<p>As stated in my answer to <a href="https://astronomy.stackexchange.com/questions/33520/would-we-have-more-than-8-minutes-of-light-if-the-sun-went-out?noredirect=1&amp;lq=1">Would we have more than 8 minutes of light, if the sun &quot;went out&quot;?</a> , the Sun would cool at roughly constant luminosity for some tens of millions of years. That means "we" would not notice anything change on human timescales (apart from the lack of neutrinos, which has no measurable effect on anything apart from the odd atom in a vast vats of cleaning fluid or water, underground in South Dakota and Japan).</p>

<p>If <span class="math-container">$dL/dt$</span> was roughly <span class="math-container">$-L_{\odot}/30$</span> in solar luminosities per million years, then it would be 1000 years before the luminosity of the Sun fell by 0.1%, which is roughly the kind of variations we see over the course of the solar cycle.</p>

<p>However, the most likely evolution of the Sun is for it to contract, maintain a stable luminosity and compensate by increasing its surface (photospheric) temperature.</p>

<p>Given that luminosity is provided by gravitational contraction and the rate of change of gravitational potential energy, then
<span class="math-container">$$ L_{\odot} \simeq  -\left(\frac{GM_{\odot}^2}{R^2}\right)\frac{dR}{dt}, \tag*{(1)}$$</span>
where <span class="math-container">$R$</span> is the radius.</p>

<p>If the luminosity is constant and given by
<span class="math-container">$$L_{\odot} = 4\pi R^2 \sigma T^4,$$</span>
where <span class="math-container">$\sigma$</span> is the Stefan-Boltzmann constant and <span class="math-container">$T$</span> is the effective (photospheric) temperature, then
<span class="math-container">$$ \frac{dL_{\odot}}{dt} = 4\pi \sigma \left(2R T^4 \frac{dR}{dt} + 4R^2 T^3 \frac{dT}{dt}\right) = 0 \tag*{(2)}$$</span></p>

<p>Combining equations (1) and (2) we find
<span class="math-container">$$\frac{dT}{dt} = \frac{T R L_{\odot}}{2 GM_{\odot}^2} = 90\ {\rm K/Myr}$$</span>
i.e. The Sun surface would heat up by 90K every million years.</p>

<p>This gradual warming would change the spectral type of the Sun, moving it towards an F-type star. The spectrum of light it emitted would shift to shorter wavelengths (according to Wien's displacement law, the peak wavelength in the spectrum is inversely proportional to temperature) and a greater fraction of the Sun's light would appear in the ultra-violet part of the spectrum. </p>

CC BY-SA 4.0
2019-09-30T14:29:09.040Z
Is that odd atom at the bottom of a cleaning vat D2O?
john doe
CC BY-SA 4.0
2019-09-30T14:55:03.983Z
@johndoe No, Chlorine.
ProfRob
CC BY-SA 4.0
2019-09-30T14:00:41.677Z
2019-09-30T14:54:51.317Z
2019-09-30T14:54:51.317Z
ProfRob
<p>(This question was <strong>stimulated by</strong> <a href="https://astronomy.stackexchange.com/questions/33520/would-we-have-more-than-8-minutes-of-light-if-the-sun-went-out">Would we have more than 8 minutes of light, if the sun &quot;went out&quot;?</a>)</p>

<p>According to <a href="https://astronomy.stackexchange.com/a/33522/19049">this answer</a>, the "Sun has enough gravitational potential energy to supply its current luminosity for tens of millions of years."</p>

<p>Does "current luminosity" mean that the same spectrum will be radiated, or will it be just as bright, but radiating at different wavelengths (like not in the violet-blue and reddish orange-red wavelengths which chlorophyll requires, or the IR that keep us warm)?</p>

CC BY-SA 4.0
2019-09-30T12:21:11.677Z
There would be no effects on Earth for "tens of millions of years" as outlined in the answer to the other question. So no, we would not "notice if the Sun stopped fusing atoms [sic]" and there would be no effects on Earth on those timescales.. Or is your question perhaps - aside from the lack of neutrinos, are there other any other experiments that could be performed that would indicate that fusion had ceased?
ProfRob
CC BY-SA 4.0
2019-09-30T13:19:23.417Z
@RobJeffries question clarified (I hope).
RonJohn
CC BY-SA 4.0
2019-09-30T13:33:45.193Z
@RonJohn The photosphere of the Sun is approximately a [blackbody radiator](https://en.wikipedia.org/wiki/Black-body_radiation). If you keep it at the same temperature it emits the same spectrum.
PM 2Ring
CC BY-SA 4.0
2019-09-30T13:44:39.233Z
@PM2Ring make that an answer, and I'll accept it.
RonJohn
<the-sun><photons>
What would we notice if the Sun stopped fusing atoms?
RonJohn
# What would we notice if the Sun stopped fusing atoms?

