I've heard in a lecture that a star like the sun would burn 3% of its Hydrogen before expiring.

I would have thought it would be much more.


1 Answer 1


It is much more. During its core-burning phase, the Sun will burn about 10-15% of its hydrogen supply. The gas is about 70% hydrogen by mass, so that translates into about $0.07$ to $0.1\,M_\odot$ of hydrogen burned. The exhausted core then contracts while hydrogen is burned in a shell that gradually moves outwards (in terms of mass). Helium ignition starts once the exhausted core is about $0.5\,M_\odot$ (so $0.35\,M_\odot$ has been burned). The burning shell will continue to burn some material but not a great deal. Off-hand, I think the Sun is expected to leave a $0.6\,M_\odot$ CO white-dwarf as a remnant, which implies that it burns about 60% of its available hydrogen or $0.42\,M_\odot$ of hydrogen. (It is possibly slightly more because some of the hydrogen in the envelope will be mixed into the burning region and transformed into helium.)

It's difficult to say how much hydrogen a star burns in general because stars lead different lives depending how massive they are. For example, up to about $2\,M_\odot$, the H-exhausted core always grows to about $0.5\,M_\odot$ before He-burning starts. Larger stars don't have to wait, so the core masses will be larger in absolute terms but smaller as a fraction of the total initial mass. i.e. a $2\,M_\odot$ star will ignite He in a $0.5\,M_\odot$ core, but a $5\,M_\odot$ star might do so in a $1\,M_\odot$ core (rather than $1.25\,M_\odot$ ).

For high-mass stars ($>10 M_\odot$) I offer this plot from a talk by Marco Limongi. The He-core mass tells you roughly the mass co-ordinate of the region that burned hydrogen into helium. Since the initial composition is uniform, that's roughly the fraction of the hydrogen that is burned. So if the He core mass is $5\,M_\odot$ in a $20\,M_\odot$ star, then roughly 25% of the hydrogen is burned. This statement is actually complicated by the fact that some of the unburnt material in the envelope will be mixed into the burning shell, but its gives a rough idea.

Mass--initial mass relation for high mass stars, from a talk by Marco Limongi. This is not meant to be definitive. It is one of a series of similar plots that were used to show how this behaviour changes according to the model. But its useful for illustrating the mass--H-burnt mass relation.

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    $\begingroup$ Is mass due to stellar wind during the red giant phase a potentially significant complication as well? If convection is mixing the core and outer layers wouldn't a significant amount of the mass loss be He ash that was pumped out of the core? $\endgroup$ Commented Jan 20, 2012 at 16:09
  • $\begingroup$ Yes, it potentially is, but maybe less than you're thinking. In the red giant phase, the convective envelope does penetrate the former core. It doesn't mix the whole star, just a fraction at the top of the core, but it definitely is a complication. Another reason it's hard to say exactly how much hydrogen a particular star will burn without running a full evolutionary calculation. $\endgroup$
    – Warrick
    Commented Jan 20, 2012 at 16:39

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