Surface brightness to luminosity

AI Thread Summary
The discussion focuses on the derivation of the surface brightness to solar luminosity conversion formula, specifically questioning the origin of the constant term 21.572. Participants note that the definition of magnitude and parsec is arbitrary, suggesting that the constant can be understood through logarithmic relationships of these definitions. There is a request for clarification on whether this constant is based on empirical observations or theoretical derivation. The conversation emphasizes the need for a deeper understanding of how these constants interact in the formula. Overall, the inquiry seeks to clarify the foundational aspects of the conversion process in astrophysics.
Warimi
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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
 
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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.
 

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