Questions about upper M-S star & red dwarf structures.

[Zero Signal]

I know a good bit about basic stellar evolution and structure. I know that lower-mass main sequence stars (excluding red dwarfs), like the Sun, have a radiative core surrounded by a radiative zone, which is in turn surrounded by the convective zone. I've read about how main sequence stars undergo a structure transition at about 1.2 solar masses, the start of the upper main sequence. At that point, the core becomes convective and the radiative and convective zones switch positions (or something like that). However, these were mostly very generalized descriptions I read, and I found only one very simple diagram (this one). I haven't found any detailed descriptions including diagrams, and (unless I overlooked something that was too technical for me to understand) I mostly found articles regarding things detailing certain specifics unrelated to what I was looking for.

So my questions are, in an upper main-sequence star (Sirius for instance), exactly how are the three main interior regions distributed? What percentage of such a star's radius do the regions take up? How does having a radiative zone where a lower MS star's convective zone would be affect its surface structure, appearance, and dynamics (e.g., granulation, starspots, flares & prominences, CMEs, magnetic field, etc.)?

Also, I know that red dwarfs have an entirely convective interior. However, I'm not sure exactly what mass does a star begin to have such a structure. I've read that it's about 0.25 solar masses. Is that right?

[The Bad Astronomer]

If you can find it, a book that might help is "Astrophysics I: Stars" by R. Bowers and T. Deeming, printed in 1984. It has equations and diagrams, IIRC. I read it many years ago while studying for my PhD qualifying exams.

This PDF document also has simple descriptions and diagrams too.

I did a web search on "stellar interiors convection", by the way.

[Spaceman Spiff]

I know a good bit about basic stellar evolution and structure. I know that lower-mass main sequence stars (excluding red dwarfs), like the Sun, have a radiative core surrounded by a radiative zone, which is in turn surrounded by the convective zone. I've read about how main sequence stars undergo a structure transition at about 1.2 solar masses, the start of the upper main sequence. At that point, the core becomes convective and the radiative and convective zones switch positions (or something like that). However, these were mostly very generalized descriptions I read, and I found only one very simple diagram (this one). I haven't found any detailed descriptions including diagrams, and (unless I overlooked something that was too technical for me to understand) I mostly found articles regarding things detailing certain specifics unrelated to what I was looking for.

So my questions are, in an upper main-sequence star (Sirius for instance), exactly how are the three main interior regions distributed? What percentage of such a star's radius do the regions take up? How does having a radiative zone where a lower MS star's convective zone would be affect its surface structure, appearance, and dynamics (e.g., granulation, starspots, flares & prominences, CMEs, magnetic field, etc.)?

Also, I know that red dwarfs have an entirely convective interior. However, I'm not sure exactly what mass does a star begin to have such a structure. I've read that it's about 0.25 solar masses. Is that right?

Like our Sun, Sirius A is a main sequence star, but it has 2.3 solar masses of material. As such it is hotter everywhere than our Sun, from its photosphere to its center in order to generate enough pressure to support its weight (within every layer).

Because of the temperature of its core, the CNO cycle dominates the energy production via the fusion of Hydrogen into Helium. This mechanism generates energy at a rate that is extremely sensitive to temperature (~ T^16) in the core. The resulting energy generation rate changes rapidly through the core, plus the total energy generated is large (again, due to the high core temperatures) and thus so is the radiative flux. These drive the temperature gradient in the core up to the adiabatic one (think formation of cumulus clouds) and the core becomes convective. Think about trying to dump too much water per unit time through a drain pipe of a given width and slope. The water backs up and becomes turbulent (a rough analogy).

Once fusion subsides (outside the core), the temperature gradient falls beneath the adiabatic one, convection stops and radiation transport takes over. Because massive main sequence stars are hotter (and less dense) on their insides than their low mass cousins, their interiors remain relatively transparent to radiation (I say relatively, with mean free paths of centimeters).

Stellar interior opacities go like:
opacity ~ 0.3 + 0.2 * density * (T/10 million K)^(-3.5) cm^2/g

and the radiative temperature gradient goes something like:
|dT/dr| ~ constant * (opacity * density/T^3) * radiative flux

Both temperature and density drop, moving from the center toward the star's surface, though the density always drops more rapidly. As long as the opacity remains sufficiently "low" (outside the energy generating core), then the envelope's temperature gradient will remain below the adiabatic one and radiative transport will carry the energy all the way into the photosphere. This is the story for stars more massive than about 1.5 M_sun or so. The transitions in PP-chain/CNO cycle (1.2 solar masses) and radiative/convective transport (1.5 solar masses) occur in stars with masses just between that our our Sun's and Sirius.

