= Absolute magnitude
{title2=$M$}
{wiki}
Absolute magnitude $M$, in the stellar convention used here, is the <apparent magnitude> a source would have at $10$ <parsecs>, with <interstellar extinction> removed. The hypothetical observation uses the specified <photometric passband> and <magnitude zero point>, preserving the source's emitted spectrum and <luminosity>. Moving every source to this common distance lets us compare intrinsic brightness without confusing it with distance. https://sites.astro.caltech.edu/~george/ay20/Ay20-Lec3x.pdf[Caltech Ay 20, Lecture 3: Apparent versus absolute magnitudes]{ref}.
For a fixed source with <isotropy> of emission, in transparent space with negligible relativistic and cosmological effects, the <inverse-square law> gives the hypothetical measurement $F_{10}$ and <absolute magnitude>
$$
F_{10}=F(d)\left(\frac{d}{10\,\mathrm{pc}}\right)^2,\qquad M=-2.5\log_{10}\left(\frac{F_{10}}{F_{\mathrm{ref}}}\right).
$$
The factor applies in the same <photometric passband>, with unchanged emitted spectrum. Thus <absolute magnitude> compares <luminosity> in that response, rather than automatically the total <bolometric luminosity> over all <wavelengths>.
Consider a toy source with $M=0$. Its <apparent magnitude> is $m=0$ at $10$ <parsecs>, $m=5$ at $100$ <parsecs>, and $m=10$ at $1000$ <parsecs>, neglecting <interstellar extinction>. Its <absolute magnitude> remains $M=0$ throughout: moving the observer changes received <radiative flux>, not emitted <luminosity>. Another toy source with $M=-5$ has $100$ times its passband output under the same <isotropy> and calibration assumptions. Negative <absolute magnitudes> are allowed too; "absolute" names the reference-distance convention, not an <absolute value>.
A calibrated <standard candle> reverses this reasoning: its known <absolute magnitude> and measured <apparent magnitude> give a <distance modulus>. This is why estimating intrinsic brightness is so useful for measuring astronomical distances. https://openstax.org/books/astronomy-2e/pages/19-3-variable-stars-one-key-to-cosmic-distances[Fraknoi, Morrison and Wolff, Astronomy 2e, 19.3: Intrinsic brightness and distance]{ref}.
Back to article page
