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The common theory is, that if the Sun "shut down", we would see the light for eight more minutes (the time that it takes the photons to reach the Earth).

However recently I have read that photons need around 100 000 years to reach the Earth, since the reactions are happening at Sun's core, and gamma rays can't leave the Sun without interacting with other particles, unlike neutrinos for example.

Is that theory correct? If the Sun's core "shut down", would we still receive photons (light) for another 100 000 years, with only neutrinos disappearing immediately?

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    $\begingroup$ IT would be better to ask just if (and why) light is supposed to take so long to reach the surface of the Sun from the core. Asking using the "what if something impossible happened" approach you have tends to put people off on science based sites like this. $\endgroup$ – StephenG Sep 28 at 11:08
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    $\begingroup$ On the other hand, science-minded people tend to like learning the truth about something (and often even educating others). $\endgroup$ – Ryan Sep 28 at 19:11
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    $\begingroup$ "photons need around 100 000 years to reach the Earth". That's a bit misleading. Yes, it takes a long time for energy to travel from the solar core to the photosphere, but no individual photon spends 100,000 years traveling through the Sun. See astronomy.stackexchange.com/a/33447/16685 $\endgroup$ – PM 2Ring Sep 29 at 2:00
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    $\begingroup$ Also the in the 'theory' the expected behaviour is the Sun instantly doesn't exist anymore, so presumably the photons within it which were trying to escape also don't exist anymore. If this is the case, then it simply would go dark, 8 minutes later on earth. (ignoring the fact the photons don't exactly exist when they are 'trapped') $\endgroup$ – djsmiley2k - CoW Sep 29 at 17:00
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    $\begingroup$ Please define "went out" and "shut down". If the sun itself was blinked out of existence then yes, we would have 8 minutes of light remaining. If the Sun's core "simply" shut down then it would take very long for that to propagate through to the surface. $\endgroup$ – MonkeyZeus Sep 30 at 15:26
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If nuclear fusion were to suddenly stop in the centre of the Sun, then the only clear signature we would have of this is the lack of detectable neutrinos received at Earth, starting about 8 minutes after the reactions ceased. The Sun however would continue to shine for tens of millions of years at roughly its current luminosity.

The power source is not "stored" photons. The Sun itself would simply resume the slow gravitational contraction that was halted about 4.5 billion years ago when nuclear reaction rates at the centre were able to increase sufficiently to supply the radiative losses from the surface of the Sun.

The characteristic timescale for the contraction is about $$\tau_{\rm KH} = \frac{GM^2}{RL},$$ which is 30 million years. i.e. The Sun has enough gravitational potential energy to supply its current luminosity for tens of millions of years.

While this is happening, the Sun would approximately maintain its current luminosity, but decrease in radius, meaning that its surface temperature would increase.

Once the Sun had contracted to a few times the size of Jupiter (so about 30% of its current radius), the contraction would begin to slow, because the electrons in the core become degenerate and the pressure increases with density by more than expected for a perfect gas. The slowing contraction decreases the rate of potential energy release and hence the solar luminosity. The contraction continues at a slow rate until the Sun becomes a hot "hydrogen white dwarf" a few times the size of the Earth, which then cools to a glowing cinder, with no further contraction, over billions of years (see What would the Sun be like if nuclear reactions could not proceed via quantum tunneling? for some more details).

Even if you were to not allow the Sun to contract, it would take some time to radiate it's thermal energy. This timescale is approximately $$\tau_{\rm therm} \simeq \frac{3k_B T M}{m_H L},$$ which assumes the Sun is a perfect gas of protons plus electrons, with an average temperature $T$. If we take $T =10^7$ K and the current solar luminosity, then $\tau_{\rm therm}=$ 40 million years.

On the other hand, if your scenario is just that light from the Sun stops being emitted, then of course it goes dark on Earth about 8 minutes later.

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    $\begingroup$ Even if you were to somehow manage to stop the gravitational contraction as well, the Sun is pretty hot - ~5800K at the "surface" up to !15 million K at the center. It would take some considerable time to cool. $\endgroup$ – jamesqf Sep 29 at 3:06
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    $\begingroup$ @nick012000 your question is ill defined and the timescales are approximate. i have not said the Sun would take 40m years to stop glowing. I said it would take 40m years to radiate away its current thermal energy at its current luminosty. If the Sun cooled at constant radius, that timescale would go up, because the luminosity would decrease considerably. The Sun would glow in some sense for billions of years. We can use white dwarfs as a model here. The oldest white dwarfs are still hotter than 3000K. $\endgroup$ – Rob Jeffries Sep 29 at 12:51
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    $\begingroup$ This is a mesmerizing read! $\endgroup$ – Hanky Panky Sep 29 at 17:15
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    $\begingroup$ @stripybadger It's like having a very, very large tank of hot water and thus not having to worry about your supply of heating fuel. $\endgroup$ – Rob Jeffries Sep 30 at 15:32
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    $\begingroup$ @PeterA.Schneider a "collapse" cannot occur because thermal energy cannot be ignored, it must be radiated away from the surface. "Core collapse", which initiates a supernova can only happen because (I) there is a huge sink of thermal energy (disintegration of iron nuclei and neutronisation) and (II) most energy can escape via neutrino emission. Neither of these is important in the Sun. $\endgroup$ – Rob Jeffries Sep 30 at 23:59
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The "common theory" you're reading is not about the processes that produce light in stars, it's just intended as a demonstration of the speed of light through space. When it talks about the Sun "shutting down", it's not talking about the nuclear fusion processes stopping, it means that the Sun as a whole stops shining. I'm not a physicist, but I don't think there's anything that would actually cause this to occur at a sudden time, such that we could measure the 8 minute time difference for the last photons to reach Earth.

It's just a thought experiment, using a simplified description of an impossible event, to make a point about some other process. In this model, the Sun either gives off light or it doesn't, and we're measuring the time since it changed that state; we're not concerned with what the photons do before they're emitted from the Sun (any more than measuring time that light travels from a light bulb cares about how the electricity that powered the bulb was produced -- we could measure that all the way back to the dinosaurs dying and eventually turning into fossil fuels that were used in the power plant, or even further back to the solar energy that powered life on earth).

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