## Saturday, June 08, 2019

### What the Hell? (Solar Luminosity)

I found the following graph on Wikipedia, when I looked up solar luminosity.

It shows that solar luminosity was significantly lower in the past, which counters the denier argument that "well if CO2 was 6000 ppm back then, why wasn't there immense warming?") But I do not understand this graph. Why is temperature so constant? The Sun is the perfect example of a blackbody -- it absorbs all radiation incident upon it. (And everything else, too.) So why doesn't it follow the Stefan-Boltzmann law, where

luminosity = sigma*T4 ?

I'm confused. Can anyone help me?

William M. Connolley said...

At a guess, because temperature is set by the physics of fusion. Radius and luminosity adjust accordingly.

Marco said...

As William notes, you also need to take into account the (change in) radius:
https://astro.unl.edu/naap/hr/hr_background2.html

Thomas said...

The fact that the Earth was at all habitable when young is called the faint young sun paradox.

I think the constant surface temperature is based on when the atmosphere is cool enough to be transparent to thermal radiation, and thus has nothing to do with the fusion inside. The core tends to get hotter over time as the amount of hydrogen drops so you need higher temperature to provide enough fusion to oppose gravity.

JoeT said...

The term on the right is in units of power per unit area. Luminosity is in units of power, so L = 4 * pi * R^2 * sigma * T^4

The surface temperature of a star is pretty much set by the mass. The sun is G-class with a T_s ~ 5800. Heavier stars can have a surface temperature up to 50,000 K, while lighter stars can go down to 2000 K.

Over time, the mass of the sun's core is very slowly shrinking because of the depleted hydrogen. From the virial theorem, about half the gravitational energy released by the shrinkage increases the core temperature and half is radiated away as luminosity.

David Appell said...

JoeT, I don't really get what you're saying.

Isn't the Sun a blackbody? IF so, isn't its luminosity proportional to its T^4?

What does T pertain to?

JoeT said...

David, the Stefan-Boltzmann equation is in units of flux or energy per unit time per unit area. Luminosity is in units of power, energy per unit time. To get the luminosity of the sun I need to multiply the SB equation by the surface area of the sun - 4 * pi * R^2. The luminosity of the sun in the figure is going up, NOT because the temperature is increasing, but because the radius of the sun is increasing.

I hope that helps.