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torque of the town
2008-Oct-07, 10:33 AM
How much faster would a blue white star like Spica with a mass 12 times greater, consume its nuclear fuel compared to the Sun.

Is there a formula using the mass differential?

Thanks in anticipation guys

David

Spaceman Spiff
2008-Oct-07, 01:46 PM
Main sequence stars are in energy equilibrium, thus the energy generated per second in their cores matches the energy lost at the surface in the form of light (neglecting small neutrino losses for MS stars). The rate at which hydrogen is consumed is therefore proportional to the star's luminosity L, and the "size of the fuel tank" scales roughly in proportion to the mass of the star. Recall that fusion involves the liberation of a fraction (~0.7%) of the rest mass energy of hydrogen as it is converted into helium. So how long a star is on the main sequence scales as M/L.

This is analogous to computing how long you could drive your car on the highway based on the size of your fuel tank and the rate at which the fuel is consumed.

So there you have it, without completely giving away the answer. :)

Eroica
2008-Oct-07, 01:56 PM
So how long a star is on the main sequence scales as M/L.
And we can go further. M and L are related by the mass-luminosity relation:

L is proportional to Mx where x = 3 to 5 depending on the type of star.

You'll need to find out what value x has for Spica, though.

Spaceman Spiff
2008-Oct-07, 03:52 PM
And we can go further. M and L are related by the mass-luminosity relation:

L is proportional to Mx where x = 3 to 5 depending on the type of star.

You'll need to find out what value x has for Spica, though.

The value of the exponent depends on the range in masses over which this approximation (a power law description of L ~ M^x) is valid. Between 1 - 10 solar masses this exponent is about 4.

An addendum to Eroica's statement concerning the value of this exponent -- this exponent diminishes as one goes up the MS in mass (due at least in part to the increasing importance of radiation pressure to the star's structure). Between 30 and 80 solar masses x has diminished to about 2, and tends towards ~1 for the very highest mass stars (i.e., Eddington's limiting luminosity criterion).

torque of the town
2008-Oct-11, 03:39 PM
Thanks guys, in the end I settled for "Considerably Faster"
in the essay.

David