<p><span class="math-container">$$[\mathrm{Fe}/\mathrm{H}] = \log_{10} \left[\frac{f_\mathrm{Fe}(\alpha)}{f_\mathrm{Fe}(0)} \frac{m_z(0)}{m_z(\alpha)} \left(\frac{Z}{X}\right)_\ast \left(\frac{X}{Z}\right)_\odot \right]$$</span></p>

<p>You can use this relation to estimate [Fe/H] from [M/H] of a star. From [M/H] you can get the (Z/X) ratio.</p>

CC BY-SA 4.0
2020-02-06T15:59:30.417Z
Is this the second part to your first answer? You can use the "edit" button to correct or add to your answers. Each post should be a self-contained answer, rather than have answers split over multiple posts.
usernumber
CC BY-SA 4.0
2020-02-07T07:20:26.967Z
Explain the symbols!
ProfRob
CC BY-SA 4.0
2020-02-06T15:23:57.830Z
2020-02-06T18:46:22.653Z
2020-02-06T18:46:22.653Z
Swastik C.
<p><span class="math-container">$$\frac{f_{Fe}(\alpha)}{f_{Fe}(0)} \frac{m_z(0)}{m_z(\alpha)}$$</span></p>

<p>This is the Value of the constant that u get. The above values you can get from any standard paper. Check fergusion et al 2005</p>

CC BY-SA 4.0
2020-02-06T15:56:38.677Z
What constant is this? Also, would you have a link to the article you mention?
usernumber
CC BY-SA 4.0
2020-02-06T15:20:40.520Z
2020-02-06T18:41:48.433Z
2020-02-06T18:41:48.433Z
Swastik C.
<p>The <a href="https://en.wikipedia.org/wiki/Metallicity#Relation_between_Z_and_%5BFe/H%5D" rel="nofollow noreferrer">Wikipedia entry on Metallicity</a> states that:</p>
<blockquote>
<p><span class="math-container">$\log_{10}\left(\frac{Z/X}{Z_\mathrm{sun}/X_\mathrm{sun}}\right) = [\mathrm{M}/\mathrm{H}]$</span></p>
<p>where <span class="math-container">$[M/H]$</span> is the star's total metal abundance (i.e. all elements heavier than helium) defined as a more general expression than the one for [Fe/H]:</p>
<p><span class="math-container">$[\mathrm{M}/\mathrm{H}] = \log_{10}{\left(\frac{N_{\mathrm{M}}}{N_{\mathrm{H}}}\right)_\mathrm{star}} - \log_{10}{\left(\frac{N_{\mathrm{M}}}{N_{\mathrm{H}}}\right)_\mathrm{sun}}$</span></p>
<p>The iron abundance and the total metal abundance are often assumed to be related through a constant A as [<em><strong>citation needed</strong></em>]:</p>
<p><span class="math-container">$[\mathrm{M}/\mathrm{H}] = A\times[\mathrm{Fe}/\mathrm{H}]$</span></p>
<p>where <span class="math-container">$A$</span> assumes values between 0.9 and 1. Using the formulas presented above, the relation between <span class="math-container">$Z$</span> and [Fe/H] can finally be written as:</p>
<p><span class="math-container">$\log_{10}\left(\frac{Z/X}{Z_\mathrm{sun}/X_\mathrm{sun}}\right) = A\times[\mathrm{Fe}/\mathrm{H}]$</span></p>
</blockquote>
<p>This all sounds reasonable, but I have two questions:</p>
<ol>
<li>Where does the <span class="math-container">$[\mathrm{M}/\mathrm{H}] = A\times[\mathrm{Fe}/\mathrm{H}]$</span> relation come from? I could not find a proper source.</li>
<li><a href="http://adsabs.harvard.edu/abs/1994A%26AS..106..275B" rel="nofollow noreferrer">This article</a> actually says (see Eq 9) that the general relation is <span class="math-container">$\log_{10}\left(\frac{Z/X}{Z_\mathrm{sun}/X_\mathrm{sun}}\right) = [\mathrm{Fe}/\mathrm{H}]$</span> i.e., they seem to equate [M/H] with [Fe/H]. I assume that it is because the aforementioned A parameter is between 0.9 and 1, but again that leaves me with the need for a proper source to state that.</li>
</ol>

CC BY-SA 3.0
2018-04-23T18:33:47.393Z
As someone who works in the field, I have not seen your middle equation (with the $A$). [Fe/H] is often lazily conflated with [M/H], but obviously it depends on the detailed composition of the star whether that is approximately true. I suspect it is approximately true for Pop I stars, but perhaps not for older, metal poor stars which have a larger predominance of alpha elements.
ProfRob
CC BY-SA 3.0
2018-04-23T18:40:12.707Z
I have never seen that $A$ parameter either, I just saw it on WP an thought is sounded reasonable. Since I could not find a "proper" general definition for the relation between the $z$ metallicity and the $[Fe/H]$ iron content (aside from the one I show above, from the Bertelli article), I was not sure about its validity. You say that "*[Fe/H] is often lazily conflated with [M/H]*", so you agree that the A parameter sounds reasonable?
Gabriel
CC BY-SA 3.0
2018-04-23T18:52:19.513Z
Maybe I'll work out some $A$ values.
ProfRob
<metallicity>
Correct relation between metallicity (z) and iron content ([Fe/H])
Gabriel
# Correct relation between metallicity (z) and iron content ([Fe/H])

