Bolometric magnitudes
 

When the properties of stars are being compared, it is advantageous to use a magnitude system which is independent of any particular detector system with its associated wavelength-selective property. It is useful to be able to know the brightness or magnitude of stars as they would be determined by a system which is equally sensitive to all wavelengths. For this purpose, a system known as the bolometric magnitude scale is frequently used. From a knowledge of the energy envelope of a star and the spectral response curve of the selective detector, it is possible to perform calculations so that the total amount of energy available for measurement by a bolometer can be predicted. In principle, any magnitude determination by a particular system can be converted to a bolometricmagnitude (m_bol) by the appropriate correction, known as the bolometric correction (BC). Thus, in general,

m_bol = m + BC
and, therefore,
BC = m_bol − m. (1)
Consider the bolometric correction in relation to the visual magnitude scale. namely
m = k − 2·5 log₁₀ B

Table 1. Bolometric corrections to V band magnitudes.

the bolometric magnitude scale can be represented as
m_bol = k_bol − 2·5 log₁₀ B_bol. (2)
Similarly, the visual band scale can be represented as
m_V = V = k_V − 2·5 log₁₀ B_V . (3)
In equation (2), kbol is an arbitrary constant while k_V in equation (3) has been chosen according to some suitable standard stars. Subtraction of equation (3) from (2) gives

mbol − mV = BC = kbol − kV − 2·5 log10 (Bbol/BV)(4)
 

The ratio Bbol/BV has a minimum value for a star with a temperature providing the maximum in its energy envelope at the same wavelength as the peak sensitivity of the selective detector. For the V -band system, this occurs when the temperature is close to 6500 K. The value of kbol is chosen so that the bolometric correction is zero for this temperature. Since Bbol/BV has a minimum value at this temperature, it is easy to demonstrate, using equation (4), that the bolometric correction is negative for stars with temperatures on either side of 6500 K. The bolometric corrections to V -band magnitudes are listed in table 1.