<p>This is an attempt to answer the question as to the value of the Eddington pulsation constant as it relates to <a href="https://en.wikipedia.org/w/index.php?title=Cepheid_variable&amp;oldid=1066470756" rel="nofollow noreferrer">Cepheid</a> variables. The constant, <span class="math-container">$Q$</span>, is defined as:
<span class="math-container">$$Q = P\sqrt{\rho} = P\sqrt{\frac{\bar{\rho}_\odot}{\bar{\rho}}}$$</span></p>
<p>where <span class="math-container">$P$</span> is the pulsation period and <span class="math-container">$\rho$</span> is the star density. Pulsation period is typically specified in days and the density is relative to the sun's mean density, <span class="math-container">$\bar{\rho}_\odot$</span>. (see eqn. 11 in <a href="https://arxiv.org/abs/1205.6407" rel="nofollow noreferrer">Asteroseismology</a>)</p>
<p>As this constant really isn't constant, <a href="https://adsabs.harvard.edu/full/1970ApJ...162..139C" rel="nofollow noreferrer">only approximately</a>, this answer will be more of a survey with references for additional details.</p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th>Period (days)</th>
<th>Reference</th>
<th>Notes</th>
</tr>
</thead>
<tbody>
<tr>
<td>0.03 - 0.04</td>
<td><a href="https://arxiv.org/abs/1205.6407" rel="nofollow noreferrer">Handler</a></td>
<td>Over the whole HR diagram for the radial fundamental mode</td>
</tr>
<tr>
<td>0.033</td>
<td><a href="https://arxiv.org/abs/1205.6407" rel="nofollow noreferrer">Handler</a></td>
<td>For the sun</td>
</tr>
<tr>
<td>0.0329</td>
<td><a href="https://arxiv.org/abs/1510.07058" rel="nofollow noreferrer">Joshi</a></td>
<td><span class="math-container">$\delta$</span> Scuti stars</td>
</tr>
<tr>
<td>0.033 <span class="math-container">$\pm$</span> 0.002</td>
<td><a href="https://www.tandfonline.com/doi/full/10.1080/20909977.2021.2000794" rel="nofollow noreferrer">Abdel-Sabour</a></td>
<td>YZ Boo</td>
</tr>
<tr>
<td>0.037</td>
<td><a href="https://adsabs.harvard.edu/pdf/1972ApJS...24..167W" rel="nofollow noreferrer">Watson</a></td>
<td>\beta Cephei stars</td>
</tr>
<tr>
<td>0.03 &lt; <span class="math-container">$Q$</span> &lt; 0.08</td>
<td><a href="http://www.astro.ulg.ac.be/%7Escuflair/sismo.pdf" rel="nofollow noreferrer">Scuflaire</a></td>
<td>Theoretical calculations</td>
</tr>
<tr>
<td>0.179</td>
<td><a href="https://www.jstor.org/stable/10.1086/316585" rel="nofollow noreferrer">Percy</a></td>
<td>89 (V441) Herculis</td>
</tr>
</tbody>
</table>
</div>
<p>There are probably a bunch more that could be added.  Some additional interesting reading related can be found in <a href="https://ui.adsabs.harvard.edu/abs/2015PhDT........45E/abstract" rel="nofollow noreferrer">The Secret Lives of Cephids</a>.</p>

CC BY-SA 4.0
2022-01-24T00:23:24.483Z
2022-01-24T00:23:24.483Z
GrapefruitIsAwesome
<p>What numerical value does the pulsation constant <span class="math-container">$Q$</span> take in the formula that Eddington derived for variable stars:
<span class="math-container">$$P\sqrt{\rho} = Q,$$</span>
where <span class="math-container">$\rho$</span> — average star density, <span class="math-container">$P$</span> — period?</p>

