<p>Based on the comments, I have changed some things.</p>
<p>Below is a graph showing the relative strength of <span class="math-container">$H_\gamma$</span> and Fe I lines of two stars. Which star is hotter?<a href="https://i.sstatic.net/L59bd.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/L59bd.png" alt="enter image description here" /></a></p>
<hr />
<p>This is a question from the book:An Introduction to
Stellar Astrophysics(2010).Francis Leblanc.
The full question is shown below.
<a href="https://i.sstatic.net/HQmRD.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/HQmRD.png" alt="enter image description here" /></a>
And also, some of my ideas:</p>
<ol>
<li>As for Fe I, based on Saha equation, we can calculate as follows:
<span class="math-container">$\frac{n_{\mathrm{II}}}{n_{\mathrm{I}}}=\frac{1}{n_{\mathrm{e}}}\left(\frac{2 \pi m_{\mathrm{e}} k T}{h^{2}}\right)^{\frac{3}{2}} \frac{2 U_{\mathrm{II}}}{U_{\mathrm{I}}} \mathrm{e}^{-\frac{E_{\mathrm{ion}}}{k T}}$</span>, suppose here <span class="math-container">$n_e$</span> is a constant.<span class="math-container">$U_{II}   $</span> and <span class="math-container">$U_{I}$</span> are the partition function for Fe II and Fe I respectively, which are also constants. <span class="math-container">$E_i   $</span> is the energy required to ionize one electron, which is obviously a constant. So as T increase, <span class="math-container">$\frac{n_{II}}{n_{I}}$</span> will increase. Because, it is relatively harder for ionize one more electron. So almost all of the Fe element are <span class="math-container">$Fe I$</span> or <span class="math-container">$Fe II$</span>. Tues the strength of spectra line of <span class="math-container">$FeI $</span> will decrease as temperature increases. So star A is hotter.</li>
<li>As for <span class="math-container">$H_{\gamma}$</span>, I have no idea about that. Although I can use Bolzmann equation to find relative number density of different state of hydrogen. But there are serval states. n=3 ,n=4, n=5.</li>
</ol>

CC BY-SA 4.0
2021-05-07T06:30:07.037Z
Exam question? What are your thoughts on the subject?
ProfRob
CC BY-SA 4.0
2021-05-07T08:51:52.030Z
Have you heard of Doppler broadening?
Jim421616
CC BY-SA 4.0
2021-05-07T10:38:03.850Z
https://astronomy.stackexchange.com/questions/27273/why-is-h-delta-prominent-in-type-a-stars
ProfRob
CC BY-SA 4.0
2021-05-07T11:54:19.180Z
Welcome to astronomy SE! This question has the potential to be interesting, but without sources (of the graph), or additional background info this question has the potential to be downvoted. For more, please refer to [ask]
B--rian
CC BY-SA 4.0
2021-05-07T17:02:40.250Z
See the question I've linked to which explains how Balmer lines change in strength with temperature.
ProfRob
<star><spectra>
How to determine the temperature of a star according to the strength of the line in the spectra?
みえみえ
# How to determine the temperature of a star according to the strength of the line in the spectra?

(Asked by: username_0 on 2021-05-07)

Based on the comments, I have changed some things.

Below is a graph showing the relative strength of $H\_\gamma$ and Fe I lines of two stars. Which star is hotter?[![enter image description here](https://i.sstatic.net/L59bd.png)](https://i.sstatic.net/L59bd.png)

---

This is a question from the book:An Introduction to
Stellar Astrophysics(2010).Francis Leblanc.
The full question is shown below.
[![enter image description here](https://i.sstatic.net/HQmRD.png)](https://i.sstatic.net/HQmRD.png)
And also, some of my ideas:

1. As for Fe I, based on Saha equation, we can calculate as follows:
   $\frac{n\_{\mathrm{II}}}{n\_{\mathrm{I}}}=\frac{1}{n\_{\mathrm{e}}}\left(\frac{2 \pi m\_{\mathrm{e}} k T}{h^{2}}\right)^{\frac{3}{2}} \frac{2 U\_{\mathrm{II}}}{U\_{\mathrm{I}}} \mathrm{e}^{-\frac{E\_{\mathrm{ion}}}{k T}}$, suppose here $n\_e$ is a constant.$U\_{II} $ and $U\_{I}$ are the partition function for Fe II and Fe I respectively, which are also constants. $E\_i $ is the energy required to ionize one electron, which is obviously a constant. So as T increase, $\frac{n\_{II}}{n\_{I}}$ will increase. Because, it is relatively harder for ionize one more electron. So almost all of the Fe element are $Fe I$ or $Fe II$. Tues the strength of spectra line of $FeI $ will decrease as temperature increases. So star A is hotter.
2. As for $H\_{\gamma}$, I have no idea about that. Although I can use Bolzmann equation to find relative number density of different state of hydrogen. But there are serval states. n=3 ,n=4, n=5.

**Tags:** star, spectra
> **Comments:**
> **username_1**: Exam question? What are your thoughts on the subject?  
> **username_2**: Have you heard of Doppler broadening?  
> **username_1**: https://astronomy.stackexchange.com/questions/27273/why-is-h-delta-prominent-in-type-a-stars  
> **username_3**: Welcome to astronomy SE! This question has the potential to be interesting, but without sources (of the graph), or additional background info this question has the potential to be downvoted. For more, please refer to [ask]  
> **username_1**: See the question I've linked to which explains how Balmer lines change in strength with temperature.  

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## 0 answers

