# How can I Mathematically Calculate the Luminosity of a Post-Main-Sequence Star from Mass and Age?

So, I saw this question (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.

• 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
Feb 18 at 22:28

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

• 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? Feb 14 at 8:27
• I edited the my answer for clarity Feb 14 at 11:12