# E(B-V) , the color excess between B and V bands, for galaxy at redshift 0

Following Mo et al. 2010 (page 479), the quantity $$E(B-V)$$, called the color excess between B and V bands, is equal to:

$$E(B-V) = A_B - A_V = (B - V) - (B - V)_0 = (m_B - m_V) - (M_B- M_V)$$

where $$m_B, m_V$$ are the apparent magnitude in B and V bands, and $$M_B, M_V$$ are the absolute magnitude in B and V bands.

Keep in mind the relation between apparent and absolute magnitudes, with $$d=10$$ pc:

$$m = M - 5 \log(d) + 5$$

If we are at redshift $$z>0$$, the color excess should be $$E(B-V)>0$$, because the extinction due to dust is greater in the B band than in the V band, and apparent magnitudes are greater than absolute magnitudes.

I'm wondering if it is correct to have $$E(B-V)=0$$ if the redshift is $$z=0$$ and $$M=m$$. The apparent magnitude is equal to the absolute magnitude and the relation above mentioned should become:

$$E(B-V) = A_B - A_V = (B - V) - (B - V)_0 = (m_B - m_V) - (M_B- M_V) = (M_B- M_V)_0 - (M_B- M_V)_0 = 0$$

Is that correct? Is it possible that we don't have color excess for galaxies at $$z=0$$, what am I missing?

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– uhoh
Aug 26, 2021 at 23:29

$$(B-V)_0$$ is the intrinsic (unreddened) colour.
The apparent magnitude does not equal the absolute magnitude at $$z=0$$. Absolute magnitude is the apparent magnitude at 10 pc.