The magnitude calculated over all wavelengths is the bolometric magnitude. The formula for the absolute bolometric magnitude in terms of the solar radius is
Example: Calculate the absolute bolometric magnitude for Antares, a star with 800 times the solar radius and a temperature of 3,500 K.
| (6.1) |
The absolute bolometric magnitude of Antares is given here as -7.5. (Antares varies in luminosity, and its absolute bolometric magnitude is usually taken to be about -7.2.)
Example: Calculate the radius of Antares, given the bolometric magnitude (-7.2) and the temperature (3500).
| (6.2) |
This is an under-estimate. The radius of Antares is actually about 800 times the radius of the Sun. The outer layers of the star are being blown off, which makes calculating the radius difficult.
Example: Calculate the temperature of Rigil Kent (Alpha Centauri A), given the bolometric magnitude (4.35) and the radius (1.227 times the solar radius).
| (6.3) |
This is a slight overestimate. The temperature of Rigil Kent is generally taken to be 5,790 K.