= Astronomical magnitude
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Astronomical magnitude expresses brightness on a <logarithmic scale>: equal steps in <astronomical magnitude> represent equal ratios of received <radiative flux>. The scale runs backwards, so a brighter source has a smaller <astronomical magnitude>. A difference of five magnitudes means exactly a factor of $100$ in flux; one magnitude means a factor of $100^{1/5}\simeq2.511886$, rather than exactly $2.5$. This compresses the enormous range of astronomical brightnesses into manageable numbers. https://openstax.org/books/astronomy-2e/pages/17-1-the-brightness-of-stars[Fraknoi, Morrison and Wolff, Astronomy 2e, 17.1: The brightness of stars]{ref}.
<Apparent magnitude> describes received brightness, while <absolute magnitude> compares sources at a shared reference distance. Both require a specified <photometric passband> and <magnitude zero point>. A <magnitude difference> turns a ratio of positive <radiative fluxes> into a difference of numbers; it does not measure an additive change in emitted <luminosity>.
\Image[/magnitude-flux-logarithmic-scale.png]
{title=Equal magnitude steps multiply flux ratios; toy measurements in one passband with one zero point}
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