Vol. Science · Astronomy · Star color

Blackbody
heat and color

A hot dense surface shines with a continuous spectrum. Planck’s law gives the shape, B_λ(T). Wien’s law puts the peak at λ_max = b/T. Stefan–Boltzmann gives the power: surface flux σT⁴, and luminosity L = 4πR²σT⁴. Slide the temperature and a radius in solar radii. The curve, the peak, and the luminosity move together. The same temperature ladder is the color lesson on the stars desk. How bright that light looks from Earth is magnitude. The wavelength ladder itself is the electromagnetic spectrum.

Classroom schematic. The curve is a perfect blackbody. NASA’s Webb caption says stars are not perfect blackbodies, and that the blackbody curve still describes the overall shape quite well. Absorption lines are missing here. The shaded band is the NASA Imagine classroom optical window, about 400–700 nm, the same cut as the EM spectrum desk. The color chip is an sRGB approximation of the chromaticity: it depends on the display and the eye, and it is not the star’s luminance. City light that hides faint red stars is the light-pollution desk. Not a stellar-atmosphere model and not a catalog.

Interactive · Curve, peak, and luminosity

Log wavelength · curve normalized to its peak · visible band shaded

B_λ / peak
Wien peak
400–700 nm

Cited presets · uncertain ones say so

Temp K

Radius R☉

The sliders need JavaScript. The cited anchors are still below. Wien’s constant is the CODATA value 2.897771955… × 10⁻³ m·K. The IAU 2015 nominal Sun is 5772 K and 1 R☉ = 6.957 × 10⁸ m. Proxima Centauri is 2980 ± 80 K and 0.146 ± 0.007 R☉ (Ribas et al. 2017). Vega’s mean temperature is 9560 ± 30 K and its equatorial radius is 2.75 ± 0.01 R☉ (Hill, Gulliver, and Adelman 2010). Rigel is 12,100 ± 150 K and 78.9 ± 7.4 R☉ (Moravveji et al. 2012). Betelgeuse is 3500 ± 200 K and 887 ± 203 R☉ (Dolan et al. 2016). The visible window shaded on the figure is about 400–700 nm.

Why the colors run that way

Blue-white is hot. Orange-red is cool.

Wien’s law slides the peak to shorter wavelengths as the temperature rises. A 40,000 K curve peaks in the ultraviolet. The visible window, about 400–700 nm, sits on the long-wavelength side, where the curve is falling toward the red. That slice has more blue than red, so the star reads blue-white even though most of the energy is invisible. A 2,000 K curve peaks in the infrared. The same window is then the short-wavelength tail, rising steeply toward the red, so blue is scarce and the star reads orange-red.

The nominal Sun, 5772 K, peaks near 502 nm. That is green. The disk is not green, because the curve is broad and the eye mixes the whole band. NASA’s Webb illustration makes the same point with round temperatures: an 8,000 K star looks bluer than a 3,000 K star. Those two figures are the illustration’s, not the presets on this page.

A real spectrum only approximately follows the curve. Atoms and ions in the atmosphere cut absorption lines out of the continuum. Vega is a fast rotator seen nearly pole-on, so one temperature was never the whole star. Betelgeuse’s radius is uncertain by about a quarter. The chip is a further approximation: sRGB on this display, at a comfortable brightness, with no absorption lines.

Literacy · the words on the curve

Planck’s law: B_λ(T) = 2hc²/λ⁵ / (e^hc/λkT − 1). Spectral radiance per wavelength of a perfect blackbody. h, c, and k are the defined SI constants. The curve on this page is that function, divided by its own peak so the shape stays on the canvas. Absolute power is the flux and luminosity readouts, not the height of the line.
Wien’s law: λ_max T = b. CODATA lists b = 2.897771955… × 10⁻³ m·K, exact. This desk computes b from hc/k divided by the root of (5 − x)e^x = 5. Hotter means a shorter peak.
Stefan–Boltzmann: Surface flux is σT⁴. Luminosity is 4πR²σT⁴. σ = 2π⁵k⁴ / (15h³c²) = 5.670374419… × 10⁻⁸ W m⁻² K⁻⁴, the CODATA exact value. This is the flux at the surface, not the sunlight at Earth.
Two solar luminosities: L / L☉ formula divides by the same expression at the IAU nominal solar radius and nominal effective temperature, so the Sun preset reads 1. L / L☉ nominal divides by the IAU nominal luminosity, 3.828 × 10²⁶ W. At those nominal inputs the two agree at the digits this desk prints.
Visible window: The shade is 400–700 nm, the NASA Imagine classroom optical band. The color integral uses the CIE 1931 2° color-matching functions from 360 to 830 nm, every 5 nm of the CIE 2019 table, which is a wider cut than the shade.
Color chip: The blackbody spectrum is weighted by those color-matching functions, converted with the IEC 61966-2-1 sRGB primaries and transfer function, and scaled so the brightest channel fills the chip. That throws away luminance on purpose. If a channel would have gone negative, it is clipped and the caption says so. Perceived color still depends on the display and the eye.

