<p>Neither. You use the <a href="https://en.wikipedia.org/wiki/Luminosity_distance" rel="nofollow noreferrer">Luminosity Distance</a>.</p>
<p><span class="math-container">$$M = m -5\log D_L + 5$$</span></p>
<p>This assumes bolometric magnitudes. If you are trying to estimate it in some photometric band then you must also calculate and apply a <a href="https://en.wikipedia.org/wiki/K_correction" rel="nofollow noreferrer">K-correction</a> that will depend upon the intrinsic spectrum of the source.</p>
<p>For <span class="math-container">$z=11.09$</span> <a href="https://home.fnal.gov/%7Egnedin/cc/" rel="nofollow noreferrer">this cosmology calculator</a> gives a model-dependent luminosity-distance modulus of 50.39 (corresponding to <span class="math-container">$D_L=1.2\times 10^{11}$</span> pc).</p>
<p>NB: The distances you quote in the question do not give the absolute magnitudes quoted.</p>

CC BY-SA 4.0
2021-03-29T22:10:42.047Z
2021-04-01T09:19:57.057Z
2021-04-01T09:19:57.057Z
ProfRob
<p>I want to calculate the absolute magnitude of GN-z11. Its light-travel distance is 13.4 billion ly (4.1 Gpc), its comoving distance is 32 billion ly (9.8 Gpc), and its apparent magnitude is <span class="math-container">$25.8$</span>. Calculating its absolute magnitude, we get <span class="math-container">$M=-76.86$</span> for light-travel, and <span class="math-container">$M=-94.09$</span> for comoving. Which one do I use? I am assuming it is the former. Is this correct, or is there a different formula for this?</p>

<galaxy><redshift><apparent-magnitude><absolute-magnitude>
When calculating absolute magnitudes of distant objects, do you use the light-travel distance or the comoving distance?
WarpPrime
# When calculating absolute magnitudes of distant objects, do you use the light-travel distance or the comoving distance?

(Asked by: username_0 on 2021-03-29)

I want to calculate the absolute magnitude of GN-z11. Its light-travel distance is 13.4 billion ly (4.1 Gpc), its comoving distance is 32 billion ly (9.8 Gpc), and its apparent magnitude is $25.8$. Calculating its absolute magnitude, we get $M=-76.86$ for light-travel, and $M=-94.09$ for comoving. Which one do I use? I am assuming it is the former. Is this correct, or is there a different formula for this?

**Tags:** galaxy, redshift, apparent-magnitude, absolute-magnitude

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## 1 answers

### Answer by username_1 on 2021-03-29. Score: 3

Neither. You use the [Luminosity Distance](https://en.wikipedia.org/wiki/Luminosity_distance).

$$M = m -5\log D\_L + 5$$

This assumes bolometric magnitudes. If you are trying to estimate it in some photometric band then you must also calculate and apply a [K-correction](https://en.wikipedia.org/wiki/K_correction) that will depend upon the intrinsic spectrum of the source.

For $z=11.09$ [this cosmology calculator](https://home.fnal.gov/%7Egnedin/cc/) gives a model-dependent luminosity-distance modulus of 50.39 (corresponding to $D\_L=1.2\times 10^{11}$ pc).

NB: The distances you quote in the question do not give the absolute magnitudes quoted.


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