What is Earth's future warming due to the Sun's increasing luminosity?

[swampwiz]

TL;DR Summary

Presuming the same CO2, etc. level as today, what would be the rise in the average temperature of Earth due solely to the Sun's future rise in luminosity?

Obviously, at some point, the Sun will be a red giant, and it's going to be very, very hot on Earth. I'd like to know what the expected rise in temperature would be due solely to the Sun, while holding the composition of the Earth's atmosphere constant - or at least constant except for the gas that would be escaping due to the hot temperature.

 

[fresh_42]

Forget about $CO_2$ et al. Long before the sun will become a red giant it will be too hot for our lifeforms. AFAIK this will start at some point when the ratio of helium fusion to hydrogen fusion gets too high.

I'm interested as well, whether this is actually true or just pop science knowledge, and when it will be the case. Certainly long before the rest of 4.5 billion years.

 

[swampwiz]

Forget about $CO_2$ et al. Long before the sun will become a red giant it will be too hot for our lifeforms. AFAIK this will start at some point when the ratio of helium fusion to hydrogen fusion gets too high.

I'm interested as well, whether this is actually true or just pop science knowledge, and when it will be the case. Certainly long before the rest of 4.5 billion years.

I abstracted out the idea of the ratio of helium fusion to hydrogen fusion with the term "luminosity".

https://en.wikipedia.org/wiki/Solar_luminosity

 

[HankDorsett]

Summary: Presuming the same CO2, etc. level as today, what would be the rise in the average temperature of Earth due solely to the Sun's future rise in luminosity?

Obviously, at some point, the Sun will be a red giant, and it's going to be very, very hot on Earth. I'd like to know what the expected rise in temperature would be due solely to the Sun, while holding the composition of the Earth's atmosphere constant - or at least constant except for the gas that would be escaping due to the hot temperature.

Based off of what I've read. A few billion years from now the sun will become a red giant. It will burn away the atmosphere, scorch the Earth and kill all life on Earth.

I'm wondering if your question is more around the sun's 11-year cycle of solar output? Sun's impact on climate change

 

[swampwiz]

Based off of what I've read. A few billion years from now the sun will become a red giant. It will burn away the atmosphere, scorch the Earth and kill all life on Earth.

I'm wondering if your question is more around the sun's 11-year cycle of solar output? Sun's impact on climate change

No, it's the very, very long-term increase in luminosity I'm getting at - the one that is shown in that Wikipedia article.

 

[Bandersnatch]

what would be the rise in the average temperature of Earth due solely to the Sun's future rise in luminosity?

Here's what I came up with:
The long-term solar luminosity evolution on the main sequence can be approximated by the following equation (Gough, 1981):
$$\frac{L(t)}{L_0}=\frac{1}{1+\frac{2}{5}(1-\frac{t}{t_0})}$$
where $L_0$ is current solar luminosity and $t_0$ is present-day.

This translates to roughly 1% increase in solar intensity per 100 million years, at least in the relatively near future.

The relationship between equilibrium temperature and radiative forcing is $$\Delta T=\lambda\Delta F$$ where $\lambda$ is climate sensitivity - here we'll use 0.8 after Wikipedia.
The relationship between solar intensity (flux) and radiative forcing is $$\Delta F=\frac{1}{4}\Delta I*(1-\alpha)$$
The 1/4 factor is from Earth cross-section to surface area. $\alpha$ is albedo (approx. 0.3).

The result, assuming climate remains as sensitive as it is today and albedo doesn't change (both unreasonable assumptions):

So, under these assumptions (including the one about me not messing up), it would be about 20 K hotter in a billion years and over 400 K total towards the end of Sun's life on the main sequence.
When it goes red giant, depending on mass loss it might (or not) envelop Earth, in which case the latter will evaporate.

 

[swampwiz]

Here's what I came up with:
The long-term solar luminosity evolution on the main sequence can be approximated by the following equation (Gough, 1981):
$$\frac{L(t)}{L_0}=\frac{1}{1+\frac{2}{5}(1-\frac{t}{t_0})}$$
where $L_0$ is current solar luminosity and $t_0$ is present-day.
View attachment 247370
This translates to roughly 1% increase in solar intensity per 100 million years, at least in the relatively near future.

The relationship between equilibrium temperature and radiative forcing is $$\Delta T=\lambda\Delta F$$ where $\lambda$ is climate sensitivity - here we'll use 0.8 after Wikipedia.
The relationship between solar intensity (flux) and radiative forcing is $$\Delta F=\frac{1}{4}\Delta I*(1-\alpha)$$
The 1/4 factor is from Earth cross-section to surface area. $\alpha$ is albedo (approx. 0.3).

The result, assuming climate remains as sensitive as it is today and albedo doesn't change (both unreasonable assumptions):
View attachment 247377
So, under these assumptions (including the one about me not messing up), it would be about 20 K hotter in a billion years and over 400 K total towards the end of Sun's life on the main sequence.
When it goes red giant, depending on mass loss it might (or not) envelop Earth, in which case the latter will evaporate.

Yes, this analysis is what I was looking for. Thanks

OK, so the concern about CO2-genic global warming at +2K would have been realized in 100 million years in a static-CO2 situation.

 

[Torbert]

I have so much and many thoughts I cannot rigorously prove I will stop myself at "That is quite a conclusion to draw."