<p>Rough reaction for stars between 0.5 and 2.5 solar masses:
We first need to know the initial(ZAMS) luminosity, the luminosity at the end of the main sequence(TAMS) and the MS lifetime:
<span class="math-container">$$L_\text{ZAMS}=0.7×M^4$$</span></p>
<p><span class="math-container">$$L_\text{TAMS}=3×L_\text{ZAMS}$$</span></p>
<p><span class="math-container">$$T=9×M^{-2.6}\text{ (in Gyr)}$$</span></p>
<p>Reg giant stage: luminosity exponentially increases from the TAMS luminosity to about 3500×solar luminosity(at the tip of RGB) lasts about 10% of main sequence</p>
<p>Helium burning:luminosity exponentially increases from 50 to 150×solar luminosity, lasts about 100 Myr</p>
<p>AGB: luminosity increases exponentially from 150×solar luminosity to 10000×mass of star(in solar masses)×solar luminosity, lasts 20 Myr</p>
<p>Planetary nebula: roughly constant luminosity at 10000×mass of star(in solar masses)×solar luminosity, lasts roughly 30000yr</p>
<p>For other mass ranges it gets much more complicated.</p>
<p>Calculations:
<a href="https://www.desmos.com/calculator/l2nelshpnx" rel="nofollow noreferrer">https://www.desmos.com/calculator/l2nelshpnx</a></p>

CC BY-SA 4.0
2023-02-14T08:27:34.987Z
Ive updated the formatting.  In English don't use a dot to separate thousands, because the dot is used as a decimal point  (ie 10.001 = 10001/1000, not ten thousand and one)  What is the meaning of "L" and "M" in 150L to 10000M×solar luminosity?
James K
CC BY-SA 4.0
2023-02-14T11:12:17.517Z
I edited the my answer for clarity
HugoF
CC BY-SA 4.0
2023-02-14T02:17:36.280Z
2023-02-15T11:04:09.767Z
2023-02-15T11:04:09.767Z
HugoF
<p>So, I saw <a href="https://astronomy.stackexchange.com/questions/32771/is-there-a-way-to-factor-age-into-the-mass-luminosity-relationship-for-stars">this question</a> (which is quite old) and that's all well and good, but what if I need to (<em><strong>very</strong></em>) roughly calculate the luminosity of a star from the end of the main sequence? Let's assume that this is a non-extreme mass star (K-A) and can use <span class="math-container">$10M^{-2.5}$</span>
To calculate (roughly) when the star will exit the main sequence. Would there be a way to include the expansion into a red giant? What about simulating the planetary nebula? Simplify as much as is needed.</p>

CC BY-SA 4.0
2023-02-18T22:28:56.153Z
Now that there's an answer posted to address all aspects of this question, I don't think closing and preventing answer posts is necessary or even productive. *voting to leave open*
uhoh
<star><stellar-evolution><mathematics>
How can I Mathematically Calculate the Luminosity of a Post-Main-Sequence Star from Mass and Age?
isdi0
# How can I Mathematically Calculate the Luminosity of a Post-Main-Sequence Star from Mass and Age?

(Asked by: username_0 on 2023-02-08)

So, I saw [this question](https://astronomy.stackexchange.com/questions/32771/is-there-a-way-to-factor-age-into-the-mass-luminosity-relationship-for-stars) (which is quite old) and that's all well and good, but what if I need to (***very***) roughly calculate the luminosity of a star from the end of the main sequence? Let's assume that this is a non-extreme mass star (K-A) and can use $10M^{-2.5}$
To calculate (roughly) when the star will exit the main sequence. Would there be a way to include the expansion into a red giant? What about simulating the planetary nebula? Simplify as much as is needed.

**Tags:** star, stellar-evolution, mathematics

> **Comments:**
> **username_1**: Now that there's an answer posted to address all aspects of this question, I don't think closing and preventing answer posts is necessary or even productive. *voting to leave open*  

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## 1 answers

### Answer by username_2 on 2023-02-14. Score: 3 | Accepted answer

Rough reaction for stars between 0.5 and 2.5 solar masses:
We first need to know the initial(ZAMS) luminosity, the luminosity at the end of the main sequence(TAMS) and the MS lifetime:
$$L\_\text{ZAMS}=0.7×M^4$$

$$L\_\text{TAMS}=3×L\_\text{ZAMS}$$

$$T=9×M^{-2.6}\text{ (in Gyr)}$$

Reg giant stage: luminosity exponentially increases from the TAMS luminosity to about 3500×solar luminosity(at the tip of RGB) lasts about 10% of main sequence

Helium burning:luminosity exponentially increases from 50 to 150×solar luminosity, lasts about 100 Myr

AGB: luminosity increases exponentially from 150×solar luminosity to 10000×mass of star(in solar masses)×solar luminosity, lasts 20 Myr

Planetary nebula: roughly constant luminosity at 10000×mass of star(in solar masses)×solar luminosity, lasts roughly 30000yr

For other mass ranges it gets much more complicated.

Calculations:
<https://www.desmos.com/calculator/l2nelshpnx>

> **Comments:**
> **username_3**: Ive updated the formatting.  In English don't use a dot to separate thousands, because the dot is used as a decimal point  (ie 10.001 = 10001/1000, not ten thousand and one)  What is the meaning of "L" and "M" in 150L to 10000M×solar luminosity?  
> **username_2**: I edited the my answer for clarity  

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