After I presented the random walk of photons from the Sun's core to the surface a student asked "why do they move outward rather than just randomly walk around in the core?" Can someone suggest a simple "Intro to Astronomy" level reply? [The answer has occurred to me while posting this but I will be interested in other's approaches]

I think that the simple answer is that in the center of the sun the density is much higher. Therefore a photon travelling through the plasma will not have a complete random walk. Towards the center the collision rate will be greater, thus the mean free path away from the center will be longer and a net outward flow will be the result.

__________________

Any comments in glorious red are to be considered in ModeratorMode.


善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

The endpoint of a "drunkard's walk" gets (on average) farther from the startpoint as the step count increases.(IIRC, it's something like the square root of the count, but that's probably the 2D situation.) So it's unlikely for a given photon to end up back in the core, and more likely for it to end up at increasing distances from the core as time passes. The increase in mean free path mentioned by the previous poster will compound this bias.

Grant Hutchison

Hmmmm...Now you're on my level...simple.

Simple...."It's random and besides, they can't stay in there (core) forever"

Cute....."Well, wouldn't you wanta get the heck out of there?"

__________________
Lighten up! This is a stellar board!

Even without a density gradient, photons would still escape. If the travel were completely random, then some would eventually escape.

Consider 1000 photon collisions with particles. Some go forward, some go backward, some go sideways, up and down. So long as it is random, some will always escape forward. The only way to "randomly walk around the core" would be if the collisions preferentially sent the photons either backward or sideways.

A silly way to think about it would be to pretend that a student is in the back of a classroom** with 10 rows of chairs. Every 6 seconds he/she flips a coin. If it is heads they move forward a row. If tails they move back. If they get to the front of the class, they can leave. If they flip "tails" at the back of the room, they stay in the last row. (Just like a photon in the center of the core cannot go "back" any further)

Also, every 6 seconds, another student is added to the last row.

After a while you'll have a steady state of ~ 1000 students in the last row, ~500 in row 9, ~250 in row 8, etc, with ~ 2 students in the first row, half of which (on the average) leave the room every 6 seconds.

**a really big, triangular shaped classroom

edited to correct numbers
edited again to add that I think my numbers are all wrong, you'd actually have about the same number of students in each row. Plus it would be better to think of having less of a chance of moving foward. (maybe they need to flip heads three times in a row to move forward), but you get the idea

And the other 1/2 are asleep :-)

This really cries out for a classroom demonstration.
I'll bet you could find several already written up, and a
good one shouldn't need more than three or four minutes
of classroom time.

At the very least, a computer animation of the process.

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

Now that you mention it, I believe that there is such an animation as an exercise in the CLEA exercise series. Its called "The Flow of Energy out of the Sun" As I recall, it was a pretty dull lab but it might make a good demo ... I will look at it and maybe run it in class tomorrow.

I didn't do the animation, but a simulation was pretty easy in a spreadsheet. (Actually, I suspect the math is easy to do on paper, but I didn't trust myself to not mess it up.)

Turns out that if you only need to flip heads once to move forwards, or tails once to move back, then at steady state row 10 has 20 students, row 9 has 18, etc...

If you make it more difficult (must flip heads 3X to move forward; flip tails 3X to move backward, rest of time stay in same row), then row 10 has 80 students, row 9 has 72, etc...

Turns out that the simulation was more boring that I would have expected.

There's a very simple demonstration.....the movement of the photon is determined by statistical mechanics....similar to the multiple gas particles in-a-box, with a door to each half-side....chance of all the particles being on one side 1/2 to the n. In like manner, shaking a container of mixed nuts of different sizes...brazil nuts, almonds, peanuts, cashews, macademia, walnuts. etc...which are originally homogeneous in distribution....will cause the smaller ones to preferentially settle into the created voids....and the larger ones to move to the top, before you open it. Statistically speaking...the smaller ones need smaller voids to fill...which occur with greater frequency. Same idea as the random walk, mean free path as mentioned.....but the availability of a box of mixed nuts from the supermarket makes it an easy and edible demonstration. As a bonus, the Brazil nuts, my favorite, are also the most radioactive food you can buy in the supermarket....about twice normal background....radioactive potassium in the jungle soils. Ciao. Pete

It's also the reason that rocks in our New England soils move slowly upwards in the farm fields.....viewed in time lapse photography....the alternating freeze/thaw cycles of rain, freeze, frost heaves, and thaw.....moves the small soil particles down, and the big rocks up like Brazil nuts in the can....so the farmer can periodically glean (her/his) fields.. .and add to those famous stone walls. Sci. American had an article on this called "Patterned Ground" I believe...circa 1986? Ciao. Pete.

Be careful about your assumptions concerning Brazil Nuts, for there is also a "Reverse Brazil Nut Effect" -- sometimes the large particles in a mixture sink to the bottom.

For instance: Vibration-Induced Granular Segregation

Search for "Brazil Nut Effect" to learn more.

__________________
0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...

It seems that the answer is just diffusion, so analogy with gas diffusion should get the point across. Photons are generated in the centre, so there the sun is photon-dense, and space is photon-sparse, so diffusion indicates that photons will show net movement toward the sparse region.

I guess that there is some argument for how to translate the photons from extreme high energy to moderate high energy, but that is definitely beyond me.

The big difference with gas-diffusion would be that gas particles
can not occupy the same place at the same time.
I understand that photons, however can.

