Understanding Stellar Lifespans: Comparing Luminosity & Mass

[tommyboo]

Hi, all how would you go about finding out how much longer a star would live compared to another if you knew the one star was x times more luminous and y times more massive?

 

[zhermes]

For a precise result, you would use a stellar evolution simulation to calculate the result numerically. For an approximate result, you can use an order of magnitude scaling for how long stars live---which is determined primarily by its mass.

$$\tau \sim 10^{10} \textrm{ yrs} \left( \frac{M}{M_\odot}\right)^{-3}$$

*The more massive the star, the (much) shorter its lifetime is, because its luminosity increases rapidly.

Depending on the mass range, the exponent can range somewhat (between about 2 and 3), but this is the general scaling. If you're curious about how to derive it, its based on a few simple assumptions---namely, the temperature of the star is determined by equipartition (i.e. its 'virialized'), the luminosity is thermal, and the amount of fuel is linearly related to the mass of the star.

 

[Chronos]

I think you inverted M/Msolar, zhermes. The customary formula is
10^10 x 1/M^2.5 where M is in solar masses
re: http://mais-ccd-spectroscopy.com/Stellar%20Evolution%20Lesson.pdf

 

[zhermes]

I think you inverted $M/Msol$zhermes.

Oh, damn. Thanks Chronos!

 

[qraal]

I think you inverted M/Msolar, zhermes. The customary formula is
10^10 x 1/M^2.5 where M is in solar masses
re: http://mais-ccd-spectroscopy.com/Stellar%20Evolution%20Lesson.pdf

The mass-luminosity index is more like 4.75 for stars from 0.7-2.0 times the Sun's mass. Very low mass stars are more convective than such Sun-like stars, and so fuse more of their fusion fuel during the Main Sequence. At the other end of the scale the index is more like 3, and high-mass stars live very rapidly indeed - typically just a few million years. Interestingly they ramp up in core temperature and fuse their way through heavier elements with very little change.

 

[jaychristian4]

Stars are having gases like hydrogen and helium as their elemental compositions.They are continiously active in their core region.The life of star is dependent on this activity and quite difficult to measure it.