Absolute Magnitude

Flux Version
The absolute magnitude of an object is the apparent magnitude the object would have if it were 10 parsecs away.

$$m _{abs} - m _{vega,abs} = -2.5log_{10}(\frac {F _{abs}}{F _{vega,abs}})$$

Absolute flux is defined as:
 * $$F _{abs}$$ is the actual flux coming from the object

$$F _{abs} = \frac {L}{4 \pi ({10pc})^2}$$

Luminosity Version
The apparent magnitude with respect to the object's luminosity is given by

$$m _{abs} - m _{abs,vega} = -2.5log_{10}(\frac {L _{obj}}{L _{vega}})$$