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ImaginalDisc
2008-Sep-20, 08:19 PM
Howdies, I've posted once before, ages ago, and I hate to ask another astronomy question but you folks were really helpful then so here goes:

I've been trying to understand the mechanisms that lead to a yellow dwarf becoming a red giant, and I understand that is has to do with the hydrogen in the core being all used up, and the fusion of hydrogen into helium then taking place in layers outside the core.

If my grasp of the mechanism is right to that point it leaves me very confused. In ordinary chemistry if a reactant was being used up in one place in a fluid, that reactant in the solution would diffuse in the direction of the decreased concentration. So, if millions of tons a second of hydrogen are transforming into helium, why isn't hydrogen outside the core diffusing into the core? How can there be large concentrations of hydrogen in one layer, and essentially none at all in another layer?

StupendousMan
2008-Sep-21, 02:50 AM
I've been trying to understand the mechanisms that lead to a yellow dwarf becoming a red giant, and I understand that is has to do with the hydrogen in the core being all used up, and the fusion of hydrogen into helium then taking place in layers outside the core.

If my grasp of the mechanism is right to that point it leaves me very confused. In ordinary chemistry if a reactant was being used up in one place in a fluid, that reactant in the solution would diffuse in the direction of the decreased concentration. So, if millions of tons a second of hydrogen are transforming into helium, why isn't hydrogen outside the core diffusing into the core? How can there be large concentrations of hydrogen in one layer, and essentially none at all in another layer?

The interior of a star is not very much like a flask of liquid chemicals in a lab on Earth. The physical mechanisms which dominate the two situations are different.

For one thing, gravity plays a much stronger role in the stellar interior than in the flask. Note that the two items in question -- hydrogen nuclei and helium nuclei -- differ in mass by a factor of four. The hydrogen tends to float on top of the helium in the solar interior.

For another thing, consider the time and distance scales involved. How long does it take molecules to diffuse from one side of a flask to the other side? How long would it take nuclei to diffuse from one side of the stellar core to the other side? At what rate is hydrogen being converted to helium?

The stellar interior is also a dynamic place. In some stars -- not the Sun, I believe, but the most massive ones -- the core may be unstable to convection, which means that material which is slowly diffusing its way from point A to point B may be picked up and carried to point C by large bulk motions.

ImaginalDisc
2008-Sep-21, 06:41 AM
Thank you, I hadn't thought about calculating the diffusion rate. . .for some reason.

I wonder what diffusion equation is most appropriate for stars. I'll start looking. I'm only studying ecology, so my math isn't terribly strong (though statistics rocks my world.) Maybe I'll learn some more math on the way.

Diffusion in fluids and geology's mostly dependent on temperature and surface area, but there are other factors, such as tortuousity and porosity and I don't even know what variables would apply inside a star.

I love it when questions lead to more question.

Romanus
2008-Sep-21, 03:28 PM
To add to what SM already said, the core is much denser--especially due to regular-old compression--than the overlying layers, which probably makes it more difficult still to mix down hydrogen. Also, in solar-type stars the core is radiative, not convective, which limits mixing. Though higher-mass stars have convective cores, they're overlain with radiative zones (opposite to the Sun's case), which probably again reduces mixing. It's worth noting that, IIRC, all stars of roughly a solar-mass and up use only about 10-12% of their hydrogen.

It is theoretically possible for stars to utilize more; for instance, "late"-type K and all M-stars are fully convective, which means they can use all of their hydrogen; combined with their low consumption it gives them potential lifetimes thousands of times longer than the Sun's, as well as a "get out of jail free" car from red gianthood, which can only happen to stars that can't use all their fuel. Also, modelled stellar collisions and mergers--such as in the "blue stragglers" found in some globular clusters--show that they can suitably stir up a star's interior enough to rejuvenate it, by mixing up "burnt" helium and mixing down fresh hydrogen.

dgavin
2008-Sep-24, 12:50 AM
To add to what both of them said, you should also consider the Solar Models of the transition into a red giant phase.

During the main sequence, a star burns hydrogen in it's core. As soon as this hydrogen burring starts, which is in the center of the core, it leaves helium in it's place. So the hydrogen burning actually migrates out from the center slowly over time, as the helium ash core grows.

As the hydrogen burning moves further away from the core, the temps reduce, and so does the rate of burning. This fits the model which show stars start out hot, and cool off as they settle into the main sequence.

The Radiative zones as the others mentioned, prevent a influx of new hydrogen from the convective zones. It's possible there is a little mixing, but it's not near enough to counteract the radiative pressure.

