# 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.

## 1 Answer

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.

Note that the relative absorption is different for different scenario, e.g., different RADEC, different host, different type of stars.

Also note that there are two types of extinction: galactic and extragalactic.

• 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
• And, finally (!), note that this is a blank-field extra-galactic source that I am referring to. Thus the reddening would be caused by dust within that galaxy, not due to dust within our galaxy. Thanks again! :-) – alex_lewis Jul 16 '18 at 13:05
• There is many dust map papers which are normally applied for the dust correction. I normally use the one by Schlegel 1998. You need RADEC of the object, then look for the relative absortion, and following the same concept as presented in the attached lecture note. Easier than that, you can use online extinction calculator such as the one by NED. Schlegel 1998: iopscience.iop.org/article/10.1086/305772/fulltext/… NED extinction calculator: ned.ipac.caltech.edu/forms/calculator.html – Kornpob Bhirombhakdi Jul 16 '18 at 14:52
• 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