__________________
Join the Illuminati

That's interesting, Thanks. trinitree88

You're welcome. There are a lot of variables. That classes of particles in a mix tend to segregate when vibrated is true. How they segregate probably depends on, among other things, sizes, shapes, densities, the waveform of the vibrations, friction between particles, friction between particles and the fluid around them, friction with the container, the geometry of the container, the properties of the fluid, the gravity, the temperature, and how much one prefers certain types of nuts. No, not the last one.

A lot of the observed behavior is non-intuitive. It's a rich field for research. People who create mixtures often desire that they stay mixed. Others are interested in how to utilize the segregation of a mixture to refine it or sort it. Geoligists spend a lot of time wondering: now how did that happen? It's interesting stuff -- and far from my field.

__________________
0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...

True, but not fundamental to diffusion. The only difference this makes is that there is no "pressure" effect that drives photons away from one another, which allows a huge density gradient with basically only the random-walk mechanism operating.

The gas-diffusion model I was thinking of, was of one (coloured) gas diffusing into another, and vice versa, so that pressure considerations were nullified in this case also.

It is important to remember that the photons are not bouncing off of each other, they are being absorbed and reemmitted by the interactions with the nuclei in the solar interior. This is how the photon field goes from gamma rays at the core to 5800K thermal radiation at the photosphere.

The simple explanation for the outward transport of diffusing photons is that photons that are in the Sun can leave it, but photons that have left the Sun do not come back. This sets the direction for the diffusion. You can see this by imagining that you surround the Sun with a mirror, such that any time a photon leaves the Sun, it gets reflected back into the Sun. If you did that, then the photons would just bounce around the Sun, with equal density everywhere. It makes no difference what the mean-free-paths are. The whole Sun would be the same temperature! So it's the uni-directional character of escape from the surface that governs everything.
This is related to Joff's post about the photon-sparse character of space. Note that the fact that photons can be in the same place, and that they don't bounce off each other, is not of fundamental importance, and also note that photons do indeed produce pressure. Pressure is momentum flux, it has nothing to do with collisions, and it can be enhanced for gas particles that cannot be in the same place at the same time ("degeneracy pressure"), but that only matters if you care how big the pressure is.

I've heard it said that if you line up economists end-to-end they will all point in different directions.

So, fill the Sun with economists and give each a ball. Have them assign a vector for next year's world economy and have them, simultaneously if you wish, pass their ball in their calculated direction (the speed component is optional). Of course, allow the balls passed into space to escape.

For the sophmores, insert a mean economist in the middle and ask them to discuss his role.

For the juniors, would an analogy exist for Heisenberg?

__________________
Lighten up! This is a stellar board!

My understanding, without reading any of the so-far answers, is a simple one. Photons DO wander around inside the sun, but random chance has it that some will be bounced out eventually. Naturally, those are the only ones that reach us.

__________________
My son is my universe.

Isn't it simply that, at any distance from the center, a larger solid angle of directions increases the distance from the center than decreases it? Photons are emitted in completely random directions so the odds are that they will slowly move away from the origin.

Hmmmm....wouldn't the solid angle for advancement away from center be the same, 2pi sr, from any point other than the center? The greatest angle is at the center itself (4 pi sr), which could add to the confussion, somewhat.

__________________
Lighten up! This is a stellar board!

If you go perpendicular to the radius vector you increase your distance from the center.

Given that the distance travelled between scatterings is not zero, IMO's point does hold in spherical symmetry. But what about plane-parallel symmetry? What about diffusion of photons from a central plane, through an atmosphere on both sides? You still get the same diffusion issues mentioned in all the posts above, but there is no solid angle difference in that case. The solid angle issue is a detail, not central to the point, though it does assist diffusion from the center of the star, it's true.

I may have misunderstood your statement. I didn't see how "a larger solid angle of directions increases the distance from the center" would work. Since a hemisphere perpendicular to the radial vector is always 2pi seradians, any movement to the outer hemisphere would increase the distance just as any movement toward the inner hemisphere would decrease it. [This would be the 50/50 coin flip analogy as stated by others.] Would solid angle amounts vary along a radius, or did I miss something (as usual)?

__________________
Lighten up! This is a stellar board!

I think IMO's point is that the tangent to a spherical surface always diverges from that surface in the outward direction. So all outward directions plus the tangent plane take you outwards.
But it seems to me that, at the limit, when the sphere is very large and the mean free path very small, this converges on a 50-50 split between "in" and "out".

Grant Hutchison

It appears, according to Martin Gardner at least, that a 2D and a 3D random walk obey the same rules: that the RMS distance from the starting point after n steps (which need not be of equal length) is equal to the average length of a step times sqrt(n). So as time goes by, photons are more likely to be found far from, rather than near to, the site of origin.
I realize that this is not necessarily intuitive to demonstrate to your students without some sort of simulation, but isn't it the fundamental explanation, given that the core of the sun produces photons and the outside of the sun doesn't?

Grant Hutchison

Yeah, man. Thermodynamics. Energy flows from hot to cold, not the other way around.

And the sun is most definitely hotter inside than out, no matter what Mozina says.

__________________
My son is my universe.

Forgive me if I'm being obtuse, but doesn't the outside of the sun produce photons simply by existing, particularly by existing at ~6000K? (I mean, I'm generating photons right now --- don't tell my boss.)

I suppose the issue is that the majority of photons are generated internally?