Eventually after about 15-20% of the Hydrogen has been burnt, the shell part of the core the hydrogen is burring in, can no longer maintain fusion at a rate to counteract gravity. The Helium ash core, the Hydrogen shell, and the radiative zone start to get compressed by gravity. Eventually the temps raise enough that the shell burring recommences, and at a slightly faster rate then before this started, until once again the shell cools and the collapse starts again.

This variable cycle repeats for millions, likely even a billion years. And matches the model of some known variable stars. (Incidentally it's very likely our Sun is starting in this phase, explaining it's 2% Variableness in its 22 year cycle).

Eventually a point of collapse is reached, where the temps in the helium ash get hot enough, it's starts to burn. This is usually indicated by the Helium Flash spectral lines. There are typically from 1 to three flashes like this (someone chime in if stars have shown more then 3 please, i might be outdated on this)

After these flashes, the star migrates into the Helium burning phase, where it also rekindles hydrogen burning in a shell, above a small radiative zone, above the helium core. Because of the increased amount of energy from helium plus the hydrogen shell burning, the radiative zone above the hydrogen expands, pushing the outer convective zone away, which cools that zone as it expands, leading it to shift color towards red, as it continually increases in size.

And wala, you have a red giant.

Spaceman Spiff
2008-Sep-27, 04:34 PM
To add to what both of them said, you should also consider the Solar Models of the transition into a red giant phase.

During the main sequence, a star burns hydrogen in it's core. As soon as this hydrogen burring starts, which is in the center of the core, it leaves helium in it's place. So the hydrogen burning actually migrates out from the center slowly over time, as the helium ash core grows.


So far, so good....

But this....



As the hydrogen burning moves further away from the core, the temps reduce, and so does the rate of burning. This fits the model which show stars start out hot, and cool off as they settle into the main sequence.

The Radiative zones as the others mentioned, prevent a influx of new hydrogen from the convective zones. It's possible there is a little mixing, but it's not near enough to counteract the radiative pressure.

Eventually after about 15-20% of the Hydrogen has been burnt, the shell part of the core the hydrogen is burring in, can no longer maintain fusion at a rate to counteract gravity. The Helium ash core, the Hydrogen shell, and the radiative zone start to get compressed by gravity. Eventually the temps raise enough that the shell burring recommences, and at a slightly faster rate then before this started, until once again the shell cools and the collapse starts again.

This variable cycle repeats for millions, likely even a billion years. And matches the model of some known variable stars. (Incidentally it's very likely our Sun is starting in this phase, explaining it's 2% Variableness in its 22 year cycle).

Eventually a point of collapse is reached, where the temps in the helium ash get hot enough, it's starts to burn. This is usually indicated by the Helium Flash spectral lines. There are typically from 1 to three flashes like this (someone chime in if stars have shown more then 3 please, i might be outdated on this)

After these flashes, the star migrates into the Helium burning phase, where it also rekindles hydrogen burning in a shell, above a small radiative zone, above the helium core. Because of the increased amount of energy from helium plus the hydrogen shell burning, the radiative zone above the hydrogen expands, pushing the outer convective zone away, which cools that zone as it expands, leading it to shift color towards red, as it continually increases in size.

And wala, you have a red giant.

:confused:
...is (with few exceptions) a series of misconceptions and otherwise inaccurate statements. There are lots of good resources on the web or in books. Sounds as if you're interested in the stuff, so why not dig in and find out what we currently understand about the evolution of stars such as our Sun? :)

Spaceman Spiff
2008-Sep-27, 05:32 PM
The interior of a star is not very much like a flask of liquid chemicals in a lab on Earth. The physical mechanisms which dominate the two situations are different.

For one thing, gravity plays a much stronger role in the stellar interior than in the flask. Note that the two items in question -- hydrogen nuclei and helium nuclei -- differ in mass by a factor of four. The hydrogen tends to float on top of the helium in the solar interior.

For another thing, consider the time and distance scales involved. How long does it take molecules to diffuse from one side of a flask to the other side? How long would it take nuclei to diffuse from one side of the stellar core to the other side? At what rate is hydrogen being converted to helium?

The stellar interior is also a dynamic place. In some stars -- not the Sun, I believe, but the most massive ones -- the core may be unstable to convection, which means that material which is slowly diffusing its way from point A to point B may be picked up and carried to point C by large bulk motions.

Picking up on this line of thought, convection does indeed occur within the central regions of MS stars more massive than our Sun. Convection is enormously more efficient in mixing material (and transporting energy) than particle diffusion (whether by photons or matter). However, it requires a sufficiently large temperature gradient (decrease in T with increasing r measured from the star's center outward) to operate. A blob of gas finding itself suddenly buoyant will continue rising only so long as it remains hotter and so less dense than its immediate surroundings (and so buoyant) -- thus the minimum temperature gradient requirement. What sets up these conditions in stars ~1.5x the mass of our Sun and greater is the transition of the means of hydrogen fusion: from the pp-chain to the CNO cycle, which becomes more efficient in energy production than the pp-chain above temperatures of about 18 million K. A strong temperature dependence in the energy production via CNO cycle hydrogen burning induces a large radiative flux, which is accompanied by a steepening of the temperature gradient to carry the energy outward.

