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If all nuclear reactions inside the Sun would have stopped somehow for ever then what all will be the consequences?

My Attempt at the Question:

  • Since the reactions were a source of Sun's radiations, therefore any new energy in the form of heat wouldn't be generated inside our Sun. Instead, the already hot Sun's layers would radiate heat to the surrounding, until the Temperature of its surroundings becomes equal to its own. (However, I am unable to comprehend as to how will we compute the temperature of surroundings, since we would have to define 'surroundings' and assign it a temperature).
  • Since certain fraction mass that was being converted to energy due to these nuclear reactions, stopping the reactions would reduce the rate of loss and mass and therefore mass will be become constant. Hence the gravitational pull of the Sun on planets remains same instead of getting reduced, as it would if nuclear reactions would've occurred. Hence the mean distance (radius) between the Sun and planets would get reduced. Since the radius of orbits is getting reduced, the velocity of the planets increases, keeping the angular momentum conserved. If the reduction in radii is significant, then some Inner Planets may also be engulfed by the Sun.
  • Due to an increase in pressure (pressure buildup) due to the unreacted gases inside the Sun, the Sun would explode like a pressure cooker.

Are any (or all) of the above statements correct? In second point will the fraction of mass being converted to energy be sufficient to cause any significant changes? (Since only about 0.7% of its mass gets converted to energy).

Please do share your own answers to the question given too.

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closed as too broad by Kyle Kanos, sammy gerbil, Yashas, John Rennie, JMac Dec 21 '17 at 13:17

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ askamathematician.com/2012/10/… $\endgroup$ – CMSnoob Nov 26 '17 at 17:55
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    $\begingroup$ The trouble with asking a question like this is that you are looking for answers in terms of conventional physics and currently understood laws, based on a physical situation which does not comply with these laws. The scenario you describe, in reality, could not happen. $\endgroup$ – user176049 Nov 26 '17 at 18:13
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    $\begingroup$ The Sun's core would shrink a bit until the pressure compensates gravity. Then the Sun would become a dwarf meaning a heated object with no power source. It would be cooling down for billions of years. There will be no significant mass change and no explosion. The only way we would know this even happened is by measuring neutrinos, as they would stop coming. There would be no practicall effect on the humanity. $\endgroup$ – safesphere Nov 26 '17 at 19:51
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    $\begingroup$ This kind of question is useful at times ... it is one that was asked of me in my first stellar physics course and one that I use in a lecture on the Virial theorem for students in upper division mechanics. The answer is that the way we could know for thousands of years is the change in the neutrino flux. $\endgroup$ – dmckee Nov 26 '17 at 20:09
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    $\begingroup$ Without fusion to maintain an internal pressure against gravitational collapse the Sun would eventually collapse into a White Dwarf (which is it's expected fate in the normal course of events). I'm not sure how long gravitational collapse would take given the issue of mean free path of photons is of the order of millions of years in the Sun - it might take a long time. $\endgroup$ – StephenG Nov 26 '17 at 21:16
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In summary: the only noticeable effect on human timescales would be the cessation of neutrino emission from the core. Over millions and then 100s of millions of years the Sun will contract and become much hotter. After about a billion years it would become an electron-degenerate H/He white dwarf, then cool back to its original surface temperature (though with a luminosity that was 10,000 times smaller) over the next billion years, and then gradually fade into obscurity.

Some details:

The Sun would behave like the pre main-sequence star it once was. It will recommence a contraction process, whereby it loses gravitational potential energy to make up for the radiative losses it experiences from its surface. The contraction takes place on a Kelvin- Helmholtz timescale - the gravitational potential energy divided by the luminosity - $\sim GM^2/(RL)$, which is 30 million years for the Sun.

At the same time, the virial theorem demands that actually only half the lost potential energy goes into radiation, whilst the other half goes into heating the interior. Thus the centre of the Sun will get hotter and hotter.

This process will only end when the sun's interior is about $10^{9}$ K and it is about a hundredth of the size it is now. At these densities, the electrons in the core become degenerate and dominate the pressure. From then on, the contraction slows to a halt because degeneracy pressure is maintained even if the Sun cools. At this point the Sun could be considered a H/He white dwarf.

From there, in the absence of further heating by contraction, neutrino losses (via beta- and inverse-beta decays and via neutrino bremsstrahlung) would rapidly cool the interior back to pre contraction values on timescales of tens of millions of years and then over billions of years the Sun would cool and fade, reaching its current surface temperature again after $\sim 1$ billion years and then further fading into obscurity as a ball of metallic hydrogen and helium.

Two points of uncertainty remain, which need a wiser person or a numerical calculation. One is the track of the Sun in the Hertzsprung-Russell diagram. I suspect that it will move more horizontally than PMS stars on the Hayashi track, following the Henyey track for contraction under radiative equilibrium. The interior will be radiative because of decreasing opacity with temperature and the surface will become hotter as the radius decreases and the luminosity stays roughly constant. The second point is how long this will take. If the luminosity stays roughly the same, then the Kelvin-Helmholtz timescale gets longer, so overall contraction to a white dwarf would likely take a timescale nearly 100 times the current KH timescale - so of order 1 billion years.

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    $\begingroup$ Can you clarify what you mean by 'neutrino losses' in your fifth paragraph? $\endgroup$ – Emilio Pisanty Nov 28 '17 at 9:05
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    $\begingroup$ @EmilioPisanty done. $\endgroup$ – Rob Jeffries Nov 28 '17 at 9:51
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The energy produced in the Sun reach the surface in roughly 1million years. So we won't see anything.

Neutrino detectors will detect the sudden lack of the solar neutrinos, so we will know, something is not okay.

Later, in the lack of heating, the Sun will degrade into a white dwarf star.

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If nuclear reactions in the sun stop suddenly then its radius would start collapsing with a rate given by $$\dot{R}=-\frac{2}{q}\frac{\mathcal{L}_{sun}R^2}{GM^2}=-\frac{8\pi\sigma\left(RT\right)^4}{q\,GM^2}$$ Where $\mathcal{L}_{sun}$ is the Sun's luminosity, $M$ its mass. $q$ is derived from the gravitational energy density $\Omega_g$, given by the formula $$\Omega_g=-\int_{0}^{M}\frac{m}{r}\mathrm{d}m=-q\frac{GM^2}{R}$$ Where, then $$q=\int_{0}^{1}\frac{mR}{rM}\mathrm{d}\left(\frac{m}{M}\right)\approx1.5$$ Note that the collapse rate can be derived by directly plugging it into the virial theorem's equations. After collapsing till a certain point electrons would then degenerate and generate degeneration pressure that would stop the Sun from collapsing even more, hence giving "birth" to a White Dwarf Star Remnant

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