CC BY-SA 4.0
2022-01-19T21:16:00.303Z
What do you get when you enter typical values for density and period?
planetmaker
CC BY-SA 4.0
2022-01-20T00:00:29.200Z
Your question is unclear.  For what specific case of values are you interested, or are you interested in a physical interpretation?
GrapefruitIsAwesome
CC BY-SA 4.0
2022-01-20T11:10:43.220Z
@GrapefruitIsAwesome the question seems clear enough to me at least, but I've added some words to make it even clearer. It's going to be *some number* in units of s kg^1/2 m^-3/2 for example, but what is that number?
uhoh
CC BY-SA 4.0
2022-01-20T11:25:32.490Z
I agree with @GrapefruitIsAwesome. What is asked beyond plugging in values into that equation?
planetmaker
CC BY-SA 4.0
2022-01-20T13:18:57.497Z
@Александр Иванов you question would become more interesting if you can expand it with a bit background to your question. Especially expand it on the level you expect an answer to be, and include the question's background with your prior knowledge. As it stands now, an answer could vary between typing two numbers from a pocket calculator up to writing a whole essay or even book on the matter.
planetmaker
<variable-star><eddington-luminosity>
What is an actual value for the Eddington pulsation constant?
Александр Иванов
# What is an actual value for the Eddington pulsation constant?

(Asked by: username_0 on 2022-01-19)

What numerical value does the pulsation constant $Q$ take in the formula that Eddington derived for variable stars:
$$P\sqrt{\rho} = Q,$$
where $\rho$ — average star density, $P$ — period?

**Tags:** variable-star, eddington-luminosity
> **Comments:**
> **username_1**: What do you get when you enter typical values for density and period?  
> **username_2**: Your question is unclear.  For what specific case of values are you interested, or are you interested in a physical interpretation?  
> **username_3**: @GrapefruitIsAwesome the question seems clear enough to me at least, but I've added some words to make it even clearer. It's going to be *some number* in units of s kg^1/2 m^-3/2 for example, but what is that number?  
> **username_1**: I agree with @GrapefruitIsAwesome. What is asked beyond plugging in values into that equation?  
> **username_1**: @Александр Иванов you question would become more interesting if you can expand it with a bit background to your question. Especially expand it on the level you expect an answer to be, and include the question's background with your prior knowledge. As it stands now, an answer could vary between typing two numbers from a pocket calculator up to writing a whole essay or even book on the matter.  

---

## 1 answers

### Answer by username_2 on 2022-01-24. Score: 2 | Accepted answer

This is an attempt to answer the question as to the value of the Eddington pulsation constant as it relates to [Cepheid](https://en.wikipedia.org/w/index.php?title=Cepheid_variable&oldid=1066470756) variables. The constant, $Q$, is defined as:
$$Q = P\sqrt{\rho} = P\sqrt{\frac{\bar{\rho}\_\odot}{\bar{\rho}}}$$

where $P$ is the pulsation period and $\rho$ is the star density. Pulsation period is typically specified in days and the density is relative to the sun's mean density, $\bar{\rho}\_\odot$. (see eqn. 11 in [Asteroseismology](https://arxiv.org/abs/1205.6407))

As this constant really isn't constant, [only approximately](https://adsabs.harvard.edu/full/1970ApJ...162..139C), this answer will be more of a survey with references for additional details.

| Period (days) | Reference | Notes |
| --- | --- | --- |
| 0.03 - 0.04 | [Handler](https://arxiv.org/abs/1205.6407) | Over the whole HR diagram for the radial fundamental mode |
| 0.033 | [Handler](https://arxiv.org/abs/1205.6407) | For the sun |
| 0.0329 | [Joshi](https://arxiv.org/abs/1510.07058) | $\delta$ Scuti stars |
| 0.033 $\pm$ 0.002 | [Abdel-Sabour](https://www.tandfonline.com/doi/full/10.1080/20909977.2021.2000794) | YZ Boo |
| 0.037 | [Watson](https://adsabs.harvard.edu/pdf/1972ApJS...24..167W) | \beta Cephei stars |
| 0.03 < $Q$ < 0.08 | [Scuflaire](http://www.astro.ulg.ac.be/%7Escuflair/sismo.pdf) | Theoretical calculations |
| 0.179 | [Percy](https://www.jstor.org/stable/10.1086/316585) | 89 (V441) Herculis |

There are probably a bunch more that could be added. Some additional interesting reading related can be found in [The Secret Lives of Cephids](https://ui.adsabs.harvard.edu/abs/2015PhDT........45E/abstract).


---

