# I How to describe the Sun's interior?

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1. Apr 14, 2018

### mjda

My question to you is this...

Can the interior of the Sun be described as an ideal gas?

From my knowledge, to describe a body of gas as an ideal gas, the separation between the particles must be much greater than the size of the actual particles.

How could one justify whether the Sun fits this?

2. Apr 14, 2018

### mathman

The interior is best described as a plasma. Nuclear reactions are going on all the time.

3. Apr 14, 2018

### JMz

It's a close approximation, in any local volume. The reason, in part, is that it's a plasma. So the dominant "particles" by mass are bare nuclei, mostly H and He, which are separated from each other by large distances: factors of 1000 or so. However, things get trickier when you include the electrons. For them, you need to include the fact that they are moving very fast, which gives them "room to move" (in phase space) freely enough to behave ideally, at solar densities. (At white-dwarf densities, in contrast, electrons do not have enough "room".)

In theory, another impediment to ideal-gas conditions can occur with a huge magnetic field. However, that's not present in the Sun. And for objects that do have such large fields, they usually have much bigger "problems" living up to the requirements of ideal gases.

FWIW, nuclear reactions in the Sun only occur in the core, and are actually rare events: Any one atom has about 1e-10 probability per year of participating in a fusion event. That's something like 1e30 times less frequent than the kinds of events (i.e., the collisions) that produce ideal-gas behavior in the core.

4. Apr 14, 2018

### mjda

Say one knows the mean density inside the Sun, and the mean temperature too, how can you use these to quantitatively justify reasoning?

5. Apr 14, 2018

### JMz

Well, to the extent that there's a layer where the local density is the approximately the mean (~ 1 g/cm^3) and the local temp. is the mean (which I don't recall, BTW), here is the reasoning I'd use:
1. For the Solar composition, local temp. => local degree of ionization (which is pretty complete, for the Sun).
2. Degree of ionization => mean particle size (basically, bare nuclei & electrons, in the Sun's case, because of nearly complete ionization).
3. Local mass density + degree of ionization => local number density (particles/cm^3, say), esp. number density of electrons & number density of nuclei. This will be ~ (Avogadro's number)/cm^3 ~ 1e24/cm^3 for both electrons & nuclei (since the dominant nucleus is H, for which the ratio is exactly 1:1).
4. Number density => mean distance between nuclei or between electrons, ~ 1e-8 cm.
5a. Mean nucleus radius ~ 1e-13 cm ~ 1e-5 times smaller than mean distance: So nuclei form an ideal gas. (In the core, the density is higher, so the ratio is more like 1e-3 instead of 1e-5.)
5b. For electrons, we need to take a detour through their energy to see how "big" they are (deBroglie wavelength) compared to their spacing. This is (h*c)/energy. At these temperatures, the energy is mostly their mass*c^2, not their kinetic energy (by a factor ~ 1e5 or so). So that wavelength is ~ (h*c/m0c^2) = h/(m0c) for Plank's constant h and electron rest mass m0: the Compton wavelength, which is ~ 1e-12 m = 1e-10 cm. As with the nuclei, this is much smaller than the mean distances, ~ 1e-8 cm. So the electrons also behave pretty much ideally.
6. For gas-law purposes, the nuclei and electrons behave independently: Dalton's law of partial pressures. :-) Since each behaves ideally, so does the composite.

6. Apr 14, 2018

### rootone

I'm sure I heard from a reasonable source which I now don't remember that ...
The amount of fusion going on in the core of the the Sun produces about the same energy per volume as does a compost heap.
It is however very much bigger than a compost heap.

7. Apr 14, 2018

### JMz

Another one: Solar flux per unit mass = 4e26 watt/2e30 kg = 2e-4 watt/kg. By comparison, a human body emits ~ 100 W, or 10,000 times as much as the Sun, gram for gram. ;-)

(But we are straying a bit from the OP.)

8. Apr 14, 2018

### Fervent Freyja

Just looking at some of the surface activity gives us reason to believe that the solar interior could be incredibly complex and that we could find there are a variety of mechanical processes at work inside of stars.

Why wouldn't a star be a complex, beautiful machine, with physical processes similar to many that occur for earth?

9. Apr 14, 2018

### JMz

Because the Sun is a plasma. It cannot support, say, plate tectonics, nor air/ocean or air/rock or ocean/rock interfaces, nor rocks at all, nor liquids, nor any chemistry at all. The interior of the Sun is far simpler than the interior of the Earth. We have known most of what's going on even in the core of the Sun for about 60 years or more, much longer than for much of the Earth's interior.

