= Apparent magnitude
{title2=$m$}
{wiki}
Apparent magnitude $m$ is a calibrated description of the <observed radiative flux> received from an astronomical source. It answers how bright the source appears in a specified <photometric passband>, rather than how much <luminosity> the source emits. Define $F_{\mathrm{ref}}>0$ as the measurement assigned zero <apparent magnitude> by the chosen <magnitude zero point>. Then
$$
m=-2.5\log_{10}\left(\frac{F}{F_{\mathrm{ref}}}\right).
$$
Here $F$ is the positive passband measurement, with the same units and response convention as $F_{\mathrm{ref}}$. For an <energy>-weighted detector this measures received <radiative flux> through its response; for a <photon>-counting detector use the corresponding calibrated count rate for both quantities. Actual <photometric passbands> include the instrument's response across <wavelength>, so naming the <photometric system> is part of reporting an <apparent magnitude>. https://www.cosmos.esa.int/web/gaia/edr3-passbands[ESA/Gaia/DPAC: Passbands and zero points]{ref}. https://xmm-tools.cosmos.esa.int/external/xmm_calibration/calib/documentation/CALHB/node597.html[ESA XMM-Newton calibration handbook: Count rate to magnitude]{ref}.
As toy examples in one <photometric passband>, $F=F_{\mathrm{ref}}$ gives $m=0$, $F=100F_{\mathrm{ref}}$ gives $m=-5$, and $F=0.01F_{\mathrm{ref}}$ gives $m=+5$. A negative <apparent magnitude> therefore means more received <radiative flux> than the reference; it is physically allowed. Zero <apparent magnitude> does not mean zero <radiative flux>. The ordinary <logarithm> formula requires $F>0$.
A small <apparent magnitude> alone cannot distinguish a nearby faint source from a distant source with large <luminosity>: this is the <flux-distance degeneracy>. <Stellar parallax> supplies independent distance information, while a calibrated <standard candle> supplies intrinsic brightness. <Interstellar extinction> also changes the received <radiative flux> and hence the measured <apparent magnitude>.
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