# Absolute magnitudes with dust extinction

I have a distant $z\sim3$ galaxy with absolute AB magnitudes $M_B$ and $M_I$, where the central wavelengths of the $B$ and $I$ passbands are $\sim0.4\,\mu\text{m}$ and $\sim0.8\,\mu\text{m}$, respectively.

If this galaxy was to experience $1\,\text{mag}$ of $V$-band extinction due to dust within it, where the central wavelength of the $V$ passband is $\sim0.5\,\mu\text{m}$, how do I work out what the absolute magnitudes $M_B$ and $M_I$ would be?

Thanks for any help with this issue.

Check this lecture note. I believe there is everything you need to understand how to proceed. In brief, you should have extra information about the relative absorption, shown in the table on p.18. Given the correction in one band (which you already have $A_V = 1)$, you can find the correction in other bands using the table.
• Thank you for your suggestion. So if I have an absolute magnitude $M_B$, then the reddened magnitude is $M'_B=M_B-1.34$? – alex_lewis Jul 16 '18 at 7:56
• And is the correction to the $B$-band magnitude of $1.34$ in AB magnitudes, too? Thanks again. – alex_lewis Jul 16 '18 at 13:00
• According to the lecture note, yes $A_B = 1.34$. Since the correction is a multiplicative constant in flux space, Vega or AB system should have the same value. However, it is worth to double check this because Vega or AB system is normally rooted by the telescopes, which might have slightly different response functions therefore slightly different corrections. The thing that you should be more concerned is the RADEC and the type of object -- an O star has different correction than a A star for example. But if it is galactic extinction, the type of object should not much of the concern. – Kornpob Bhirombhakdi Jul 16 '18 at 14:56