Flux Version
Edit
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}}) $
- $ F _{abs} $ is the actual flux coming from the object
Absolute flux is defined as:
$ F _{abs} = \frac {L}{4 \pi ({10pc})^2} $
Luminosity Version
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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}}) $