<p>The answer is as complex as stellar evolution. H-burning takes place in the core during the main sequence; in a shell after the star has left the main sequence until it reaches the tip of the red giant branch and then ignites He in the core; then it also burns intermittently in shells during the asymptotic giant branch.</p>
<p>The later phases are much shorter than the main sequence phase, but the luminosities and hence rate of H-burning are orders of magnitude larger. Thus one would have to integrate the rate of H-burning over the lifetime of each phase.</p>
<p>A further complication is that much of the mass of a star is lost through stellar winds in the later phases of evolution. That material will be mostly hydrogen and is unavailable for burning.</p>
<p>All this will be very sensitive to the initial mass of the star.</p>
<p>We can put some sort of limits on this for a solar-type star of initial mass <span class="math-container">$1M_\odot$</span>. Such stars will end their lives (or at least end their nuclear burning lives) as white dwarfs with a mass of about <span class="math-container">$0.5M_\odot$</span>.</p>
<p>These white dwarfs have a composition that is almost entirely carbon and oxygen. Almost none of this will have been present when the star was born, so assuming an initial composition of about 74% H and 25% He by mass, then the <span class="math-container">$0.5M_\odot$</span> of C/O must have been synthesised by burning about <span class="math-container">$0.74\times 0.5M_\odot$</span> of H.</p>
<p>This will be a <em>lower</em> limit to the amount of H that has been burned, since some of the nucleosynthesis products will be lost as part of the <span class="math-container">$0.5M_\odot$</span> that escapes into space via the stellar wind. But assuming this is a small component because mixing is quite ineffective on the main sequence, we have that at least <span class="math-container">$0.74\times 0.5\times 100/0.74 = 50$</span>% of the initial H would be burned.</p>
<p>If you calculate this fraction for shorter lived, higher mass stars then it is lower. This is because the relationship between initial mass and final white dwarf mass is very non-linear. For example, a <span class="math-container">$8M_\odot$</span> main sequence star might produce a <span class="math-container">$1.2M_\odot$</span> white dwarf, meaning the fraction of H burned is at least <span class="math-container">$(1.2/8\times 0.74)\times 0.74 \times 100 = 15$</span>%. We would have to factor in though that more nucleosynthesis products will be lost into space in the vigorous winds from high-mass stars.</p>
<p>Even higher mass stars will likely burn more hydrogen as a fraction than <span class="math-container">$8M_\odot$</span> stars since they will ignite their C/O cores and there will be additional opportunities for mixing and H-burning as the star evolves towards a supernova and the fully-burned core mass grows substantially with mass.</p>
<p>The burnt fraction will increase towards lower masses because the white dwarfs they form will not be much less massive than <span class="math-container">$0.4M_\odot$</span>. The fraction will become approximately 100% when stars are fully convective at <span class="math-container">$\leq 0.35 M_\odot$</span>. In practice, the H is simply locked up in these stars at the moment because their low rate of H-burning means they have lifetimes of <span class="math-container">$10^{11}-10^{12}$</span> years.</p>

CC BY-SA 4.0
2022-01-24T17:34:23.213Z
2022-01-24T23:25:48.590Z
2022-01-24T23:25:48.590Z
ProfRob
<p>A main sequence star will fuse some of its hydrogen, but not all. In massive stars ($&gt;1.5M_\odot$) the core is convective but the rest of the atmosphere radiative and hence does not mix much: as it undergoes shell fusion it will produce an onion-like structure with unused hydrogen on top. Solar mass stars only do this up to helium, but again leave a mantle of unused hydrogen. Stars less than $0.35M_\odot$ are fully convective and can in principle use up all hydrogen. However, I suspect this is not complete except for very low-mass M dwarves that have trillions of years to mature.</p>

<p>Looking at planetary nebulae, I have seen statements that they are about 90 percent hydrogen, 10 percent helium. This seems to fit with papers I have found (<a href="https://www.aanda.org/articles/aa/pdf/2007/47/aa8655-07.pdf" rel="noreferrer">example</a>, <a href="https://arxiv.org/pdf/0709.0711.pdf" rel="noreferrer">example</a>) although in some cases helium may reach 29% (<a href="http://outters.fr/wp/wp-content/uploads/2015/12/Frew_thesis_2008_final.pdf" rel="noreferrer">example</a>). Given that for a G star about half of the mass is ejected, that would suggest a fraction $0.9\times 0.5 = 0.45$ of unused hydrogen. But surely the fractions will be different for other masses.</p>

<p>So, to sum up, what is known about the fraction of hydrogen that is never fused over a stellar lifetime? </p>

