Why planetary nebulae?

[sculptor]

Why do planetary nebulae form? The usual story goes:

(1) core fusion normally heats star and prevents gravitational collapse. Fusion rate extremely temperature sensitive. Very stable. Tiny collapse causes tiny increase in temperature and pressure, causing huge increase heat production causing negative feedback fluffing up of atmosphere to stop collapse. Ok fair enough.

(2) Now we run out of hydrogen. Core fusion energy production drops. Core starts to collapse. Core collapse runs away. Power output from gravitational energy thus liberated exceeds earlier nuclear power output by huge factor. This fluffs up outer atmosphere to planetary nebula size.

Ok, why is it that in para 1, a tiny reduction in radius causes an increase in heat production by the fusion process which causes the core to expand stably, by just the right amount, so the core is self supporting, but in para 2 a tiny reduction in radius (which also leads to immense heating from gravitational collapse) does not also cause the core to thermally support itself?

What is it about the dynamics that makes (1) stable but (2) unstable?

[sculptor]

Why indeed red giants? Perhaps this is really the place to start. The usual argument seems to go that when the inner core runs out of hydrogen, but there is still hydrogen in a shell just outside the core, then the core starts to collapse gravitationally. When it is smaller, same mass but smaller radius means it produces a hugely greater gravitational "compression" of the hydrogen layer just above it, thereby causing enormously higher fusion rates in the shell just above it, thereby heating up the atmosphere, thereby fluffing up to a red giant.

But same problem: why is the gravitational collapse UNSTABLE? I can see that a partial answer is that gravitational collapse on its own does not produce enough local heating per unit reduction in radius to increase the pressure enough to prevent further collapse, whereas if there is hydrogen present, there is enough heating per unit reduction in radius to increase the pressure enough to prevent collapse, hence stable.

Am I even right this far?

But even if this explains why a hydrogen-fusing core is stable but a hydrogen depleted core is unstable, it doesn't explain why the next shell out, where there IS hydrogen fusion going on, doesn't fluff up to the point where the fusion rate drops back to normal. So, even if cores without hydrogen are unstable and collapse, why red giants?

[bojan]

Some answers to the question "why red gians" can be found here:
http://zebu.uoregon.edu/~js/ast122/lectures/lec16.html

[sculptor]

Brilliant! The answer to my question, 'why does the core not expand as it heats, thereby preventing further contraction' seems to be that the mechanism of the collapse is that the electrons become degenerate, an analogy being steam condensing to water - density now constant independent of temperature. There also seems to be "a latent heat of degeneration" in which the state change releases energy. Conversely, the atmosphere is not degenerate, and so it expands when heated from within.

My next question is, why is the red giant "giant" if its surface is cool. The article didn't really address this.

Presumably a quasi-answer is that the very deep layers near to the core are intensely hot, and therefore fluffed up compared with usual. Then the next-to-deep layers are exposed to a lower gravitational field because they are futher out, and are therefore "fluffed up" compared with usual, and so on.

The surface layer doesn't "know" that there is a degenerate core. All it knows is what is happening locally, the three obvious variables being radius, local heat flux, and amount of matter contained within. It would be nice to see some digestible exposition on what sets the radius of the photosphere.

Many thanks for your pointer.

[bojan]

Now, if stellar core runs on higher temperature, its power output is also higher and so is radiation pressure. To get back into equilibrium, stellar radius (and surface) must increase, to be able to radiate all this power.
The new equilibrium condition is Red Giant.
Because such star is older, and has higher content of heavier elements in its outer core and mantle, complicated ionization - recombination processes take place, resulting in variability (energy is absorbed by ionization, this reduces surface temperature and power output and stars shrinks, which in turn provokes recombination process which releases energy, temperature rises and star expands.....
Variable star condition is temporary and happens only for certain range of stellar masses and composition.

[bojan]

Red giant surface is HUGE. And because it is huge, it requires that (lower) temperature to radiate that amount of heat (energy) produced in the core.
It is just equilibrium.....
If you try to squeeze the star, its surface will become smaller and it will not be able to get rid of this power, temperature will go higher so it has to expand...
The equations for black body radiation deal with these issues...
I would have to dig out those details from my uni notes :-)
but I remember the calculation is fairly straightforward, if you know power output from core for "normal" and degenerate core cases...

[bojan]

Originally Posted by sculptor

Brilliant! The answer to my question, 'why does the core not expand as it heats, thereby preventing further contraction' seems to be that the mechanism of the collapse is that the electrons become degenerate, an analogy being steam condensing to water - density now constant independent of temperature. There also seems to be "a latent heat of degeneration" in which the state change releases energy. Conversely, the atmosphere is not degenerate, and so it expands when heated from within.

My next question is, why is the red giant "giant" if its surface is cool. The article didn't really address this.

Presumably a quasi-answer is that the very deep layers near to the core are intensely hot, and therefore fluffed up compared with usual. Then the next-to-deep layers are exposed to a lower gravitational field because they are futher out, and are therefore "fluffed up" compared with usual, and so on.

The surface layer doesn't "know" that there is a degenerate core. All it knows is what is happening locally, the three obvious variables being radius, local heat flux, and amount of matter contained within. It would be nice to see some digestible exposition on what sets the radius of the photosphere.

Many thanks for your pointer.

The convection inside star plays some role here too, mainly in outer layers I think.. but you are right, the main energy transfer mechanism inside star is radiation.

As I said in my previous reply, the star radius is determined by power output, mass (gravitational pressure) and temperature, all this being in equilibrium.
This has to be accepted as a first approximation, of course... things in reality are much more complicated, as usual :-)

[bojan]

This is a bit better link, for the same batch of lectures (it contains images and other links)
http://abyss.uoregon.edu/~js/ast122/lectures/lec12.html

[bojan]

Bad Astronomer has done it again :-)
Very interesting and easy to read article (with plenty of links) can be found here:
http://www.badastronomy.com/bablog/2...ock-tick-tock/