How much of a star undergoes fusion?

[lavinia]

A star dies when fusion in its core stops. Presumably this means that there is no longer any fusionable material in the core. Does this mean that there is no longer any fusionable material in the entire star or just that the stuff in the center is used up?

For instance, suppose the star stats out as a ball of hydrogen. The hydrogen in the core is fused into helium - but the hydrogen away from the core is not. Is this exterior hydrogen cycled into the core and eventually depleted or does most of the hydrogen remain unfused at star death? What percentage of the hydrogen actually gets fused?

 

[nikkkom]

Depends on the mixing of material (usually via convection) between core and outer layers. It turns out low mass stars (red dwarfs) are fully convective, whereas more massive ones, including our Sun, have non-convecting interiors and expected to form a "burnt-out" core at the end of their lives while there is still hydrogen on the surface.

 

[Matterwave]

This question is a bit vague because 1. Fusion in different stars is different so the answer would depend on which particular star you are asking about, and 2. What exactly do you mean by the "death" of a star?

Generally speaking, the answer is "no" - a star will not burn 100% of its "fusionable material".

Taking our Sun as an example, it is expected to burn only roughly 10-15% of its supply of hydrogen during its main phase - but while it's "dying" (i.e. turning into a red giant then white dwarf) it will burn another 30-50% of its supply of hydrogen and leave behind a CO white dwarf with mass ~ 0.6 solar masses.

P.S. It's the "core" not the "corps" even though the two are pronounced the same in English.

 

[lavinia]

This question is a bit vague because 1. Fusion in different stars is different so the answer would depend on which particular star you are asking about, and 2. What exactly do you mean by the "death" of a star?

Generally speaking, the answer is "no" - a star will not burn 100% of its "fusionable material".

Taking our Sun as an example, it is expected to burn only roughly 10-15% of its supply of hydrogen during its main phase - but while it's "dying" (i.e. turning into a red giant then white dwarf) it will burn another 30-50% of its supply of hydrogen and leave behind a CO white dwarf with mass ~ 0.6 solar masses.

P.S. It's the "core" not the "corps" even though the two are pronounced the same in English.

I understood that fusion is different in different stars but wanted a general answer. The question was motivated by videos that say that we are in the Age of Stars but at some point they will all burn out. So one wonders what the rate of extinction of starlight is.

 

[lomidrevo]

I understood that fusion is different in different stars but wanted a general answer. The question was motivated by videos that say that we are in the Age of Stars but at some point they will all burn out. So one wonders what the rate of extinction of starlight is.

I don't think there is a general answer in the context of your question. For stars of different masses (and composition) lifecycle of the stars can be very different, involving differencies in final age, fusion rates, synthesis of heavier elements, ways of transporting energy to surface, rates of loosing the material in the upper layers, etc. The lost material is very important, because it enriches the interstellar medium from which new generations of stars are born, and the process continuous like that in cycle. Not forever, of course, because the amount of material available to star formation decreases, and in the expanding universe where the gravitational bounds will be still weaker on the large scales, the stars will burn out indeed. But anyway, the answer to your question strongly depends on the initial mass of the star, and partially on the composition (or metallicity) of the medium from which it formed.

 

[Tatjana Gobold]

The Question has already been answered, but I would like to add that the life cycle of a specific star strongly depends on ist initial mass. If a star starts out very massive, it will largely produce Energy by the CNO-Fusion cycle and as already said, this star would have many convection layers. At About 10-20 solar masses, the star could even end its life by collapsing into a black hole, as far as I can remember.
But usually fusion stops inside the core when it gets to iron, after that the Radiation pressure of the star is too low to hold up against gravity.

 

[lavinia]

Thank you all

I would be interesting to understand what determines the convectiveness of a star.

 

[newjerseyrunner]

Generally the bigger a star is, the less of its mass is used in fusion. Tiny stars will end up fusing most of their fuel because everything is kind of mixing around. Huge stars create layers of nuclear ash in their cores which sinks because it’s denser than hydrogen. The pressure is so great that as fuel in the core starts running low, it’ll shrink and heat up enough to start fusing the heavier elements. This creates a ton of extra heat which causes the Star to puff out, causing more hydrogen to be pushed away from the core. Once the pressure is high enough to start burning iron, the stars pretty much done and all the remaining hydrogen will be blasted away in short order. Timing is a major pet, big stars die within a hundred million years, so they don’t have time to burn a lot of fuel where tiny stars will live for trillions of years.

