Wien approximation

The Wien approximation is a formula that approximates black-body radiation, converging to the true value (the Planck function) at shorter wavelengths, i.e., a good approximation of one of the two tails of the spectrum. The Wien approximation has the advantage of being a simpler function, easier to manipulate algebraically and to incorporate into formulae describing astronomical phenomena. It consists of the Planck function with the denominator's "subtraction of 1" removed: at short wavelengths, this fraction is quite small and such a modification to the denominator affects the total only slightly. The Wien approximation and the Rayleigh-Jeans law are analogous, each approximating one end of a black-body spectrum. The Wien approximation formula (in the form based on frequency):

• B(ν,T) - spectral radiance (specific intensity).
• ν - frequency.
• h - Planck constant.
• T - temperature.
• c - speed of light in a vacuum.
• k_B - Boltzmann constant.

         2hν3    1
B(ν,T) = ———— ————————
          c2  ehν/(kBT)

(Sometimes the equation is cited including π as an additional factor: this form produces the total energy per unit area of the black body per wavelength or frequency, i.e., the spectral flux density it produces.)

Much of astrophysics uses the term intensity for the quantity of radiation emitted through a surface into a given solid angle, specific intensity being the intensity at a given wavelength or frequency. More common terms for these, in other sciences (including other astrophysics), are radiance and spectral radiance.