Blackbody Curves and Wien's Law

A blackbody curve is a graph showing how much radiation a blackbody (i.e. an ideal or 100% absorber and emitter of thermal radiation, or heat) will emit based on its temperature. All objects with a non-zero temperature will emit thermal radiation.

Cool objects like humans, planets, and brown dwarf stars emit infrared light (which has long wavelengths between 1 micrometer (10^-6 m) and a meter). Hotter objects like stars emit more visible light (wavelengths between 200 and 750 nanometers, or 2 * 10^-7 and 7.5 * 10^-7 m) than infrared light, while the hottest objects like massive stars and accretion disks around black holes (over 50,000 Kelvins) emit mostly ultraviolet light (wavelengths below 200 nanometers); far more than longer wavelengths. Because these hot objects emit mostly blue in the visible spectrum, they appear blue-hot. (We assume all of these objects are black bodies.)

A blackbody curve tells how much of each wavelength across the electromagnetic spectrum an object emits based on temperature. The peak wavelength, or the wavelength of light emitted the most by a black body, is the highest peak in these graphs.

Examples of black body curves for stars. Notice that for cool red stars like Antares, the peak wavelength is in the infrared; for the Sun, it is in the green part of the visible spectrum, while for blue hot stars it is in the ultraviolet part of the spectrum. Courtesy NASA/JPL-Caltech.

The peak wavelength can be determined by Wien's Law:

λ = b / T

Where λ is the peak wavelength in meters, b the proportionality constant of (2.897 771 955 * 10^-3 m * K), and T the temperature in Kelvins. See if you can find out the peak wavelengths for the five stars in the NASA/JPL picture above:

• Antares - 3,660 Kelvin (source)
• Sun - 5,772 Kelvin (IAU)
• Sirius A - 9,940 Kelvin (source)
• Spica A - 25,300 Kelvin (source)
• Gamma Velorum Ab - 57,000 Kelvin (source)

For reference, here is a table showing a number of star types and their peak wavelengths:

All Glory to God, and Happy 19th Dannyversary Danny Phantom!

4 April 2023