(Asked by: username_0 on 2018-04-23)

The [Wikipedia entry on Metallicity](https://en.wikipedia.org/wiki/Metallicity#Relation_between_Z_and_%5BFe/H%5D) states that:

> $\log\_{10}\left(\frac{Z/X}{Z\_\mathrm{sun}/X\_\mathrm{sun}}\right) = [\mathrm{M}/\mathrm{H}]$
>
> where $[M/H]$ is the star's total metal abundance (i.e. all elements heavier than helium) defined as a more general expression than the one for [Fe/H]:
>
> $[\mathrm{M}/\mathrm{H}] = \log\_{10}{\left(\frac{N\_{\mathrm{M}}}{N\_{\mathrm{H}}}\right)\_\mathrm{star}} - \log\_{10}{\left(\frac{N\_{\mathrm{M}}}{N\_{\mathrm{H}}}\right)\_\mathrm{sun}}$
>
> The iron abundance and the total metal abundance are often assumed to be related through a constant A as [***citation needed***]:
>
> $[\mathrm{M}/\mathrm{H}] = A\times[\mathrm{Fe}/\mathrm{H}]$
>
> where $A$ assumes values between 0.9 and 1. Using the formulas presented above, the relation between $Z$ and [Fe/H] can finally be written as:
>
> $\log\_{10}\left(\frac{Z/X}{Z\_\mathrm{sun}/X\_\mathrm{sun}}\right) = A\times[\mathrm{Fe}/\mathrm{H}]$

This all sounds reasonable, but I have two questions:

1. Where does the $[\mathrm{M}/\mathrm{H}] = A\times[\mathrm{Fe}/\mathrm{H}]$ relation come from? I could not find a proper source.
2. [This article](http://adsabs.harvard.edu/abs/1994A%26AS..106..275B) actually says (see Eq 9) that the general relation is $\log\_{10}\left(\frac{Z/X}{Z\_\mathrm{sun}/X\_\mathrm{sun}}\right) = [\mathrm{Fe}/\mathrm{H}]$ i.e., they seem to equate [M/H] with [Fe/H]. I assume that it is because the aforementioned A parameter is between 0.9 and 1, but again that leaves me with the need for a proper source to state that.

**Tags:** metallicity

> **Comments:**
> **username_1**: As someone who works in the field, I have not seen your middle equation (with the $A$). [Fe/H] is often lazily conflated with [M/H], but obviously it depends on the detailed composition of the star whether that is approximately true. I suspect it is approximately true for Pop I stars, but perhaps not for older, metal poor stars which have a larger predominance of alpha elements.  
> **username_0**: I have never seen that $A$ parameter either, I just saw it on WP an thought is sounded reasonable. Since I could not find a "proper" general definition for the relation between the $z$ metallicity and the $[Fe/H]$ iron content (aside from the one I show above, from the Bertelli article), I was not sure about its validity. You say that "*[Fe/H] is often lazily conflated with [M/H]*", so you agree that the A parameter sounds reasonable?  
> **username_1**: Maybe I'll work out some $A$ values.  

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## 2 answers

### Answer by username_2 on 2020-02-06. Score: -1

$$[\mathrm{Fe}/\mathrm{H}] = \log\_{10} \left[\frac{f\_\mathrm{Fe}(\alpha)}{f\_\mathrm{Fe}(0)} \frac{m\_z(0)}{m\_z(\alpha)} \left(\frac{Z}{X}\right)\_\ast \left(\frac{X}{Z}\right)\_\odot \right]$$

You can use this relation to estimate [Fe/H] from [M/H] of a star. From [M/H] you can get the (Z/X) ratio.

> **Comments:**
> **username_3**: Is this the second part to your first answer? You can use the "edit" button to correct or add to your answers. Each post should be a self-contained answer, rather than have answers split over multiple posts.  
> **username_1**: Explain the symbols!  

---

### Answer by username_2 on 2020-02-06. Score: -3

$$\frac{f\_{Fe}(\alpha)}{f\_{Fe}(0)} \frac{m\_z(0)}{m\_z(\alpha)}$$

This is the Value of the constant that u get. The above values you can get from any standard paper. Check fergusion et al 2005

> **Comments:**
> **username_3**: What constant is this? Also, would you have a link to the article you mention?  

---

