The alpha star in a constellation has the highest brightness, but does that mean it has the highest flux density among the other stars in the constellation?
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2$\begingroup$ "The alpha star in a constellation has the highest brightness": often, but not always. Beta Orionis (Rigel) is brighter than Alpha Orionis (Betelgeuse), and there are other examples. $\endgroup$– James KNov 4 '21 at 6:24
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Stars were historically grouped into constellations due to their (angular) proximity, as seen from Earth, but can have vastly different distances. As apparent magnitude depends on distance, a star's brightness is not an indication of its absolute magnitude.
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$\begingroup$ I don't think this is the answer to the question asked. I don't think "flux density" means "absolute magnitude" $\endgroup$– James KNov 4 '21 at 21:30
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$\begingroup$ I think the author interpreted brightness as absolute magnitude, and flux density as apparent magnitude? $\endgroup$– TosicDec 4 '21 at 16:19