Absorbed starlight becomes infrared light

Interstellar Dust Heating and Polarization

Where does the light blocked by a dust cloud go? Dust absorbs starlight and radiates the energy at longer wavelengths. Its illuminated face is warmer than its shielded interior. Aligned grains absorb the two electric-field directions differently; along the same viewing direction, transmitted and thermal light favor perpendicular polarization axes.

Move an illuminated cloud and its prescribed alignment direction. Follow the same absorbed power into grain temperatures, infrared emission and polarization.

Stellar power intercepted $f_{\rm abs}=0.344\%$

Mass-weighted grain temperature $\langle T\rangle_M=51.4\,\mathrm K$

Observer thermal linear polarization $p=28.8\%$

Omitted infrared absorption bound $\epsilon_{\rm IR}\le 0.0653\%$

Follow absorbed light into heat

Stellar luminosity

300

L_\star/L_\odot

Dust mass

0.500

M_{\rm d}/(10^{-3}M_\odot)

Star-to-cloud centre distance

0.114

d/\mathrm{pc}

Alignment inclination to the observer

90.0

\vartheta_B/{}^\circ

Drag the cloud centre or the purple direction handle. Moving inside the direction disk also changes the component out of the scene plane.

Accepted default cloud; absorbed power and thermal image are available.

Alignment and model limits

Sky azimuth of the alignment

0^\circ

\varphi_B/{}^\circ

Prescribed absorption anisotropy

0.350

\eta

Static prescribed density, absorption-only equilibrium large grains and a fixed stellar spectrum. Alignment is an input. There is no scattering, RAT evolution, stochastic PAH heating or dynamical clock.

Infrared escape and omitted CMB heating have explicit bounds. Outside the warm/thin model, the last accepted state stays visible. Sampled convergence evidence does not prove one error bound over every continuous setting.

The source marker is enlarged. Cloud points show computed temperature and mass, while the image below uses the fixed far-field observer.

Temperature colors saturate outside $30\text{–}80\,\mathrm K$ ; point area is proportional to cell mass.

The direction glyph represents a unit axis. Its projected length is an out-of-plane effect, not field strength.

Recompute the separate real-photometry exercise

Model assumptions

A static compact ellipsoid and a fixed stellar spectrum define the source. Positive anisotropic absorption attenuates two transverse modes; the removed power heats the same cell masses, whose checked equilibrium temperatures produce directional thermal Stokes spectra and images. This is an absorption-only equilibrium large-grain teaching material, separate from the native Astrodust reference. Alignment is prescribed, with no RAT evolution, MHD feedback, scattering, spinning dust or stochastic PAHs. Thermal self-absorption and the CMB are omitted only below saved bolometric/heating bounds; unsupported candidates retain the last accepted state. The production grid is independently compared on fixed and continuous sampled inputs; those samples are not a uniform error theorem. The observer uses fixed distant parallel rays, independently of the physical scene projection. The source marker is enlarged; cloud points visualize quadrature masses and computed temperature, while the separate PSF image is actual integrated flux. Real galaxy photometry belongs to a separate conditional observer-frame colour exercise, without inferred physical dust mass or a unique three-dimensional field.

The same accepted cloud in light and heat

The scene projects physical $x,z$ ; the fixed observer image uses the sky plane $x,y$ with light propagating along $+z$ .

Source, absorbed power and thermal emission

Gold: incident source. Blue: power deposited in this cloud. Pink: emission from the same cells. The curves are power per logarithmic frequency.

Fixed-observer thermal image and electric-field axes

Brightness is stretched for display. White bars show thermal electric-field orientation; their lengths do not encode polarization fraction.

The observer is fixed independently of the scene. These are model fluxes from accepted cells, with a declared Gaussian PSF; real galaxy photometry is a separate saved-data tutorial. Export contains the same inputs, arrays, spectra, map and physical bounds.

Start with the essentials

Focus question: How do cloud position and grain alignment change the same absorbed and emitted light?
One-sentence intuition: The light removed from each source ray heats the same cell mass that later emits. Along one specified viewing direction, alignment makes transmitted and thermal polarization favor perpendicular axes.

Core mathematical model

Two absorbing directions

I_j^{\rm out}=I_j^{\rm in}e^{-\Sigma\kappa_j}

Each transverse polarization mode has an absorption opacity per dust mass. Dust column and opacity set its transmitted fraction.

Equilibrium of the same cell

P_{\rm abs}=4\pi m\int_0^\infty\frac{\operatorname{tr}\boldsymbol\kappa_\nu}{3}B_\nu(T)\,d\nu

The removed source power sets the cell temperature. Cooling sums emission over every direction, using the tensor angular mean rather than one observer ray.

Linear polarization

p=\frac{\sqrt{Q^2+U^2}}{I}

Intensity and the two signed linear components come from the same observer image. A zero projected preference gives zero linear polarization.

Common difficulties

The point colours are temperatures

Typical misconceptionThe cloud-point colours are a measured infrared photograph.

Better mental modelThe physical scene colours the calculated cell temperatures. The image in the separate data row integrates those cells’ directional emission through a fixed PSF.

Alignment is prescribed

Typical misconceptionMoving the direction tip solves magnetic alignment or measures field strength.

Better mental modelThe direction and anisotropy are inputs to a positive absorption tensor. The calculation follows their radiative consequences; it does not evolve RAT alignment or the gas.

Run the experiment

01
Look for the warm face
Start with A warm illuminated face. Follow the gold source rays and compare cell colours on the near and shielded sides.
What to observe: The spectrum separates the incident star, the power absorbed here and the radiation emitted by the same cells.
02
Move the actual cloud
Drag the cloud centre toward the star, then change dust mass. Watch temperature and intercepted power together.
What to observe: Distance changes illumination. More mass changes columns and shielding as well as the amount of emitting material.
03
Turn a real direction
Drag the purple tip or choose Turn the polarization axes. Then choose Alignment along the line of sight.
What to observe: Thermal electric-field bars rotate with the projected anisotropy. Their projected preference vanishes along the observer direction.
04
Read the accepted state
Try a large mass and bright source, then export. If the thin/warm limits reject the request, compare the displayed accepted inputs with the rejected request.
What to observe: Scene, spectra, image and export keep the same accepted cell arrays. A numerical temperature root alone does not justify omitting reabsorption.

Interstellar Dust Heating and Polarization

The same accepted cloud in light and heat

Follow light into a warm cloud

Core mathematical model

Two absorbing directions

Equilibrium of the same cell

Linear polarization

Common difficulties

The point colours are temperatures

Alignment is prescribed

Run the experiment

Look for the warm face

Move the actual cloud

Turn a real direction

Read the accepted state

Related experiments and articles

Interstellar dust, infrared light and polarization