# Bolometric correction

In astronomy, a bolometric correction is a correction that must be made to the absolute magnitude of an object in order to convert an object's visible magnitude to its bolometric magnitude. Mathematically, such a calculation can be expressed:

$BC = M_b - M_v\!\,$

The following is subset of a table from Kaler[1] (p. 263) listing the bolometric correction for a range of stars. For the full table, see the referenced work.

Class Main Sequence Giants Supergiants
O3 -4.3 -4.2 -4.0
G0 -0.10 -0.13 -0.1
G5 -0.14 -0.34 -0.20
K0 -0.24 -0.42 -0.38
K5 -0.66 -1.19 -1.00
M0 -1.21 -1.28 -1.3

The bolometric correction is large both for early type (hot) stars and for late type (cool) stars. The former because a substantial part of the produced radiation is in the ultraviolet, the latter because a large part is in the infrared. For a star like our Sun, the correction is only marginal because the Sun radiates most of its energy in the visual wavelength range.

The bolometric correction scale is set by the absolute magnitude of the Sun and an adopted bolometric magnitude for the Sun. The choice of adopted solar absolute magnitude, bolometric correction, and absolute bolometric magnitude are not arbitrary, although some classic references have tabulated mutually incompatible values for these quantities .[2] The bolometric scale historically had varied somewhat in the literature, with the Sun's bolometric correction in V-band varying from -0.19 to -0.07 magnitude. Since the Sun is also a variable star, and there are minor differences in adopted solar luminosity values (albeit at a subtle level), in 1999 two IAU commissions (Commissions 25: Stellar Photometry and Polarimetry, and Commission 36: Theory of Stellar Atmospheres) agreed to separate the definition of bolometric correction and magnitude from the variable Sun. The 1999 IAU statements define that absolute bolometric magnitude zero correlates to a bolometric luminosity of 3.055e28 Watts. This particular luminosity was selected as the zero-point for the absolute bolometric magnitude scale so that the Sun's luminosity (3.842e26 Watts) would correspond to absolute bolometric magnitude 4.75 (the value that was most commonly used by most astronomers). As the Sun has an apparent V magnitude of -26.75, and absolute V magnitude of 4.82, then the IAU bolometric magnitude scale implies that the bolometric correction for the Sun (with effective temperature of 5778 K) is -0.07 magnitude.[3] The new IAU definition means that theoretical evolutionary models for stars can define brightnesses in terms of bolometric and absolute magnitudes on a scale that is tied to a physical quantity (the luminosity zero-point of 3.055e28 Watts) rather than to the Sun (which is intrinsically variable, and there are systematic uncertainties in the value of the solar flux constant as measured at 1 AU).