# Why is the sun's surface so cool?

1. Oct 7, 2004

### Joop

Hello.

If the sun's core is several hundred million degrees (Fahrenheit), why is it that the surface is only a scant 11,000 degrees? I understand science is still confounded by the atmospheric heat of the sun (again, tens of millions of degrees in the corona), but I've been lead to believe that modern science can answer the surface temperature question.

If this is so, what is a reasonable explination for this?

To work this out for myself, I pondered why the surface of the earth wasn't warm in light of the apparent heat radiating from the core. To my limited knowledge of how heat, as a radiation of agitated atoms, interacts with non-agitated atoms, it stands to reason that the enegry levels (that we experience as heat_) are absorbed (and disfussed) by the many layers of non-agitated atoms in the rock. This - it seems - reduces the overall heat (as it's now shared between the two parties).

The sun, on the otherhand, doesn't seem to have anything to absorb the heat. Is it that the atoms that make up the radiation and conductive layers of the sun are SO vast that the temperature just drops off to 11,000~ degrees by the time it crests to the surface? How deep is the sun, pole to pole?

Just curious.. thanks.

2. Oct 7, 2004

### chroot

Staff Emeritus
Energy is only liberated within the Sun's core, which is just the inner few percent of the Sun's radius. The energy escapes into the much larger volume of the envelope, and the energy density falls accordingly.

- Warren

3. Oct 7, 2004

### Joop

Thank you for the prompt reply.

Care to take a stab at why the atmosphere of the sun is warmer than the surface based on your knowledge of physics?

4. Oct 8, 2004

### cepheid

Staff Emeritus
Well, the term "atmosphere" of the sun is vague, to put it mildly. It does not have a solid, definable surface, and atmosphere is meaningless, for it consists entirely of gas! (as you know), the different layers of which we have defined based only on their differing compositions/properties.The layers above the photosphere (the "optical" surface) I guess could be called the "atmosphere", in which case your question would be: "Why does the temperature increase from the base of the chromosphere up through the corona?" We got some sort of "hand-waving" explanation in first year astronomy, and unfortunately, after all that, I don't know the answer. Maybe chroot does.

:rofl:

5. Oct 8, 2004

### Tide

The reason why the photosphere is so cool (relative to the interior) has less to do with geometry than it does with simple radiative cooling. While its core temperature is millions of degrees Kelvin, the Sun is embedded in essentially empty space whose temperature is only a few degrees Kelvin. Heat flows from hot (in this case, very hot) to cold (again, in this case, very cold!).

Regarding the corona, I believe it's still an outstanding problem in physics to explain why it is so hot. In any case, its heat capacity and opacity have relatively little influence in impeding the radiative flux of energy from the Sun.

6. Oct 8, 2004

### Clausius2

Where have you seen that figure?. That is not the temperature of the sun's surface.. That's the Black-Body temperature equivalent. The spectrum of radiation of the sun arrives at the earth with some average radiation. The temperature you posted (approximately 6000ºC) is obtained by means of the Abbot Solar Constant "G":

G=1357 W/m^2 is the amount of power per square meter that collides with a surface situated in our external atmosphere.

Thus, one can figure out the equivalent sun temperature (supposing it as a Black Body) that has the same radiation spectrum:

$$q=G 4\pi L^2$$ are the watts that reaches our atmosphere, where L is the distance sun-earth.

Due to energy conservation: $$q=4 \pi R_s^2 \sigma T_s^2$$ which is the expression of the Stefan-Boltzmann law applied to the sun. Rs is the sun radius.

Working Ts out we obtain:

$$T_s=(\frac{G*L^2}{\sigma R_s^2})^{1/4}=(\frac{1357*(1.5*10^{11})^2}{5.67*10^{-8}*(6.96*10^8)^2)})^{1/4}=5774K$$

But this is not the sun temperature in the upper corona!. It's a simplified method for calculating an equivalent sun temperature. The real temperature is about 1.000.000 K. See this:

http://hypertextbook.com/facts/2000/CCoraThomas.shtml

In Solar Energy engineering this 6000K temperature is adopted as the mean temperature of the sun. But this is because usually thermal engineers are a bit rude. :rofl:

:surprised

Last edited: Oct 8, 2004
7. Oct 8, 2004

### LURCH

Perhaps that is the reason for the higher temp in the corona; it's innefficiency at radiating heat away.

8. Oct 8, 2004

### Joop

Just for clarification, the corona is considered the atmosphere of the sun.

http://www.astro.uva.nl/demo/sun/corona.htm

Figured this was a well known terminology, I apologize if you were unaware of it.

Last edited: Oct 8, 2004
9. Oct 8, 2004

### Joop

You make my point, then attempt to break it by conjecturing the corona is the surface of the sun, which it isn't. So, is the surface (photosphere) 11,000 in actuality? If so, then why did you post this?

To answer your initial question, I've seen this figure in numerous locations. Discover, scientific american, national geographic. Just put "11,000", "sun" and "surface" through google and you'll bring up 3,000 more.

Last edited: Oct 8, 2004
10. Oct 8, 2004

### CJames

I don't see how this can possibly be true. I suppose it is possible that the side facing away from the sun would be exceedingly cold, but the side facing the sun would be extremely hot, just as is the case on Mercury and even the moon. I suppose the point here is that it wouldn't be the corona itself that is burning you, rather the radiation from the sun. But unless I'm totally missing something, you wouldn't freeze to death.

In curiosity relating to the corona, could it be that the particles are so hot because, by some unknown mechanism, they have traversed the distance from the core to the corona in a relatively incredible short amount of time?

11. Oct 8, 2004

### CJames

This link is useful in answering the question of why the corona is so hot:
http://www.space.com/scienceastronomy/astronomy/solar_corona.html
Scientists observed a shockwave formed during a solar flare. The shockwave didn't vibrate nearly as long as suspected, suggesting that the corona has a much higher viscosity than was previously thought due to high turbulence. This viscosity may relate to its ability to retain heat.

12. Oct 8, 2004

### Nereid

Staff Emeritus
The mechanisms responsible for the heating of the corona have been the subject of much research, going back over a century. Here and here are links to APOD, which provide lots of links to sites which discuss various theories.