# Length of the life of a red supergiant.

#### crawleen

hey,

thought i would throw this problem out there....

if you have the luminosity of a red supergiant 400,000 times more luminous than the sun and a mass of 30 times greater than the sun how would you go about answering how much longer or shorter than the sun would you expect it to liv?

i know luminosity is related to mass but i dont have any actual figures and im contemplating looking for the circumference /radius and using that.

any smarter thoughts?!?

cheers!

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#### Drakkith

Staff Emeritus
2018 Award
Red supergiants are a phase of the lifecycle of massive stars that they go through after they are no longer main sequence, IE they are no longer burning hydrogen in their core. Before this they are usually blue supergiants, which are typically much smaller than red supergiants in the same way that stars like the Sun are much smaller in their main sequence phase than they are in the red giant phase. Are you wanting to know how long a star with 30 solar masses would live, or how long it would remain in the red supergiant phase?

#### Chronos

Gold Member
The general rule for life expectancy of a main sequency star is roughly 10 billion divided by its solar mass to the power of 2.5 [1E10/M^2.5]. This formula is less accurate for very small, or large stars. A 30 solar mass star would definitely qualify as very large. The naive life expectancy for such a star would be around 2 million years [but probably closer to 1 million years in reality]. Calculating the life expectancy for the red giant phase is ... complicated. It is safe to say it is less than the main sequence life expectancy because helium fusion is less efficient than hydrogen fusion and the star is far more luminous [using more fuel] than it was during its main sequence phase. The estimate for the sun is around 500 million years, or about 5% of its main sequence life expectancy of 10 billion years. For a 30 solar mass star, we could be talking only a matter of tens of thousands of years before it went boom.

#### Drakkith

Staff Emeritus
2018 Award
Plus the amount of fuel available for a red supergiant is significantly reduced after hydrogen burning. Hydrogen fusion turns 4 hydrogen into 1 helium, so there is only 1/4 the amount of fuel once Helium fusion starts. (Depending on if you view two hydrogen fusing together as 1 reaction or the process of fusing 4 together into helium as one reaction) As further elements are fused the amount of fuel continues to decrease as more nucleons are tied up in larger and larger nuclei.

#### twofish-quant

if you have the luminosity of a red supergiant 400,000 times more luminous than the sun and a mass of 30 times greater than the sun how would you go about answering how much longer or shorter than the sun would you expect it to liv?
You can do some rough guesses based on fusion rates, but if you want a detailed answer, you'll need to dump it all into a computer program.

http://mesa.sourceforge.net/

i know luminosity is related to mass but i dont have any actual figures and im contemplating looking for the circumference /radius and using that.
There are some scaling relationships for blue supergiants, but when you talk about red ones, those are off the main sequence so it becomes more difficult.

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