Could a fully convective Sun double its lifespan?

[bbbl67]

How much longer would the Sun live if it were fully convective, just like a red dwarf star. I mean keep everything else exactly the same, the Sun has the same mass and temperature as it does now, but it goes on to burn every last drop of hydrogen it has in its atmosphere, rather than just the hydrogen inside its core.

Just on my back-of-the-envelope calculation, I'm thinking that the actual Sun will turn into a white dwarf of 0.5 solar masses, meaning it will have converted 50% of its hydrogen into something higher. So if it were fully convective would it last twice as long? Would it have a total lifespan of 20 billion years rather than 10 billion?

 

[Janus]

A 0.5 solar mass white dwarf formed from our Sun would not mean that it has burned 50% of it hydrogen. On its way to becoming a white dwarf our sun will expand into a red giant. Eventually it will get so big that the outer hydrogen layers will be blown away by the solar wind. The White dwarf is formed from what is left behind. The hydrogen blown away is never burned or converted to anything else.

 

[bbbl67]

A 0.5 solar mass white dwarf formed from our Sun would not mean that it has burned 50% of it hydrogen. On its way to becoming a white dwarf our sun will expand into a red giant. Eventually it will get so big that the outer hydrogen layers will be blown away by the solar wind. The White dwarf is formed from what is left behind. The hydrogen blown away is never burned or converted to anything else.

Yes fine, so what would its lifespan be if were able to completely convert all of its hydrogen?

 

[Grinkle]

if were able to completely convert all of its hydrogen?

IMO to get a meaningful answer there needs to be some proposed mechanism that allows this to happen; that mechanism may have other effects that come into play and determine what the end life of a star looks like. What prevents the expansion? Or, if the expansion happens, what prevents the solar wind? Etc.

 

[phinds]

IMO to get a meaningful answer there needs to be some proposed mechanism that allows this to happen; that mechanism may have other effects that come into play and determine what the end life of a star looks like. What prevents the expansion? Or, if the expansion happens, what prevents the solar wind? Etc.

 

[bbbl67]

IMO to get a meaningful answer there needs to be some proposed mechanism that allows this to happen; that mechanism may have other effects that come into play and determine what the end life of a star looks like. What prevents the expansion? Or, if the expansion happens, what prevents the solar wind? Etc.

How about the same mechanism that allows a red dwarf to be fully convective? It's all hypothetical anyways.

 

[snorkack]

A 0.5 solar mass white dwarf formed from our Sun would not mean that it has burned 50% of it hydrogen. On its way to becoming a white dwarf our sun will expand into a red giant. Eventually it will get so big that the outer hydrogen layers will be blown away by the solar wind. The White dwarf is formed from what is left behind. The hydrogen blown away is never burned or converted to anything else.

Just because it´ s called "hydrogen". Red giants do shed metals produced in them... therefore presumably some helium as well.

 

[phinds]

How about the same mechanism that allows a red dwarf to be fully convective? It's all hypothetical anyways.

"Hypothetical" does not mean "let's just ignore physics"

 

[Grinkle]

It's all hypothetical anyways.

It sounds to me like you want to ask something along the lines of of 'assuming a burn rate equal to the rate hydrogen is consumed in a red dwarf, how long would the sun's hydrogen last'.

I guess you can do some Googling and approximate the average consumption rate of a red dwarf over its life and then find an estimate of how much hydrogen initially formed the sun and then divide. If I knew those numbers I'd do it, not being stand-offish, I don't know them.

 

[Bandersnatch]

Yes fine, so what would its lifespan be if were able to completely convert all of its hydrogen?

In some astronomy exercises I keep seeing the information that over its lifetime the Sun will have 13% (or thereabouts) of its hydrogen available for fusion. I don't know how that's arrived at, and whether it's just for the main sequence or total (or if that distinction even makes much of a difference).
But taking it at face value, and naively taking fractions (i.e. assuming the burning rate doesn't increase significantly over the lifetime despite ash accumulation), fusing all of hydrogen should take about 7.5 times longer.

 

[snorkack]

The mechanism that allows red dwarfs to be fully connective is that at low temperatures, the opacity of plasma is high (lots of bound-bound, bound-free and free-free transitions) such that it is poorly conductive and the heat can only be transmitted by convection. At higher temperatures, hydrogen, helium and the light metals (CNO) get completely stripped of electrons and the opacity drops, allowing the interiors of hotter stars to become radiative and stagnant.
If a modest amount of heavy metals - I mean, nuclear charges 50...80, of which there are only trace amounts in Sun now, rather than the modest amounts of light metals nuclear charges 6...8 - were to be added to Sun´´ s core, they would not be fully ionized, and their inner electrons would undergo bound-bound, bound-free and free-free transitions, increasing opacity. Could this cause Sun to become completely convective?

 

[Ken G]

It's actually true that the Sun will burn about half its hydrogen (stars like the Sun pretty much all evolve until their cores have 0.5 solar masses, because that's what halts their evolution as it causes the helium flash, and it isn't hydrogen in there, so that's about half the hydrogen burned). If the Sun was fully convective, it would not become a red giant until all its hydrogen had burned. So on the surface, that would approximately double its lifetime.

