black-body radiation

Black-body radiation is a kind of thermal radiation (aka thermal emission, electromagnetic radiation (EMR) from a body due to its heat), specifically that from a body that is in thermodynamic equilibrium, which implies a constant, uniform temperature. It is a continuum emission, i.e., producing continuous spectrum, with a specific shaped spectral energy distribution (SED), dependent only on the temperature of the body (a black-body spectrum). The SED is "hill-shaped", its peak at a wavelength calculable from the temperature by Wien's displacement law. Planck's law (Planck function) describes the whole spectrum:

I(ν,T) = 2hν3/c2 × 1/(ehν/(kT)-1)

• I(ν,T) is power per unit area per solid angle in normal direction.
• h - Planck constant.
• c - speed of light in a vacuum.
• k - Boltzmann constant.
• ν - frequency of the electromagnetic radiation.
• T - temperature of the body in kelvins.

The black-body spectrum represents an ideal case, given that thermodynamic equilibrium and uniform temperature is never perfect, but all materials produce radiation associated with their temperature. The ideal case and its equation represent a useful first approximation, e.g., for stars' spectra.

The terms Planckian and non-Planckian (NP) are used to describe an EMR source (or its spectrum) as adhering to the black-body spectrum or not. Thermal radiation from optically thin plasma diverges a bit from the black-body spectrum.

Given the temperature-dependent black-body spectrum with its hill and peak, particular bands have some association with the temperature of the source of radiation. Given two bodies of different temperatures, the one with a higher temperature has its peak at a shorter wavelength (though assuming the bodies are of the same size, the one with the higher temperature emits more energy at every wavelength). Extremely low temperatures produce a peak in the "radio" band, and extremely high temperatures in the "gamma ray" band. Below are the temperature ranges that place the peak (based upon the log of the wavelength) within each EMR band:

Black-body radiation from astronomical sources is typically infrared, visible light, or ultraviolet.