(Asked by: username_0 on 2019-09-30)

(This question was **stimulated by** [Would we have more than 8 minutes of light, if the sun "went out"?](https://astronomy.stackexchange.com/questions/33520/would-we-have-more-than-8-minutes-of-light-if-the-sun-went-out))

According to [this answer](https://astronomy.stackexchange.com/a/33522/19049), the "Sun has enough gravitational potential energy to supply its current luminosity for tens of millions of years."

Does "current luminosity" mean that the same spectrum will be radiated, or will it be just as bright, but radiating at different wavelengths (like not in the violet-blue and reddish orange-red wavelengths which chlorophyll requires, or the IR that keep us warm)?

**Tags:** the-sun, photons
> **Comments:**
> **username_1**: There would be no effects on Earth for "tens of millions of years" as outlined in the answer to the other question. So no, we would not "notice if the Sun stopped fusing atoms [sic]" and there would be no effects on Earth on those timescales.. Or is your question perhaps - aside from the lack of neutrinos, are there other any other experiments that could be performed that would indicate that fusion had ceased?  
> **username_0**: @RobJeffries question clarified (I hope).  
> **username_2**: @RonJohn The photosphere of the Sun is approximately a [blackbody radiator](https://en.wikipedia.org/wiki/Black-body_radiation). If you keep it at the same temperature it emits the same spectrum.  
> **username_0**: @PM2Ring make that an answer, and I'll accept it.  

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## 1 answers

### Answer by username_1 on 2019-09-30. Score: 2 | Accepted answer

As stated in my answer to [Would we have more than 8 minutes of light, if the sun "went out"?](https://astronomy.stackexchange.com/questions/33520/would-we-have-more-than-8-minutes-of-light-if-the-sun-went-out?noredirect=1&lq=1) , the Sun would cool at roughly constant luminosity for some tens of millions of years. That means "we" would not notice anything change on human timescales (apart from the lack of neutrinos, which has no measurable effect on anything apart from the odd atom in a vast vats of cleaning fluid or water, underground in South Dakota and Japan).

If $dL/dt$ was roughly $-L\_{\odot}/30$ in solar luminosities per million years, then it would be 1000 years before the luminosity of the Sun fell by 0.1%, which is roughly the kind of variations we see over the course of the solar cycle.

However, the most likely evolution of the Sun is for it to contract, maintain a stable luminosity and compensate by increasing its surface (photospheric) temperature.

Given that luminosity is provided by gravitational contraction and the rate of change of gravitational potential energy, then
$$ L\_{\odot} \simeq -\left(\frac{GM\_{\odot}^2}{R^2}\right)\frac{dR}{dt}, \tag\*{(1)}$$
where $R$ is the radius.

If the luminosity is constant and given by
$$L\_{\odot} = 4\pi R^2 \sigma T^4,$$
where $\sigma$ is the Stefan-Boltzmann constant and $T$ is the effective (photospheric) temperature, then
$$ \frac{dL\_{\odot}}{dt} = 4\pi \sigma \left(2R T^4 \frac{dR}{dt} + 4R^2 T^3 \frac{dT}{dt}\right) = 0 \tag\*{(2)}$$

Combining equations (1) and (2) we find
$$\frac{dT}{dt} = \frac{T R L\_{\odot}}{2 GM\_{\odot}^2} = 90\ {\rm K/Myr}$$
i.e. The Sun surface would heat up by 90K every million years.

This gradual warming would change the spectral type of the Sun, moving it towards an F-type star. The spectrum of light it emitted would shift to shorter wavelengths (according to Wien's displacement law, the peak wavelength in the spectrum is inversely proportional to temperature) and a greater fraction of the Sun's light would appear in the ultra-violet part of the spectrum.

> **Comments:**
> **username_3**: Is that odd atom at the bottom of a cleaning vat D2O?  
> **username_1**: @johndoe No, Chlorine.  

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