CC BY-SA 4.0
2018-06-15T08:07:20.963Z
physics.SE has a [good answer](https://physics.stackexchange.com/a/25916/70207) on this.
pela
CC BY-SA 4.0
2018-06-15T15:35:40.553Z
Probably a large fraction does not get fused. Big Bang Nucleosynthesis calculations predict the early universe was about 75% hydrogen. Measurements of our galaxy show it is about 74% hydrogen. In the lifetime of the universe, almost none of the hydrogen has been fused into heavier elements within stars..
zephyr
CC BY-SA 4.0
2018-06-16T21:47:34.000Z
Pela's answer is helpful. You might want to check out [The BONNSAI project](https://www.astro.uni-bonn.de/stars/bonnsai/), "[The hydrogen profile, previous mixing, and loops in the H-R diagram during core helium burning](https://www.researchgate.net/publication/234208191_The_hydrogen_profile_previous_mixing_and_loops_in_the_H-R_diagram_during_core_helium_burning)" [2nd Source](http://adsabs.harvard.edu/full/1977ApJ...212..507S), "[Chapter 9: Post-main sequence evolution through helium burning.PDF](https://astro.uni-bonn.de/~nlanger/siu_web/ssescript/new/chapter9.pdf)", continued ...
Rob
CC BY-SA 4.0
2018-06-16T22:00:49.207Z
"[Massive stars on the main sequence - Karen Köhler](http://hss.ulb.uni-bonn.de/2017/4653/4653.htm)", "[Main Sequence Stars](http://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolution_mainsequence.html)", or search for "Astrophysical Concepts Martin Harwit Fourth Edition". -- There's a lot of variables that make for a busy chart and a lengthy explanation. Mass, rotational velocity, initial composition, etc. are all factors in the calculations - after a few hours I'll leave you with the links as a starting point and move on to an easier question ... Closing 30+ tabs.
Rob
CC BY-SA 4.0
2018-12-03T00:06:08.440Z
Watching the amount of hydrogen drop... 75%... 74%... depresses me. Only 74% to go before it moves on to fusing helium... I only have a few hundred billion years left to live...
Alonda
CC BY-SA 4.0
2021-03-09T19:21:44.463Z
Another one of your questions which amaze me and I would love to know the answer as well. @ProfRob If you had time, maybe you could help here, please?
B--rian
CC BY-SA 4.0
2021-04-04T09:26:28.087Z
@B--rian the answer on Physics SE looks good to me.
ProfRob
CC BY-SA 4.0
2021-08-13T23:03:51.800Z
@Rob I've added a bounty. Your profile reminds me of my first days in college (a million years ago). My room mate greeted me with perception-altering substances, I looked out the window, and to my amazement and confusion I saw a full-grown tiger sitting under a tree across the street. Hmm...  It turns out there was an auditorium in the building and some show used a tiger in their act. My room mate laughed and noted that the tiger was on a leash. But still, only a few meters from the sidewalk...
uhoh
CC BY-SA 4.0
2021-08-13T23:10:52.297Z
@uhoh, I can confirm having the same profile for a long time, that's me shortly after breaking leash and making my way here; it's not a result of any residual effects.
Rob
CC BY-SA 4.0
2021-08-13T23:40:08.860Z
@Rob Good to know :-) Now I can't stop thinking of VN food, which was wonderful in southern California but surprisingly hard to find here because for business reasons everything gets adapted to local tastes.
uhoh
<stellar-evolution><hydrogen>
What fraction of a star's hydrogen store will be fused over its lifespan?
Anders Sandberg
# What fraction of a star's hydrogen store will be fused over its lifespan?

(Asked by: username_0 on 2018-06-14)

A main sequence star will fuse some of its hydrogen, but not all. In massive stars ($>1.5M\_\odot$) the core is convective but the rest of the atmosphere radiative and hence does not mix much: as it undergoes shell fusion it will produce an onion-like structure with unused hydrogen on top. Solar mass stars only do this up to helium, but again leave a mantle of unused hydrogen. Stars less than $0.35M\_\odot$ are fully convective and can in principle use up all hydrogen. However, I suspect this is not complete except for very low-mass M dwarves that have trillions of years to mature.

Looking at planetary nebulae, I have seen statements that they are about 90 percent hydrogen, 10 percent helium. This seems to fit with papers I have found ([example](https://www.aanda.org/articles/aa/pdf/2007/47/aa8655-07.pdf), [example](https://arxiv.org/pdf/0709.0711.pdf)) although in some cases helium may reach 29% ([example](http://outters.fr/wp/wp-content/uploads/2015/12/Frew_thesis_2008_final.pdf)). Given that for a G star about half of the mass is ejected, that would suggest a fraction $0.9\times 0.5 = 0.45$ of unused hydrogen. But surely the fractions will be different for other masses.

So, to sum up, what is known about the fraction of hydrogen that is never fused over a stellar lifetime?

