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?


1 Answer 1


Neither. You use the 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 that will depend upon the intrinsic spectrum of the source.

For $z=11.09$ this cosmology calculator 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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