Cepheid variable stars cause of light variance

[Glenn G]

Have been reading about cepheid. Can I just check I've got this?
'When at their hottest (when gravity has squashed them) have more doubly ionised He so star becomes more opaque'
Now was just wondering what the main mechanism is here? Because He2+ doesn't have any electrons left to absorb photons to promote electrons to higher energy levels! So is the interaction a Compton scattering between the free electrons and or He2+ ions and the photons and this is why photons don't get out or is it particle antiparticle pair productions as the photon gets near the He2+ nucleus or a combination or something else?
Regards as always knowledgeable people,
Glenn.

 

[davenn]

Now was just wondering what the main mechanism is here? Because He2+ doesn't have any electrons left to absorb photons to promote electrons to higher energy levels! So is the interaction a Compton scattering between the free electrons and or He2+ ions and the photons and this is why photons don't get out or is it particle antiparticle pair productions as the photon gets near the He2+ nucleus or a combination or something else?

No, the singly ionised helium at the star's surface absorbs the energy producing some opacity.
As it continues to absorb energy ( photons / EM radiation) it heats up more causing it to become even more opaque.
the temperature of the star doesn't increase significantly till all the He¹⁺ becomes He²⁺ and can no longer absorb any more energy so then there is nothing to stop the temperature of the star increasing. As the star increases in temperature, the star swells in size. That then causes a temperature drop that allows the He²⁺ to be able to gain free electrons and become singly ionised again releasing energy in the process and halting the temperature drop.
The process is then repeated in the observed cycleDave

 

[Ken G]

It's hard to find a good explanation of the Cepheid effect, so it's not surprising you would have this question. I've thought about it, and concluded that what you really need is an interplay between a free-electron provider, like helium 1+, and an opacity provider, like bound-free states in metals. What's more, you need the opacity provider to increase the opacity when the temperature rises, which is not the normal state of affairs (thankfully, or our Sun would be a Cepheid too!).

So the way this happens is, the ionization of helium is much more T sensitive than the ionization of the opacity-providing metals, so when T goes up, the helium ionizes much more so than the metals. Importantly, ionizing the helium produces more free electrons that can recombine with the metals, so rising T actually reduces the degree of ionization of the metals (metal ionization depends on both T and free-electron density, so make the latter increase more, and you get more bound electrons in the metals and so more opacity). So that's the key, the degree of ionization of the electron provider has to go in the opposite sense with T as for the ionization of the opacity provider, that makes the opacity rise when T rises and fall when T falls, which creates a thermodynamic engine for pumping work into the stellar oscillation.

The reason you get a thermodynamic engine is that higher opacity means putting heat into the layers of the atmosphere in question, and that means you are putting heat into the system when its T is high and taking heat out of the system when its T is low, that's precisely what you need to allow the system to do work, like the pistons in a car engine. The work done by the heat engine goes into increased amplitude oscillations, so this is all happening in the energy equation. The force equation looks pretty much just like a static equilibrium, so it requires many many cycles to build up a significant amplitude.

 

[davenn]

Hi Ken

So the way this happens is, the ionization of helium is much more T sensitive than the ionization of the opacity-providing metals, so when T goes up, the helium ionizes much more so than the metals.

What metals ?
none of the explanations I read mentioned anything about metals or interaction with such

Dave

 

[Ken G]

Well as I said, it is difficult to find a good explanation, largely because opacity is a difficult topic involving many different processes. But sources that present a reasonably complete analysis often invoke "Kramers opacity", which in the stellar context is going to be bound-free and bound-bound metal opacity most of the time. The weird thing about Kramers opacity, in the context of radial pulsations, is that it normally drops as temperature rises, and that's why most stars don't radially pulsate. The key with Kramers opacity is that its drop with rising temperature is much steeper than its rise with rising density, so that's why the Sun doesn't pulsate and why we are here. The only way to get Kramers opacity to rise with temperature is to find a way to stabilize the temperature as you let the density rise, so that the temperature doesn't rise nearly as much as the density does. That's where partial ionization comes in, it acts like a thermostat. But of course, that also means you need the electron providers to ionize when the gas compresses, so they can do their temperature stabilization act. Then the rising electron density, due to the compression, causes the metals to recombine, and this is what is raising the opacity. So you see the essential feature that is rarely mentioned-- the degree of ionization of the metals must change oppositely to the degree of ionization of whatever is serving as the thermostat (often partial helium ionization).

It should also be mentioned that for delta Cepheids, the opacity that rises with temperature is an "iron bump", so there is no need for a partial ionizaton zone and its thermostatic effects there, it's just the opacity dependence on temperature all by itself that does it. Also, I would point out that some sources that seem credible talk about transitions in hydrogen and/or helium themselves as being the culprit, on the grounds that these get more excited at higher temperature and put more lines into the relevant part of the spectrum, so those cannot be ruled out as possible contributors as well. It appears that the situation is complicated.

 

[davenn]

Thanks, Ken

you have given me some more food for thought Dave