<p>The website on <a href="https://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolution_mainsequence.html" rel="nofollow noreferrer">Main sequence stars</a> fromr the Austalian national telescope facility lists star mass, temperature and life span:</p>
<div class="s-table-container">
<table class="s-table">
<thead>
<tr>
<th>Mass/MSun</th>
<th>Luminosity/LSun</th>
<th>T=Effective Temperature/K</th>
<th>Radius/RSun</th>
<th>t=Main sequence lifespan/yrs</th>
</tr>
</thead>
<tbody>
<tr>
<td>0.10</td>
<td><span class="math-container">$3×10^{-3}$</span></td>
<td>2,900</td>
<td>0.16</td>
<td><span class="math-container">$2×10^{12}$</span></td>
</tr>
<tr>
<td>0.50</td>
<td>0.03</td>
<td>3,800</td>
<td>0.6</td>
<td><span class="math-container">$2×10^{11}$</span></td>
</tr>
<tr>
<td>0.75</td>
<td>0.3</td>
<td>5,000</td>
<td>0.8</td>
<td><span class="math-container">$3×10^{10}$</span></td>
</tr>
<tr>
<td>1.0</td>
<td>1</td>
<td>6,000</td>
<td>1.0</td>
<td><span class="math-container">$1×10^{10}$</span></td>
</tr>
<tr>
<td>1.5</td>
<td>5</td>
<td>7,000</td>
<td>1.4</td>
<td><span class="math-container">$2×10^9$</span></td>
</tr>
<tr>
<td>3</td>
<td>60</td>
<td>11,000</td>
<td>2.5</td>
<td><span class="math-container">$2×10^8$</span></td>
</tr>
<tr>
<td>5</td>
<td>600</td>
<td>17,000</td>
<td>3.8</td>
<td><span class="math-container">$7×10^7$</span></td>
</tr>
<tr>
<td>10</td>
<td>10,000</td>
<td>22,000</td>
<td>5.6</td>
<td><span class="math-container">$2×10^7$</span></td>
</tr>
<tr>
<td>15</td>
<td>17,000</td>
<td>28,000</td>
<td>6.8</td>
<td><span class="math-container">$1×10^7$</span></td>
</tr>
<tr>
<td>25</td>
<td>80,000</td>
<td>35,000</td>
<td>8.7</td>
<td><span class="math-container">$7×10^6$</span></td>
</tr>
<tr>
<td>60</td>
<td>790,000</td>
<td>44,500</td>
<td>15</td>
<td><span class="math-container">$3.4×10^6$</span></td>
</tr>
</tbody>
</table>
</div>
<p>If we suspect a lifespan, <span class="math-container">$t$</span> is related to the temperature <span class="math-container">$T$</span> by a power relationship, <span class="math-container">$t=aT^k$</span>, we can plot log(t) against log(T) and look for a linear relationship
<a href="https://i.sstatic.net/ZOyRQ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZOyRQ.png" alt="enter image description here" /></a></p>
<p>That looks plausible, and gives a relationship of <span class="math-container">$t = 10^{28}\times T^{-4.7}$</span> (rounding to 2sf)</p>
<p>looking more closely, this tends to underestimate the life span of mid-range stars, but overestimate large and small stars. You can adapt for this by considering smaller and larger stars separately: For stars less than 10000K, a model <span class="math-container">$t = 10^{37}\times T^{-7.6}$</span> and for hotter stars <span class="math-container">$t = 10^{20}\times T^{-3.0}$</span> gives reasonable fit to the data.</p>
<p>This is, of course, a purely empirical fitting of a curve, and isn't based on an astrophysical model. (though I speculate that the change in gradient is related to the change from the proton-proton to the CNO cycle fusion of hydrogen.)</p>

CC BY-SA 4.0
2021-02-21T15:39:32.647Z
I tested your two formulas for $T=5778$ and it didn't work very well. Am I doing something wrong?
slowerthanstopped
CC BY-SA 4.0
2021-02-21T16:15:38.903Z
Also, is there any place where I can find a detailed table of temperature-lifespan relations (of step 100 K or something up to a reasonable degree of accuracy)?
slowerthanstopped
CC BY-SA 4.0
2021-02-20T23:27:55.367Z
2021-02-21T10:21:46.543Z
2021-02-21T10:21:46.543Z
James K
<p>I have a generic zero-age main sequence star. The only thing I know about it is its temperature. How can I estimate time time it spends on the main sequence (in millions of years)? I've seen equations that estimate it based on mass, like <span class="math-container">$L=M^{-2.5}\cdot10^{10}$</span>, but I do not have the mass, only the temperature. Is there any definite formula (accurate to a reasonable degree) for this?</p>