 

[lavinia]

Generally the bigger a star is, the less of its mass is used in fusion. Tiny stars will end up fusing most of their fuel because everything is kind of mixing around. Huge stars create layers of nuclear ash in their cores which sinks because it’s denser than hydrogen. The pressure is so great that as fuel in the core starts running low, it’ll shrink and heat up enough to start fusing the heavier elements. This creates a ton of extra heat which causes the Star to puff out, causing more hydrogen to be pushed away from the core. Once the pressure is high enough to start burning iron, the stars pretty much done and all the remaining hydrogen will be blasted away in short order. Timing is a major pet, big stars die within a hundred million years, so they don’t have time to burn a lot of fuel where tiny stars will live for trillions of years.

So fusion of heavier elements actually prevents external hydrogen from cycling into the core?

 

[stefan r]

So fusion of heavier elements actually prevents external hydrogen from cycling into the core?

Diffusion of energy by radiation and conduction prevent convective cycling in the Sun. If you compact a kilogram of hydrogen its temperature rises. If you expand a kilogram of hydrogen it cools down. Hotter hydrogen radiates heat faster and it is less opaque. In the Sun's radiation zone the center is hotter only because it is under more pressure. A convection cycle would not transfer energy (or not enough).

When the Sun starts to fuse helium the luminosity will drop and the Sun will change from red giant branch to red clump. The red clump is less luminous than the red giant branch. So not only preventing hydrogen from cycling to the center helium fusion can suppress hydrogen fusion. Radiation pressure lifts the hydrogen burning shell too far away from the core.

 

[Matterwave]

Thank you all

I would be interesting to understand what determines the convectiveness of a star.

This is bringing me back to undergraduate stellar interiors class...the horror! I'm very hazy on the specifics so I can't go into much detail, but I just want to point out that stellar interiors is actually a very complicated topic - and I'm not sure exactly how much is "well known" and how much is more or less educated conjecture. We can do Helioseismology to get at some properties of the interior of the Sun, but for other, far away stars, I would imagine the experimental capabilities are very limited (to wit: can we perform extra-solar-stellar-seismology? I've never heard of such a thing).

Even for our Sun, the interior situation is pretty complicated. The Sun is divided into zones and there is a zone where convection occurs, but the Sun is not expected to be fully convective (i.e. it's probably not sending hydrogen from its surface to the center of the core). What exactly determines the method of heat transfer (radiative, conductive, or convective)...I can not recall clearly enough to be able to expound on.

 

[stefan r]

...(to wit: can we perform extra-solar-stellar-seismology? I've never heard of such a thing)...

Asteroseismology.

 

[Matterwave]

Asteroseismology.

Thanks for the link! It's interesting. I hadn't considered that something like Kepler was being used to do those kinds of experiments - but it makes sense given that Kepler is looking for variations in stellar luminosity.

 

[snorkack]

I understood that fusion is different in different stars but wanted a general answer. The question was motivated by videos that say that we are in the Age of Stars but at some point they will all burn out. So one wonders what the rate of extinction of starlight is.

The answer is that we do not have any low mass old stars yet, and do not know exactly how they would behave.

 

[lomidrevo]

Diffusion of energy by radiation and conduction prevent convective cycling in the Sun.

Conduction plays insignificant role in majority of the stellar environments (maybe except the white dwarfs) so it can be ignored as mechanism of energy transport.

Hotter hydrogen radiates heat faster and it is less opaque. In the Sun's radiation zone the center is hotter only because it is under more pressure. A convection cycle would not transfer energy (or not enough).

Talking about the Sun, it is not that because convection would not transfer enough energy. It is because the radiation transfer itself is effective enough to transport all the generated energy from core to upper layers (where the conditions are different, and due to large opacity, the radiation is not sufficient anymore). So in summary, the Sun's core is convectively stable. The stability condition depends on the temperature gradient, ie. how rapidly the temperature is decreasing with distance from the center. If the gradient is too steep, convection takes over, as radiation is not effective enough. This is happens in the stars more massive than Sun, their cores are convective.
For more details, you might want to check the slides 54-60 here.

