Spectroscopic system, AB magnitudes

[sketos]

Suppose we have a galaxy at redshift z=4 with monochromatic UV luminosity λUV *LUV = 4.2×1046 erg /s and an absolute K -band magnitude of K = −23.5 mag (in the AB system). Assuming a K -band absolute magnitude M⊙,AB = 5.14 for the sun, how can i determine the luminosity L_K of the galaxy ??

I am a little confused with the AB magnitude system. Should i also take into account K-correction ?

 

[Chronos]

You need to take bolometric corrections into account. Earth's atmosphere screens out wavelengths less than about 3000 Angstroms, K corrections depend on filter bandwidth. See https://www.cfa.harvard.edu/~dfabricant/huchra/ay202/k.correction.pdf for details. For an even uglier discussion see http://www.astro.wisc.edu/~mab/education/astro500/lectures/a500_lecture2_s13.pdf .

 

[sketos]

The treatment that is described in those link concerns the apparent magnitudes, where clearly K-corrections play an important role. However in the exercise that i described we already have the absolute magnitudes in the AB system of the sun and the galaxy ( which are already related with the intrinsic luminosity ). So the relation to find the luminosity of the galaxy in the K-band in the AB system,

$$\frac{L_K}{L_{\odot}} = 10^{\frac{M_{\odot} - M_K }{2.5}}$$