Burning Out Stars

  • In the book "A Really Short History Of Nearly Everything", I read that the larger the star is, the faster it burns itself. Whys that? Wouldn't there be more energy to burn if it's larger, and just be brighter? Our sun can burn for billions of years, but a planet bigger than our sun will only burn for millions of years. Why is that?

    How is it that my comment has been deleted here? o.O

    What comment? You never did.

    Uhm, yes I did, at the very beginning.

    Maybe it got flagged and removed.

  • Takku

    Takku Correct answer

    8 years ago

    Nuclear fusion rates in the core of a star have very non-linear and strong dependences on temperature, pressure and density (for temperature it's like T^40 for some processes - http://www.astro.soton.ac.uk/~pac/PH112/notes/notes/node117.html). So, as the star gets bigger, denser and hotter at the centre, the rates of fusion rise much faster and the star loses energy quicker, hence living a shorter life.

    Note that the star tries to balance itself to maintain stability, so the actual dependence is not that high, and ends up being related to the mass luminosity relationship, where the dependence is not that steep.

    "tries" is probably a bit too metaphorical here. Can you describe *how* the process is balanced?

    It has to maintain hydrostatic equilibrium (HSE) to be stable (or else the net force will drive it towards HSE, and hence stability). If it compresses too much, the core temperature increases, causing the nuclear reaction rates to increase steeply, which creates enough thermal/radiation pressure to push the star outwards and balance the compression. If it expands too much, it cools, lowers the thermal pressure, allowing gravity to pull the star inwards again. That's what I meant by 'tries to balance', as often it can't, for example in the instability strip containing variable/pulsating stars.

    More massive stars have *less* dense cores. The density dependence of the nuclear burning rate, it is all about the central temperature.

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Content dated before 7/24/2021 11:53 AM