 

[stefan r]

...
Talking about the Sun, it is not that because convection would not transfer enough energy. It is because the radiation transfer itself is effective enough to transport all the generated energy from core to upper layers (where the conditions are different, and due to large opacity, the radiation is not sufficient anymore). So in summary, the Sun's core is convectively stable. The stability condition depends on the temperature gradient, ie. how rapidly the temperature is decreasing with distance from the center. If the gradient is too steep, convection takes over, as radiation is not effective enough. This is happens in the stars more massive than Sun, their cores are convective.
For more details, you might want to check the slides 54-60 here.

A hot air balloon could radiate enough energy to cool off eventually. They sink (or rise less quickly) when the pilot turns off the burner. Smaller hot air balloons work less efficiently because they radiate heat faster. But small balloons to rise.

You could take gas from your freezer and compress it. The compressed air could have a temperature higher than the temperature of the air in a floating hot air balloon. If you used that hot compressed air to inflate a balloon it would not float in room temperature atmospheric pressure air.

I do not think it matters which process moves more heat. A hot gas will rise when it is more buoyant. In the radiative zone of the Sun the pressure gradient dominates over the temperature gradient. The deep hot gas is not more buoyant.

 

[lomidrevo]

I do not think it matters which process moves more heat.

But it does matters, because the energy must be transported through the star at the same rate as it is generated in the core (for a stable star in equilibrium). Stellar structure and consequently the evolution of the star are directly influenced by the "distribution" of radiation and convection zones.

I would be interesting to understand what determines the convectiveness of a star.

Actually, in each layer of the the star, some portion of energy is transported via radiation, and some other portion via convection. But which of the mechanism is dominating, is depending on the local temperature gradient, as I mention above. If the temperature gradient is very steep (so called superadiabatic), the stellar medium is not stable against the convection, and nearly all energy is carried by "hot material" raising outward a characteristic distance (until it dissolve in the upper layers, giving up any excess heat). In such case, radiation contributes to the transport very little. On the other hand, if the local temperature gradient is not so steep (i.e. the superadiabatic condition is not fulfilled), radiation is capable to transport nearly all the energy. That is the case of the core of our Sun.
How the temperature changes with the distance from the core in a particular star, is (similarly as for other stellar structure quantities like pressure, luminosity..) consequence of the initial mass of the star. So the zones of radiation and/or convection also depends (although indirectly) on the initial mass of the star. We can say roughly: "The initial mass defines everything".

 

[alantheastronomer]

In stars of all masses, only the inner 10% becomes hot enough to commence nuclear fusion. As this nuclear fuel gets used up, this core begins to contract until it becomes hot enough for the next element to undergo nuclear fusion. Until it reaches this point, a thin shell of unburnt material starts contracting towards the core and begins fusing. It needs to reach a higher temperature than needed for the core to burn, because it is less dense than the core. This "shell burning" contributes an appreciable amount of material to the core, adding to it's mass. For stars with masses less than about 8 solar masses, nuclear burning stops when the core is made of mostly carbon. Then the core contracts and becomes a white dwarf, while the rest of the star becomes a planetary nebula and gets returned to the interstellar medium. Stars with a mass greater than 8 solar masses continue core nuclear burning all the way up to iron, where core nuclear burning no longer produces enough energy to keep the star stable, and the core contracts and becomes a neutron star, while the rest of the star is blown out into the interstellar medium in a cataclysmic supernova explosion. Because of these two processes a lot of material is returned to the interstellar medium and is recycled into new stars, so it will be trillions of years before the "age of the stars" ends.

 

[Vanadium 50]

Alan,
I have to ask - are you actually an astronomer? That is, someone paid to do astronomy? Your message seems to be authoratitative, but it goes against everything I have learned about red dwarf cores: that is, they are fully convective - i.e. their hydrogen is continually refreshed in the core from the rest of the star.

 

[anorlunda]

The question was motivated by videos that say that we are in the Age of Stars but at some point they will all burn out.

That makes it sound like you are not interested in any particular star but rather the "heat death of the universe".

From the Big Bang through the present day, matter and dark matter in the universe are thought to have been concentrated in stars, galaxies, and galaxy clusters, and are presumed to continue to be so well into the future. Therefore, the universe is not in thermodynamic equilibrium, and objects can do physical work. The decay time for a supermassive black hole of roughly 1 galaxy mass (10¹¹ solar masses) due to Hawking radiation is on the order of 10¹⁰⁰ years, so entropy can be produced until at least that time. Some monster black holes in the universe are predicted to continue to grow up to perhaps 10¹⁴ M☉ during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10¹⁰⁶ years. After that time, the universe enters the so-called Dark Era and is expected to consist chiefly of a dilute gas of photons and leptons.

