Stellar lifespan question...plz help?

Question

I'm told that the sun with a mass of 1 and a luminosity of 1 is expected to live 10 billion years......

Then what is a star with a mass of 50 and a luminosity of 40,000 supposed to live?

The expected answer is approximately 1million years but the best i've come up with is 12.5million

anyone have any insight?

yes it's involving ratio's.....i'm trying to help this girl friend of mine and this is all she has told me...a little more info would be that a star of .8 mass lives 14billion years....thats' about it man....

I've done a lot of research on the web too....and found that a 1 to 1 star lives 10billion....a 10 to 1,000 star lives 10mill....

that's all the info i have man...we need to know what a 50 mass 40,000 lumin...lives to be

Answer 1

In one of James Kaler's books he said that stellar life expectancy is roughly proportional its mass to the -2.5 power, that is, L/L(sun) = (M/M(sun))^-2.5. By that, a star of 50 solar masses should live 50^(-2.5) = .57E-6 solar lives, or 570,000 years. A little less than your 1 million year figure, but Kaler did warn the relationship drifted a bit at the extremes, and you've got to expect both uncertainty and variation with metallicity and such in the results. If you've got some actual data points you could try fitting them to an exponential curve, such that ln(L) = A ln(M), with L and M in solar units.

If you can come up with some estimates of the size and mean fusion rate of the core versus mass, you could try to derive an equation.

Answer 2

The lifespan of a star isn't a pure ratio. If a star of 1 mass and luminosity of 1 lives 10 billion years, it doesn't mean that a star of 10 mass and 10 luminosity will only live 1 billion years - its not a one-to-one relationship.

The Hertzsprung-Russel diagram plots luminosity and temperature on a graph - that might help work it out.

Answer 3

are you using ratios?

heavy stars may actually only live a few tens of thousands of years, a few hundreds of thousands sometimes.