CC BY-SA 4.0
2021-02-21T03:16:22.600Z
@slowerthanstopped I don't exactly understand the previous comment, but if you are using two different user accounts on the same site to interact with each other this is called a "sock puppet" and it's against the rules. If you are a new user you may not be aware of this but it's important to ask for moderator help if indeed you might have done this accidentally.
uhoh
CC BY-SA 4.0
2021-02-22T08:42:32.907Z
Main sequence stars don't have a fixed temperature (or luminosity) during their main sequence lifetimes, so which temperature would you be using?
ProfRob
CC BY-SA 4.0
2021-02-22T13:08:39.410Z
@uhoh Actually, having multiple accounts in and of itself is not against the rules, *per se*. It just isn't encouraged. There's a nice list over at [MSE](https://meta.stackexchange.com/questions/57682/how-should-sockpuppets-be-handled-on-stack-exchange) about which behaviors are inappropriate for a user of multiple accounts. It doesn't appear slowerthanstopped has performed any of these problematic actions, so whatever their reasons for having multiple accounts they can keep them for now if they wish.
called2voyage
CC BY-SA 4.0
2021-02-22T14:10:30.163Z
@called2voyage yep, I said "if... interact with each other" and that says "Supporting your own arguments", so as long as the sock is either silent towards the "hand's" point or actively argues against it it's okay :-)
uhoh
CC BY-SA 4.0
2021-02-22T14:18:33.587Z
@uhoh Well "interact with each other" is a bit unclear. It could be interpreted as any interactions, like editing posts. Editing posts is allowed.
called2voyage
CC BY-SA 4.0
2021-02-22T14:23:01.447Z
@called2voyage ah I see, okay. Now I can't stop thinking about [Shari Lewis and Lamb Chop](https://en.m.wikipedia.org/wiki/Shari_Lewis)
uhoh
<star><stellar-evolution><temperature><main-sequence><stellar-classification>
How can I estimate how long will a main sequence star stay on the main sequence given its temperature?
slowerthanstopped
# How can I estimate how long will a main sequence star stay on the main sequence given its temperature?

(Asked by: username_0 on 2021-02-20)

I have a generic zero-age main sequence star. The only thing I know about it is its temperature. How can I estimate time time it spends on the main sequence (in millions of years)? I've seen equations that estimate it based on mass, like $L=M^{-2.5}\cdot10^{10}$, but I do not have the mass, only the temperature. Is there any definite formula (accurate to a reasonable degree) for this?

**Tags:** star, stellar-evolution, temperature, main-sequence, stellar-classification
> **Comments:**
> **username_1**: @slowerthanstopped I don't exactly understand the previous comment, but if you are using two different user accounts on the same site to interact with each other this is called a "sock puppet" and it's against the rules. If you are a new user you may not be aware of this but it's important to ask for moderator help if indeed you might have done this accidentally.  
> **username_2**: Main sequence stars don't have a fixed temperature (or luminosity) during their main sequence lifetimes, so which temperature would you be using?  
> **username_3**: @uhoh Actually, having multiple accounts in and of itself is not against the rules, *per se*. It just isn't encouraged. There's a nice list over at [MSE](https://meta.stackexchange.com/questions/57682/how-should-sockpuppets-be-handled-on-stack-exchange) about which behaviors are inappropriate for a user of multiple accounts. It doesn't appear slowerthanstopped has performed any of these problematic actions, so whatever their reasons for having multiple accounts they can keep them for now if they wish.  
> **username_1**: @called2voyage yep, I said "if... interact with each other" and that says "Supporting your own arguments", so as long as the sock is either silent towards the "hand's" point or actively argues against it it's okay :-)  
> **username_3**: @uhoh Well "interact with each other" is a bit unclear. It could be interpreted as any interactions, like editing posts. Editing posts is allowed.  
> **username_1**: @called2voyage ah I see, okay. Now I can't stop thinking about [Shari Lewis and Lamb Chop](https://en.m.wikipedia.org/wiki/Shari_Lewis)  

---

## 1 answers

### Answer by username_4 on 2021-02-20. Score: 2

The website on [Main sequence stars](https://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolution_mainsequence.html) fromr the Austalian national telescope facility lists star mass, temperature and life span:

| Mass/MSun | Luminosity/LSun | T=Effective Temperature/K | Radius/RSun | t=Main sequence lifespan/yrs |
| --- | --- | --- | --- | --- |
| 0.10 | $3×10^{-3}$ | 2,900 | 0.16 | $2×10^{12}$ |
| 0.50 | 0.03 | 3,800 | 0.6 | $2×10^{11}$ |
| 0.75 | 0.3 | 5,000 | 0.8 | $3×10^{10}$ |
| 1.0 | 1 | 6,000 | 1.0 | $1×10^{10}$ |
| 1.5 | 5 | 7,000 | 1.4 | $2×10^9$ |
| 3 | 60 | 11,000 | 2.5 | $2×10^8$ |
| 5 | 600 | 17,000 | 3.8 | $7×10^7$ |
| 10 | 10,000 | 22,000 | 5.6 | $2×10^7$ |
| 15 | 17,000 | 28,000 | 6.8 | $1×10^7$ |
| 25 | 80,000 | 35,000 | 8.7 | $7×10^6$ |
| 60 | 790,000 | 44,500 | 15 | $3.4×10^6$ |

If we suspect a lifespan, $t$ is related to the temperature $T$ by a power relationship, $t=aT^k$, we can plot log(t) against log(T) and look for a linear relationship
[![enter image description here](https://i.sstatic.net/ZOyRQ.png)](https://i.sstatic.net/ZOyRQ.png)

That looks plausible, and gives a relationship of $t = 10^{28}\times T^{-4.7}$ (rounding to 2sf)

looking more closely, this tends to underestimate the life span of mid-range stars, but overestimate large and small stars. You can adapt for this by considering smaller and larger stars separately: For stars less than 10000K, a model $t = 10^{37}\times T^{-7.6}$ and for hotter stars $t = 10^{20}\times T^{-3.0}$ gives reasonable fit to the data.

This is, of course, a purely empirical fitting of a curve, and isn't based on an astrophysical model. (though I speculate that the change in gradient is related to the change from the proton-proton to the CNO cycle fusion of hydrogen.)

> **Comments:**
> **username_0**: I tested your two formulas for $T=5778$ and it didn't work very well. Am I doing something wrong?  
> **username_0**: Also, is there any place where I can find a detailed table of temperature-lifespan relations (of step 100 K or something up to a reasonable degree of accuracy)?  

---

