Surface brightness to luminosity

[Warimi]

Can anyone offer insight into the derivation of the surface brightness to solar luminosity conversion

S(mag/arcsec^2) = Mabs + 21.572 - 2.5log S (Solar luminosities/pc^2)

More or less my concern is the constant term, is it empirically observed value or is there a derivation for it?

thanks

 

[mfb]

The definition of magnitude and parsec are arbitrary, and if you take the log of those (multiplicative) constants and add everything you should get 21.572 in some way.