On the other hand if the envelope's opacity becomes too high (density too high relative to a temperature too low; see equation above), then the situation is like the drain pipe again with bunch of crud jamming it up. Again, the water backs up and becomes turbulent (again, only a rough analogy). In real life, the increased opacity increases the temperature gradient to the adiabatic one and convection takes over (like at the bottom of a hot pan of water). In stars less massive than our sun, this transition zone moves inward from 71% the way out to the star's surface (Sun's situation), until for the lowest mass stars their outer convection zones reach all the way into the center and they become completely convective.

The transition to all convection at around 0.2-0.3 solar masses is about right. Of course, all of the details depend upon the choice of chemical abundances (solar-like or metal deficient?) which affect the opacity, gas pressure, temperature gradients, and energy generation.

These differences in energy generation mechanism and transport mechanisms have profound impacts upon the star's future evolution.

Hope this helps.

[Zero Signal]

Sorry to drag this nearly 3 week old thread back out, but I forgot to mention something regarding Spaceman Spiff's reply.

What exactly does "temperature sensitivity" mean, anyway? For example, Spiff stated "Because of the temperature of its core, the CNO cycle dominates the energy production via the fusion of Hydrogen into Helium. This mechanism generates energy at a rate that is extremely sensitive to temperature (~ T^16) in the core." I've read about the T^16 figure and sensitivity to temperature, but I don't know what it means. Could someone clarify this for me? Thanks.

[daver]

Sorry to drag this nearly 3 week old thread back out, but I forgot to mention something regarding Spaceman Spiff's reply.

What exactly does "temperature sensitivity" mean, anyway? For example, Spiff stated "Because of the temperature of its core, the CNO cycle dominates the energy production via the fusion of Hydrogen into Helium. This mechanism generates energy at a rate that is extremely sensitive to temperature (~ T^16) in the core." I've read about the T^16 figure and sensitivity to temperature, but I don't know what it means. Could someone clarify this for me? Thanks.

It means (i think) that the rate of energy production is extremely sensitive to temperature--drop the temperature a fraction and the amount of energy generated via the CNO cycle goes way down. Increase the temp a bit and the energy from CNO goes way up.

[Diamond]

Sorry to drag this nearly 3 week old thread back out, but I forgot to mention something regarding Spaceman Spiff's reply.

What exactly does "temperature sensitivity" mean, anyway? For example, Spiff stated "Because of the temperature of its core, the CNO cycle dominates the energy production via the fusion of Hydrogen into Helium. This mechanism generates energy at a rate that is extremely sensitive to temperature (~ T^16) in the core." I've read about the T^16 figure and sensitivity to temperature, but I don't know what it means. Could someone clarify this for me? Thanks.

It means (i think) that the rate of energy production is extremely sensitive to temperature--drop the temperature a fraction and the amount of energy generated via the CNO cycle goes way down. Increase the temp a bit and the energy from CNO goes way up.

It means that the temperatures generated and the energy produced are much higher per unit mass for stars like Sirius than for the Sun. it also means that large stars burn their hydrogen fuel much quicker than sol-type stars....

[Spaceman Spiff]

Sorry to drag this nearly 3 week old thread back out, but I forgot to mention something regarding Spaceman Spiff's reply.

What exactly does "temperature sensitivity" mean, anyway? For example, Spiff stated "Because of the temperature of its core, the CNO cycle dominates the energy production via the fusion of Hydrogen into Helium. This mechanism generates energy at a rate that is extremely sensitive to temperature (~ T^16) in the core." I've read about the T^16 figure and sensitivity to temperature, but I don't know what it means. Could someone clarify this for me? Thanks.

It means (i think) that the rate of energy production is extremely sensitive to temperature--drop the temperature a fraction and the amount of energy generated via the CNO cycle goes way down. Increase the temp a bit and the energy from CNO goes way up.

Yes, that's right. Increase the temperature by 10%, and the energy released goes up by roughly (1.1)^16, or a factor of 4.6. This is why luminosity of the main sequence star is strongly dependent upon its mass.

(please note: size is not mass. When you mean mass, say mass. Size means radius or diameter -- not mass.)

[Zero Signal]

Yes, that's right. Increase the temperature by 10%, and the energy released goes up by roughly (1.1)^16, or a factor of 4.6. This is why luminosity of the main sequence star is strongly dependent upon its mass.

'kay. So if the temp doubles, the energy released in CNO fusion goes up 65,536, and if it triples, it goes up by by over 43 million times. Similarly, in the P-P chain (T^4, IIRC), if the temperature doubles, the energy released goes up by only 16 times, and if it triples, 81 times. Is that correct?