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Stars have to be a certain size to initiate fusion to begin with, correct?

Isn't this why brown dwarfs are considered 'failed stars'?

But wouldn't the Sun (and other stars with sufficient mass, like even the smallest red dwarf) achieve much or even most of its heat, energy and light production simply via the crashing and smashing together of particles?

After all, a star must be at least four million Kelvin in its core to initiate sustained fusion, right?

What percentage of the Sun's total energy release is simply from its blackbody temperature that it would have due to size alone without radioactive decay or fusion?

P.S.: If the smallest Red Dwarf must be at least about 4,000,000 Kelvin to initiate fusion, near the beginning of its life, how hot would the Sun have gotten? About 5 or 6 million K? Without any fusion/decay energy?

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    $\begingroup$ Consider conservation energy. A big thing can't just sit there radiating energy indefinitely without some kind of energy source. $\endgroup$
    – PM 2Ring
    Sep 18, 2023 at 16:19

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If you calculate the total thermal energy of the Sun now - i.e. the sum of the thermal (kinetic energy) of its constituent particles - then it could be used to supply it's current luminosity for 40 million years.

You ask what percentage of the Sun's output luminosity is due to this thermal energy? The answer is all of it. The radiation we see from the photosphere is entirely due to the thermal energy of the photospheric gas.

If you switched off the nuclear reactions in the core, then the luminosity of the Sun would decrease slowly over the course of tens of millions of years. The Sun would be kept hot instead by contracting and releasing gravitational potential energy.

Ultimately (a few hundred million years) the core would become electron-degenerate, the contraction would cease and the Sun would become a cooling hydrogen white dwarf.

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    $\begingroup$ Would the Sun have gone through a Red Giant phase without any radioactive decay energy or fusion energy? Or straight to a white dwarf of some sort? $\endgroup$
    – Kurt Hikes
    Sep 18, 2023 at 19:33
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    $\begingroup$ @KurtHikes I suppose it depends what physics you are altering to say that fusion of hydrogen does not occur. But yes, a hydrogen white dwarf about 4 times the diameter of the earth is a possible endpoint. $\endgroup$
    – ProfRob
    Sep 18, 2023 at 20:20
  • $\begingroup$ If you switched off the sun's fusion, it would almost instantly collapse into degenerate matter, wouldn't it? That's what happens when a star tries to fuse iron and stops generating the energy to hold up against gravity, after all. You would presumably not get a supernova because the outer layers collapsing couldn't trigger rebound fusion if affected by the magic no-fusion switch, but I think it would go degenerate very, very quickly. $\endgroup$ Sep 19, 2023 at 20:25
  • $\begingroup$ @DarthPseudonym no that wouldn't happen. Core collapse prior to a supernova occurs because pressure does not grow with density and temperature and internal energy is immediately removed by neutrinos. Switching off fusion in the Sun leads to contraction on the Kelvin-Helmholtz timescale of 30 million years (a timescale that increases as the Sun contracts). $\endgroup$
    – ProfRob
    Sep 20, 2023 at 7:02
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A collapsing cloud of gas will generate heat from the release of gravitational potential energy, and it's core temperature will continue to rise. Indeed this is the mechanism that Kelvin and Helmholz proposed as the source of energy of the sun.

As the surface radiates heat, it cools and contracts, which in turn causes the interior to be compressed and hotter. This is a dynamic process. The gas must be collapsing to release energy. It doesn't generate energy just from being big and having a high pressure. The pressure must be increasing.

But once fusion begins in the core, this process is halted. The core is able to generate its own heat which prevents further contraction. The core of a star reaches a temperature to initiate fusion, this prevents further heating of the core. If there were no fusion, the core would continue to get hotter, until electron degeneracy prevented the gas from contracting further.

There is only enough gravitational potential energy to power the sun for a few tens of million years at its current power output. Another source of power (ie fusion) is required to explain how the sun can have existed for 4.6 billion years.

In its current state, the sun is not collapsing and so it isn't converting potential energy into heat. So the answer to your last question is 0%.

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    $\begingroup$ How long would the Sun have lasted from its initial collapse (it's birth) until it became some sort of white dwarf? About 40 million years? Again, assuming no radioactive decay or fusion? $\endgroup$
    – Kurt Hikes
    Sep 18, 2023 at 19:31
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    $\begingroup$ That seems about right. I seem to recall that Kelvin suggested that the sun was between 10 and 50 million years old. I doubt it would have the same combination of radius/temperature/luminosity that the sun does now. $\endgroup$
    – James K
    Sep 18, 2023 at 19:36

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