<p>When accounting for extinction, the number you count will be the number you would have seen at a brighter (numerically smaller) magnitude given by <span class="math-container">$m - \Delta m$</span> if there were no extinction, where <span class="math-container">$\Delta m$</span> is the extinction out of our Galaxy in the direction you are looking.</p>
<p>Hence the formula in your book is correct and
<span class="math-container">$$\log N(m,b) = 0.6m - \Delta m(b) + C\ . $$</span></p>

CC BY-SA 4.0
2024-07-16T19:09:14.637Z
Thank you! I initially thought the number to count should be the one we SEE (i.e. fainter magnitude) since the phrasing of my book was a bit confusing to me.
M. Islam Nafees
CC BY-SA 4.0
2024-07-16T18:55:25.953Z
2024-07-16T18:55:25.953Z
ProfRob
<p>If galaxies are uniformly distributed in space, then in the absence of extinction, the number of galaxies per square degree brighter than magnitude m is given by <span class="math-container">$$\log_{N_0}(m) = 0.6m + C$$</span>
How will the formula look like if extinction in the interstellar medium is counted? I know that a galaxy situated at galactic latitide b with apparent magnitude x (without extinction) will have the apparent magnitude due to extinction: <span class="math-container">$$m(b) = x + \frac{\Delta m}{\sin(b)}$$</span>
where Delta m= extinction in direction of galactic pole.
It makes sense to me that substituting m(b) in the first expression will give me the observable number of galaxies at galactic latitude b. But in the textbook I am using (Fundamental Astronomy), a different expression is given-</p>
<p><span class="math-container">$$\log N(m, b) = \log N_0 (m - \Delta m(b))$$</span></p>
<p>which makes no sense to me. Could anyone provide me with the correct formula?</p>

CC BY-SA 4.0
2024-07-15T17:40:24.220Z
Why not give the other formula and the name/reference of the textbook?
ProfRob
CC BY-SA 4.0
2024-07-16T14:11:07.920Z
@ProfRob edited
M. Islam Nafees
<galaxy><distances><apparent-magnitude><interstellar-medium><extinction>
How to count observable number of galaxies at a given latitude considering interstellar extinction?
M. Islam Nafees
# How to count observable number of galaxies at a given latitude considering interstellar extinction?

(Asked by: username_0 on 2024-07-15)

If galaxies are uniformly distributed in space, then in the absence of extinction, the number of galaxies per square degree brighter than magnitude m is given by $$\log\_{N\_0}(m) = 0.6m + C$$
How will the formula look like if extinction in the interstellar medium is counted? I know that a galaxy situated at galactic latitide b with apparent magnitude x (without extinction) will have the apparent magnitude due to extinction: $$m(b) = x + \frac{\Delta m}{\sin(b)}$$
where Delta m= extinction in direction of galactic pole.
It makes sense to me that substituting m(b) in the first expression will give me the observable number of galaxies at galactic latitude b. But in the textbook I am using (Fundamental Astronomy), a different expression is given-

$$\log N(m, b) = \log N\_0 (m - \Delta m(b))$$

which makes no sense to me. Could anyone provide me with the correct formula?

**Tags:** galaxy, distances, apparent-magnitude, interstellar-medium, extinction
> **Comments:**
> **username_1**: Why not give the other formula and the name/reference of the textbook?  
> **username_0**: @ProfRob edited  

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## 1 answers

### Answer by username_1 on 2024-07-16. Score: 1 | Accepted answer

When accounting for extinction, the number you count will be the number you would have seen at a brighter (numerically smaller) magnitude given by $m - \Delta m$ if there were no extinction, where $\Delta m$ is the extinction out of our Galaxy in the direction you are looking.

Hence the formula in your book is correct and
$$\log N(m,b) = 0.6m - \Delta m(b) + C\ . $$

> **Comments:**
> **username_0**: Thank you! I initially thought the number to count should be the one we SEE (i.e. fainter magnitude) since the phrasing of my book was a bit confusing to me.  

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