**Tags:** stellar-evolution, hydrogen
> **Comments:**
> **username_1**: physics.SE has a [good answer](https://physics.stackexchange.com/a/25916/70207) on this.  
> **username_2**: Probably a large fraction does not get fused. Big Bang Nucleosynthesis calculations predict the early universe was about 75% hydrogen. Measurements of our galaxy show it is about 74% hydrogen. In the lifetime of the universe, almost none of the hydrogen has been fused into heavier elements within stars..  
> **username_3**: Pela's answer is helpful. You might want to check out [The BONNSAI project](https://www.astro.uni-bonn.de/stars/bonnsai/), "[The hydrogen profile, previous mixing, and loops in the H-R diagram during core helium burning](https://www.researchgate.net/publication/234208191_The_hydrogen_profile_previous_mixing_and_loops_in_the_H-R_diagram_during_core_helium_burning)" [2nd Source](http://adsabs.harvard.edu/full/1977ApJ...212..507S), "[Chapter 9: Post-main sequence evolution through helium burning.PDF](https://astro.uni-bonn.de/~nlanger/siu_web/ssescript/new/chapter9.pdf)", continued ...  
> **username_3**: "[Massive stars on the main sequence - Karen Köhler](http://hss.ulb.uni-bonn.de/2017/4653/4653.htm)", "[Main Sequence Stars](http://www.atnf.csiro.au/outreach/education/senior/astrophysics/stellarevolution_mainsequence.html)", or search for "Astrophysical Concepts Martin Harwit Fourth Edition". -- There's a lot of variables that make for a busy chart and a lengthy explanation. Mass, rotational velocity, initial composition, etc. are all factors in the calculations - after a few hours I'll leave you with the links as a starting point and move on to an easier question ... Closing 30+ tabs.  
> **username_4**: Watching the amount of hydrogen drop... 75%... 74%... depresses me. Only 74% to go before it moves on to fusing helium... I only have a few hundred billion years left to live...  
> **username_5**: Another one of your questions which amaze me and I would love to know the answer as well. @ProfRob If you had time, maybe you could help here, please?  
> **username_6**: @B--rian the answer on Physics SE looks good to me.  
> **username_7**: @Rob I've added a bounty. Your profile reminds me of my first days in college (a million years ago). My room mate greeted me with perception-altering substances, I looked out the window, and to my amazement and confusion I saw a full-grown tiger sitting under a tree across the street. Hmm...  It turns out there was an auditorium in the building and some show used a tiger in their act. My room mate laughed and noted that the tiger was on a leash. But still, only a few meters from the sidewalk...  
> **username_3**: @uhoh, I can confirm having the same profile for a long time, that's me shortly after breaking leash and making my way here; it's not a result of any residual effects.  
> **username_7**: @Rob Good to know :-) Now I can't stop thinking of VN food, which was wonderful in southern California but surprisingly hard to find here because for business reasons everything gets adapted to local tastes.  

---

## 1 answers

### Answer by username_6 on 2022-01-24. Score: 6

The answer is as complex as stellar evolution. H-burning takes place in the core during the main sequence; in a shell after the star has left the main sequence until it reaches the tip of the red giant branch and then ignites He in the core; then it also burns intermittently in shells during the asymptotic giant branch.

The later phases are much shorter than the main sequence phase, but the luminosities and hence rate of H-burning are orders of magnitude larger. Thus one would have to integrate the rate of H-burning over the lifetime of each phase.

A further complication is that much of the mass of a star is lost through stellar winds in the later phases of evolution. That material will be mostly hydrogen and is unavailable for burning.

All this will be very sensitive to the initial mass of the star.

We can put some sort of limits on this for a solar-type star of initial mass $1M\_\odot$. Such stars will end their lives (or at least end their nuclear burning lives) as white dwarfs with a mass of about $0.5M\_\odot$.

These white dwarfs have a composition that is almost entirely carbon and oxygen. Almost none of this will have been present when the star was born, so assuming an initial composition of about 74% H and 25% He by mass, then the $0.5M\_\odot$ of C/O must have been synthesised by burning about $0.74\times 0.5M\_\odot$ of H.

This will be a *lower* limit to the amount of H that has been burned, since some of the nucleosynthesis products will be lost as part of the $0.5M\_\odot$ that escapes into space via the stellar wind. But assuming this is a small component because mixing is quite ineffective on the main sequence, we have that at least $0.74\times 0.5\times 100/0.74 = 50$% of the initial H would be burned.

If you calculate this fraction for shorter lived, higher mass stars then it is lower. This is because the relationship between initial mass and final white dwarf mass is very non-linear. For example, a $8M\_\odot$ main sequence star might produce a $1.2M\_\odot$ white dwarf, meaning the fraction of H burned is at least $(1.2/8\times 0.74)\times 0.74 \times 100 = 15$%. We would have to factor in though that more nucleosynthesis products will be lost into space in the vigorous winds from high-mass stars.

Even higher mass stars will likely burn more hydrogen as a fraction than $8M\_\odot$ stars since they will ignite their C/O cores and there will be additional opportunities for mixing and H-burning as the star evolves towards a supernova and the fully-burned core mass grows substantially with mass.

The burnt fraction will increase towards lower masses because the white dwarfs they form will not be much less massive than $0.4M\_\odot$. The fraction will become approximately 100% when stars are fully convective at $\leq 0.35 M\_\odot$. In practice, the H is simply locked up in these stars at the moment because their low rate of H-burning means they have lifetimes of $10^{11}-10^{12}$ years.


---

