directional resonance gradient

\tau(\mu,r)=\frac{\kappa_V\rho}{\mu^2v^\prime+(1-\mu^2)v/r}

The gradient contains radial acceleration and the changing projection of a spherical flow. A tangential ray cannot use the radial derivative alone.

Transmission and scattered light

I_{\rm out}=I_{\rm in}e^{-\tau}+S(1-e^{-\tau})

The source function is calculated from finite-star illumination and local Sobolev escape probabilities. The two terms then give transmitted and scattered photons on the same ray.

Common difficulties

An absorption trough does not destroy every photon

Typical misconceptionEvery missing blue photon is destroyed by the gas.

Better mental modelConservative resonance scattering changes direction. Some photons reach the observer from the halo, some return to the opaque star and some miss the aperture.

A deep line is not a unique mass-loss measurement

Typical misconceptionA single trough depth gives the true mass-loss rate.

Better mental modelIon fraction and line opacity multiply mass flow. Saturation can also hide additional material, so the model keeps these assumptions explicit.

Run the experiment

01
Find the front resonance
Start with Blue absorption, scattered emission. Follow the highlighted front-side ray and compare the separate saved spectrum.
What to observe: The approaching front wind attenuates a stellar-disk ray. Off-disk gas contributes scattered emission.
02
Let the aperture lose light
Drag the amber aperture handle inward, keeping the full stellar disk inside.
What to observe: The local wind and source function stay the same. Halo emission drops while the stellar continuum remains, deepening the net absorption area.
03
Change speed and opacity together
Drag the blue velocity arrow outward. Compare the Doppler span, density tracers and saved spectrum.
What to observe: At fixed mass flow, greater speed lowers density and changes the resonance gradient. The line changes depth as well as width.
04
Separate line formation from wind launch
Open the force diagnostic and compare the one-line force with the force required by the prescribed flow.
What to observe: The illustrative one-line force is far too small. The displayed velocity law is a prescribed input, so this calculation explains line formation rather than solving wind acceleration.

Stellar Wind P Cygni Lines

The same flow leaves a saved photon spectrum

Follow a resonance photon through an expanding wind

Core mathematical model

Density from steady mass flow

Directional resonance gradient

Transmission and scattered light

Common difficulties

An absorption trough does not destroy every photon

A deep line is not a unique mass-loss measurement

Run the experiment

Find the front resonance

Let the aperture lose light

Change speed and opacity together

Separate line formation from wind launch

Related experiments and articles

Reading a stellar wind