10. Apr 15, 2018 at 6:28 AM

### snorkack

The pressure inside Sun is dominated by ideal gas pressure.
Which is actually important for the stability condition of Sun.

11. Apr 15, 2018 at 10:44 AM

### JMz

Quite right. In fact, we have known much of story of the interior of the Sun for 100 years, precisely because it is so nearly an ideal gas.

12. Apr 15, 2018 at 2:45 PM

### Fervent Freyja

No, we do not know. We do not even understand the cause of surface temperatures- predictions are way off.

The variety and complexity, especially those occuring in specific periods and cycles, of activity on the solar surface has deeper implications for interior mechanics- I doubt a uniform pot of plasma could give rise to all the established surface phenomenon we observe.

13. Apr 15, 2018 at 3:31 PM

### JMz

The outer layers of the Sun are not entirely plasma, and they are subject to both large-magnitude (but small-scale) magnetic distortions and to a thermal environment that is far from isotropic. (Outward-going photons have a good chance of escaping without further interactions, obviously. Not so in the deeper layers.)

But this thread is about the interior. We know the interior very well indeed -- much better than the Earth's interior or the Sun's outer layers -- and we have known it very well since the 1950s at the latest. The fact that you personally doubt this doesn't matter here: If you would like it seriously considered in PF, just find some recent peer-reviewed science to support your POV, and cite it.

14. Apr 15, 2018 at 3:38 PM

### Fervent Freyja

Please cite the work claiming to have direct observations of the solar interior.

15. Apr 15, 2018 at 3:57 PM

### JMz

Let's not be silly. Beyond neutrinos (for which we do have such observations), we don't have direct observations of the interiors of any astronomical bodies, including Earth. But the idea that we can't know without direct observations isn't something we require. Do you have direct observations of the surface of Mars? No person has been there. But we do know how all the steps in reasoning work, so we can relate what our radio receivers pick up from the orbiters to what the surface looks like, and even (often) consists of.

We learned most of the required physics in the 19th Century -- specifically including the requirements to draw the correct inferences. This isn't speculation. Really.

16. Apr 15, 2018 at 4:09 PM

### Ken G

It should probably be stressed that there are two levels of processes going on inside the solar interior, one level that is pretty simple (gravity, radiative diffusion, ideal gas physics, not even much in the way of plasma physics), and one that is very complicated (convection physics, magnetic dynamo physics, plasma wave physics, etc.). That we understand so much about the solar interior is not because we understand both those levels of complexity so well, it is because we only need to understand the first level to get most of the global behavior right (and can often approximate the second level in a fairly rough way but it suffices). But one thing we don't get right is the complicated surface phenomena, so for that, we would need to know more about the interior than we actually do. Thus, in a sense, you are both right.

Still, the reason we think we have the basic picture right is the diagnostics we do get from the interior: neutrino observations and helioseismology observations of the surface fluctuations that come from the "ringing" of pressure waves throughout the solar interior, as well as population synthesis over the behaviors of whole classes of stars like the Sun.

17. Apr 15, 2018 at 4:12 PM

### Fervent Freyja

Silly? Let's see how an experimental particle physicist doesn't go ballistic at anyone trying to pin something without direct obsevation to the SM...

We do have direct observation of the surface on Mars.

So, you don't have any evidence to cite? You realize you are referring to unproven, hypothetical models when referring to the solar interior. The problem I pointed out is that predictions derived from those models have been very, very incorrect about important parameters regarding solar surface temperatures- so, why should I not question the model if it cannot produce accurate predictions to begin with, something so silly and simple as surface temperature?

18. Apr 15, 2018 at 4:14 PM

### Ken G

Because it can produce the surface temperature in a global or averaged sense, it just cannot produce all the detailed variations that the surface temperature shows. There's a difference. There's no need to see these issues with black-or-white glasses-- there is much we understand and can predict well, and there are still some important details we cannot predict well. So the study of the Sun continues, it's not like there is no journal called "Solar Physics" that still receives submissions!

19. Apr 15, 2018 at 4:19 PM

### Ken G

Relevant to all this is an interesting story in the history of solar physics. Since we did think we understood the solar interior quite well, in a general sense, we thought we could predict the neutrinos it would emit to pretty good accuracy. Then, the neutrinos were observed, and they turned out to be only 1/3 what we expected! Crisis-- could our solar models be so off? Actually, no-- it turned out that it was the neutrino observations that were being misinterpreted because there was something we didn't know about neutrinos. They oscillate between the three "flavors"! So something we did understand about the solar interior taught us something we did not understand about neutrinos.

20. Apr 15, 2018 at 5:33 PM

### davenn

and where are your citations for these claims ?