So getting back to the original question -- in these more massive types of stars, the hydrogen IS mixed continuously within the H burning core, but mixed via convection, rather than by matter diffusion. This means their main sequence lifetimes are actually increased over those of lower mass stars (with radiative cores -- meaning that energy is transported via terribly inefficient photon diffusion) that cannot efficiently transport fresh supplies of hydrogen to the central most regions where fusion is most efficient --- all else being equal. Of course, not all else is equal, since the power demands (far greater surface luminosity in the face of the star maintaining energy equilibrium) of more massive stars is so much greater than that of lower mass stars, and thus the power requirements then dominate the MS lifespan. Nevertheless, if you look at the fraction of the star's mass that is converted into He over the MS lifespan of a star such as our Sun, that number is about 10%. But for the more massive MS stars, that mass fraction is something like a factor of ~2 larger.

More massive stars have larger "gas tanks"and "burn" a larger fraction thereof, but these advantages don't matter much in the end because they are the Hummers of the cosmos due to their enormous power demands relative to their masses (power requirement scales something like (mass)^3-4 during for stars on the main sequence).

Stellar rotation can also induce mixing currents, but that's a whole 'nother story (and is important mainly in rapidly rotating stars).

Finally, matter diffusion IS important in stars whose MS lifespans are long, such as our Sun, but not so much due to concentration gradients as due to simple buoyancy (like oil and vinegar separation). Over the 4.57 billion years of our Sun's existence, the hydrogen abundance mass fraction in the well-mixed outer convection zone of our Sun (outer 30% in radius) has increased by a few % in proportion to that of helium which has decreased by a few% (having sunk inward toward the deeper interior). Heavy elements (being, well, heavy) also can diffuse inward, but find it difficult to do so due to opposing radiative forces (heavy elements have lots of electrons initially attached to them that can absorb photon energy and momentum). So inward helium diffusion is apparently the most important effect.

This is fair (and brief) appraisal of what we understand, although I am sure any experts in stellar interiors out there can clarify some of the finer points.

dgavin
2008-Sep-28, 12:46 AM
So far, so good....

But this....



:confused:
...is (with few exceptions) a series of misconceptions and otherwise inaccurate statements. There are lots of good resources on the web or in books. Sounds as if you're interested in the stuff, so why not dig in and find out what we currently understand about the evolution of stars such as our Sun? :)

I have, and the models are so varied and so many, that there doesn't seem to be one acceptable model. And none of the current models i've seen even attempt to account for impurities in the core, such as iron.

However you are right on one point, and the the red giant phase starts as the hydrogen burning starts to lessen. At least a majority of models support that.

If there are other innacruacies you don't like, let me know what those are, i'll certainly take a look at them.

Spaceman Spiff
2008-Sep-28, 01:23 AM
I have, and the models are so varied and so many, that there doesn't seem to be one acceptable model. And none of the current models i've seen even attempt to account for impurities in the core, such as iron.

However you are right on one point, and the the red giant phase starts as the hydrogen burning starts to lessen. At least a majority of models support that.

If there are other innacruacies you don't like, let me know what those are, i'll certainly take a look at them.

It isn't that the models themselves "are so varied", but I can believe that various website's explanations of them are. It's the good, the bad and the ugly, as far as the info one can find on the internet. The models, while not complete in their ability to reproduce all observables of stellar behavior, are quite successful in reproducing the overall trends of the evolution of individual stars as well as that in large populations of stars (e.g., star clusters).

For a fairly good elementary introduction to the evolution of sun-like stars, read this (http://cass.ucsd.edu/public/tutorial/StevI.html). You can also try reading this chapter (http://www.astronomynotes.com/starsun/s1.htm) and the next one (http://www.astronomynotes.com/evolutn/s1.htm) of this on-line introductory textbook (http://www.astronomynotes.com/index.html) in astronomy (you can select subchapters of interest from this link (http://www.astronomynotes.com/evolutn/chindex.htm)).

As for the inaccuracies, the whole section I cut out in my post above (http://www.bautforum.com/astronomy/79101-diffusion-hydrogen-main-sequence-star.html#post1332311) is full of them.


And none of the current models i've seen even attempt to account for impurities in the core, such as iron.

I have no clue as to how one could ever draw this conclusion. The models most certainly do include the physics involving all of the heavy elements, in addition to hydrogen and helium.

ToSeek
2008-Sep-28, 09:38 PM
Moved from Astronomy to Q&A