However, to conclude that, we'd have to keep the Sun's luminosity fixed. On its way to burning half or so of its hydrogen, its luminosity is greatly enhanced as a red giant, so that shortens its lifetime compared to what you might think. Also, it is unlikely that changing its energy transport from radiative diffusion to pure convection would not lower its luminosity below what it is now. Normally, fully convective stars have a surface temperature about half that of the Sun, though there could also be an increase in radius. It would depend on how the convection was maintained, but if you, for example, drastically increased the opacity, it seems like the Sun would continue its progress to lower luminosity that it had when it was fully convective previously. Thus, the answer is probably that if the Sun could have been kept fully convective, it's lifetime would have been even more than doubled, possibly even a factor of ten.

 

[alantheastronomer]

According to the Schonberg-Chandrasekar limit, stars on the main sequence all have hydrogen burning cores of approximately 12% their total mass, not 50%. For stars with the same mass as the sun, this translates to a main sequence lifetime of 12 billion years. If the sun were to become fully convective, burning 100% of it's mass, this would mean that it's main sequence lifetime would be 100 billion years. It also means that, since all of it's mass is consumed, there is no outer layer to be blown off, and it never becomes a red giant - instead, as it contracts it gets hotter and bluer and travels up the main sequence as it does so until the helium flash which would send it to the right of the main sequence, bluer on the H-R diagram.

 

[mfb]

It also means that, since all of it's mass is consumed, there is no outer layer to be blown off

Wouldn't it have helium to blow off?

 

[alantheastronomer]

Wouldn't it have helium to blow off?

If it's fully convective, the entire star is at the same temperature. So, come to think of it, if it's heavy enough to initiate helium burning( and I'm not sure where the cutoff is for that to happen) then it should explode like a dimmer type Ia supernova. If it's not heavy enough for that, then it will just turn into a helium white dwarf, turn bluer and off the main sequence.

 

[mfb]

If the entire star would have the same temperature there wouldn't be convection. Convection is driven by temperature differences - they have to exist.

In addition to the temperature differences there are also density differences. The core can ignite without the rest.

 

[alantheastronomer]

If the entire star would have the same temperature there wouldn't be convection. Convection is driven by temperature differences - they have to exist.

In addition to the temperature differences there are also density differences. The core can ignite without the rest.

Oh, that's right of course - in order to have convection you need a temperature gradient greater than that for radiative diffusion, my mistake! With a fully convective star though, the entire mass gets to participate in nuclear burning, so no envelope gets to form and that results in the entire star becoming a uniform composition.

 

[Ken G]

According to the Schonberg-Chandrasekar limit, stars on the main sequence all have hydrogen burning cores of approximately 12% their total mass, not 50%.

The 50% referred not to how much is in the core on the main sequence, but rather, how much burns in its evolution, including the red giant branch. But since the luminosity is much higher then, your approach is better-- just compare main-sequence phases. So that would indeed mean you get about 8 times more mass to burn. However, the same luminosity could not be assumed because fully convective stars have lower surface temperature than the Sun.

For stars with the same mass as the sun, this translates to a main sequence lifetime of 12 billion years. If the sun were to become fully convective, burning 100% of it's mass, this would mean that it's main sequence lifetime would be 100 billion years.

Probably quite a bit more, since in the Sun's early days, it was fully convective, and did have a much lower surface temperature. So had it stayed fully convective, it would never have made the right turn onto the main sequence, which occurs when radiative diffusion takes over. Without that turn, the luminosity continues to drop down more to red dwarf levels. This might mean something like half the luminosity it has now, so maybe 200 billion years is a better (albeit rough) estimate.

It also means that, since all of it's mass is consumed, there is no outer layer to be blown off, and it never becomes a red giant - instead, as it contracts it gets hotter and bluer and travels up the main sequence as it does so until the helium flash which would send it to the right of the main sequence, bluer on the H-R diagram.

If it stayed convective after running out of hydrogen, it would continue straight down to lower luminosity but similar low surface temperature. It would never have a helium flash, because either it would reach its ground state before ever getting hot enough to fuse helium, or it would start to fuse helium before the core was degenerate. It would have to be one or the other, because a fully convective star doesn't have an inner core that is degenerate, the degeneracy is pretty much constant over the whole star because convection mostly preserves the entropy. (A helium flash occurs in a red giant because you can pile up more and more degenerate material-- you need a radial transition from nondegenerate to degenerate to allow further evolution to occur.)

 

[snorkack]

If the entire star would have the same temperature there wouldn't be convection. Convection is driven by temperature differences - they have to exist.

If the whole star has the same temperature - or if the interior is colder - then neither convection nor radiation would happen.
For radiation, existence of temperature difference is sufficient. For convection, the temperature difference must reach a certain substantial threshold.

 

[sophiecentaur]

Yes fine, so what would its lifespan be if were able to completely convert all of its hydrogen?

I think that would require a star to not behave according to the laws of the Physics that govern what stars do. I'm not sure what you actually want to know but perhaps you could put your question in more realistic terms.

 

[Ken G]

Actually it wouldn't have to violate any laws, you could just imagine cranking up the opacity. Yes it would be artificial, but the fact that the Sun went from being fully convective when it was very young to being largely radiative before it reached the main sequence is just a matter of the opacity that happened to be in there. Had the opacity been larger, this question would not be hypothetical, we'd have a fully convective Sun on the main sequence right now. And some of the planets they are interested in now that have the potential for life are orbiting fully convective main-sequence stars, they are just lower mass than our Sun.

 

[sophiecentaur]

Actually it wouldn't have to violate any laws

What I meant was that, if it were allowed to follow its natural course then that would be determined by the 'laws' and the initial conditions (mass and angular momentum). If you could tinker with things in a massive experiment ( = "artificial") then OK. It's interesting that you say there are less massive, fully convective stars.