 

[willem2]

Alan,
I have to ask - are you actually an astronomer? That is, someone paid to do astronomy? Your message seems to be authoratitative, but it goes against everything I have learned about red dwarf cores: that is, they are fully convective - i.e. their hydrogen is continually refreshed in the core from the rest of the star.

There's another thread "Red dwarf death" going on. According to this paper: http://adsabs.harvard.edu/abs/1997ApJ...482..420L linked in it, a 0.1 solar mass star will remain convective for its whole life and burn about 99% of its hydrogen. Somewhat larger stars will form a non-convective core later in life, but still burn much more of the hydrogen than the sun will, during the main sequence. A 0.25 solar mass star will form a radiative core before half of the hydrogen is finished. (see table 2).

 

[stefan r]

...Your message seems to be authoratitative, but it goes against everything I have learned about red dwarf cores: that is, they are fully convective - i.e. their hydrogen is continually refreshed in the core from the rest of the star.

It could be totally convective and still fusion could take place exclusively near the center.

Wikipedia says this:

The core inside 0.20 of the solar radius contains 34% of the Sun's mass, but only 0.8% of the Sun's volume. Inside 0.24 solar radius, the core generates 99% of the fusion power of the Sun.

So 10% is a much larger volume. 10% would be too small by mass. It is not completely clear if Alan was referring to the mass or volume.

I think you are mostly correct about the red dwarfs. Wikipedia says quite clearly that red dwarfs burn almost all of their hydrogen. A red dwarf's surface will become bluer over time.
This paper agrees with you for a few trillion years. However, the graphs show a little notch where the core becomes radiative. [They point out that a 0.16 solar mass dwarf will linger at 1/3rd solar luminosity for over 5 billion years which is long enough to evolve life. :) ] It is not a red giant but it does have a hydrogen burning shell and radiative/conductive core. It will still have convection from the surface to the shell. No star has lasted for more than 14 billion years so there is no example of this.

Alan,...
I have to ask - are you actually an astronomer? That is, someone paid to do astronomy? Your message seems to be authoratitative, ...

Amateur astronomers are often quite good at astronomy. Professional development and experience will improve pedagogy for those who are teaching. Working on a large expensive apparatus will give you experience working on large expensive apparati. Getting funding involves interview skills and grant writing skills.

Astronomers look at the exterior surface of stars. You could be extremely well informed about the position and motion of stars without understanding astrophysics. Copernicus, Galileo, and Kepler were unaware of nuclear fusion, the atomic nucleus, or atoms. They made very significant contributions to astronomy. Kepler was actually paid as an astrologer and mathematician. Kepler's optics and astronomy crap were unpaid side projects he did on his own time.

When I go to lectures at the astronomy club I occasionally hear incorrect numbers. Some people who are very good at presenting a planetarium show cannot answer questions about astro-physics. I saw an order of magnitude error in a power point presentation about the Milky Way. Regardless, I would say it was one of the better lectures I have seen there. The audience responded well and most people in the public would have learned a lot. Other astronomy presentations are targeted toward children. Keeping children focused on learning a topic takes a lot of skill.

 

[stefan r]

There's another thread "Red dwarf death" going on. According to this paper: http://adsabs.harvard.edu/abs/1997ApJ...482..420L linked in it, a 0.1 solar mass star will remain convective for its whole life and burn about 99% of its hydrogen. Somewhat larger stars will form a non-convective core later in life, but still burn much more of the hydrogen than the sun will, during the main sequence. A 0.25 solar mass star will form a radiative core before half of the hydrogen is finished. (see table 2).

Your link abstract says something different from what you wrote:

We find that stars with masses M < 0.20 M⊙ will never evolve through a red giant stage. After becoming gradually brighter and bluer for trillions of years, these late M dwarfs of today will develop radiative-conductive cores and mild nuclear shell sources; these stars then end their lives as helium white dwarfs.

 

[lavinia]

That makes it sound like you are not interested in any particular star but rather the "heat death of the universe".

I am interested in everything.

 

[Vanadium 50]

Amateur astronomers are often quite good at astronomy.

Sure, but if someone uses "the astronomer" in his name, it suggests that his posts are authoritative.