Sources · CODATA, IAU, CIE, NASA, and the papers

Cited, not invented

NIST CODATA — Wien wavelength displacement law constant — b = 2.897771955… × 10⁻³ m·K, exact. The ASCII table is allascii.txt.
NIST CODATA — Stefan–Boltzmann constant — σ = 5.670374419… × 10⁻⁸ W m⁻² K⁻⁴, exact, from the defined h, c, and k. This desk computes σ = 2π⁵k⁴ / (15h³c²) and b from the Wien root, using h = 6.62607015 × 10⁻³⁴ J·s, c = 299792458 m/s, and k = 1.380649 × 10⁻²³ J/K.
IAU 2015 Resolution B3 (Prša et al. 2016, AJ 152, 41) — nominal solar radius 6.957 × 10⁸ m, nominal solar luminosity 3.828 × 10²⁶ W, nominal solar effective temperature 5772 K. Conversion constants, exact, not a measurement of the Sun. The resolution text is also at the IAU archive.
NASA Imagine the Universe — Wavelength, frequency, and energy — classroom optical band about 400–700 nm. The same chart is the visible slice on the EM spectrum desk. Boundaries are conventions.
CIE 2019 — colour-matching functions of the CIE 1931 2° standard observer (DOI 10.25039/CIE.DS.xvudnb9b, from CIE 018:2019 Table 6). This desk samples that 1 nm table every 5 nm from 360 to 830 nm.
IEC 61966-2-1:1999 — sRGB primaries (red 0.6400, 0.3300; green 0.3000, 0.6000; blue 0.1500, 0.0600), D65 white (0.3127, 0.3290), and the transfer function. The readable restatement this desk follows is the W3C CSS Color Module account of sRGB.
NASA / ESA / CSA — Continuous spectra (blackbody curves) of stars — an 8,000 K star looks bluer than a 3,000 K star. Stars are not perfect blackbodies; the curve still describes the overall shape quite well. Those two temperatures are the illustration’s examples.
NASA / ESA / CSA — Types of spectra — a stellar continuum, and absorption lines where gas removes wavelengths. The Hubble glossary defines a blackbody as the model, and an absorption line as a dark cut in a continuous spectrum.
Ribas et al. 2017, A&A 603, A58 — Proxima Centauri: T_eff = 2980 ± 80 K, R = 0.146 ± 0.007 R☉, L = 0.00151 ± 0.00008 L☉.
Hill, Gulliver, and Adelman 2010, ApJ 712, 250 — Vega: mean T_eff = 9560 ± 30 K, equatorial radius 2.75 ± 0.01 R☉, polar radius 2.40 ± 0.02 R☉, polar T_eff = 10,000 ± 30 K, pole-to-equator drop 1410 K, luminosity 44 ± 2 L☉. Seen nearly pole-on.
Moravveji et al. 2012, ApJ 747, 108 — Rigel: T_eff = 12,100 ± 150 K (Przybilla et al.), R = 78.9 ± 7.4 R☉ from the Aufdenberg et al. 2008 angular diameter and the Hipparcos distance, and log(L/L☉) = 5.08 with uncertainties +0.07 and −0.10. The radius error is mostly the distance.
Dolan et al. 2016, ApJ 819, 7 — Betelgeuse, adopted: T_eff = 3500 ± 200 K, R = 887 ± 203 R☉, log(L/L☉) = 5.10 ± 0.22. The radius uncertainty follows the distance 197 ± 45 pc in Harper, Brown, and Guinan 2008, AJ 135, 1430.

Classroom picture of a blackbody. λ_max = b/T with the CODATA constant. L = 4πR²σT⁴, compared with the same formula at the IAU 2015 nominal Sun. The chip is an sRGB approximation. Real stellar spectra have absorption lines. Not a catalog. Earthrise preview: NASA / Bill Anders (public domain).

Keep going

Letters

Axes	Wavelength is logarithmic, from 50 nm to 3,000 nm. Height is B_λ divided by its peak, so every temperature fits the frame. Absolute power is in the readouts.
Shade	400–700 nm, the NASA Imagine classroom optical window.
Peak	A mark at λ_max = b/T. The readout is in nanometres.

Temperature	Log slider from 2,000 K to 40,000 K. The number field accepts the same range. Arrow keys nudge the slider.
Radius	Log slider from 0.05 to 1,500 solar radii. Luminosity uses L = 4πR²σT⁴ with the IAU nominal solar radius.
Presets	Sun, Proxima, Vega, Rigel, Betelgeuse. Each button sets a cited temperature and radius. Uncertain ones say so in the note. Left and Right move through the buttons when one of them has focus.
Custom	Moving a slider or typing a value leaves the preset. The note then describes the blackbody, not a named star.

Surface flux	σT⁴ in watts per square metre, at the surface. Not the solar constant at Earth.
L / L☉ formula	Divided by the same formula at 5772 K and 1 nominal solar radius. The Sun preset is 1.
L / L☉ nominal	Divided by 3.828 × 10²⁶ W, the IAU nominal luminosity. At the Sun preset it matches the formula ratio at the printed digits.
Chip	sRGB chromaticity. Scaled to the screen. Clipped channels are labeled. Not a photograph of the star.

Sliders	Arrow keys nudge the focused slider. The number field is where a cited figure is typed exactly.
Buttons	Enter or Space selects. Left and Right step through the presets. The pressed button is aria-pressed.
Touch	Buttons, the question mark, Close, and the fields are at least 44 pixels on a side.
This dialog	The question mark, or ?, opens it. Escape closes it. Tab stays inside until you close it. Click the dim page behind the card to close it.

Blackbody
heat and color

Blue-white is hot. Orange-red is cool.

Cited, not invented

Stars

Magnitude

Nearest stars

EM spectrum

Light pollution

Solar map

Blackbody desk

The curve

Controls

Readouts

Keyboard and touch

Blackbodyheat and color

Blue-white is hot. Orange-red is cool.

Cited, not invented

Stars

Magnitude

Nearest stars

EM spectrum

Light pollution

Solar map

Blackbody
heat and color