Where did the Sun get hydrogen to work with if it is in the 3rd generation of stars?

Question

As I see here, the Sun belongs to the Population I group of stars, which is the 3rd generation of the stars in our universe. 1st generation stars are Population III, 2nd generation are Population II, and 3rd generation are Population I.

When the 1st generation (Population III) of stars died, that means most of the hydrogen was burned to helium. Stars die when there is no hydrogen left. Later, the 2nd generation of stars (Population II) appeared and they fuse another portion of hydrogen into heavier elements.

If 1st and 2nd star generations burned hydrogen to helium and more heavier elements, then shouldn't like 90% of all universe hydrogen already be converted to helium and something else? If yes, then there should not be enough hydrogen to make the Sun.

UPDATE 1

Thanks for all your answers. They are very useful. Now a new subquestion appeared. When the star dies, like our Sun, it sends out external layers and core becomes white/other dwarf. In this case, new star can be formed only from the hydrogen from the external layer. The questions what is the percentage of initial star hydrogen after burning it to helium goes from this external layer to outer space?

Answer 1

Most of the galaxy's gas is not incorporated into stars and remains as gas and dust. This is not really my area of expertise, but papers such as Evans et al. 2008 and Matthews et al. 2018 seem to suggest that in the Giant Molecular Clouds where most stars in the Milky Way Galaxy form, the star formation efficiency is about 3-6%. So the vast majority of the gas (94-97%) is not made into stars. In very dense environments such as globular clusters, which were formed much earlier in the Milky Way's history, the star formation efficiency get as high as approx. 30%. The canonical quoted rate for "regular" spiral galaxies like the Milky Way is about 1 solar mass of new stars are made per year, which is very low summed across the whole galaxy.

Stars also give off a fair amount of their outer, hydrogen rich outer layers during the later red giant phases when the stellar wind is stronger and the atmosphere expands a huge amount (radius of the Sun during the red giant phase will be about what the Earth's orbit is now). Also in the end state when the white dwarf is formed, it's only the core and inner layers that form the white dwarf. The typical white dwarf mass is about 0.6 times the mass of the Sun (S. Kepler et al. 2006) and so there will be a fair amount of unfused hydrogen-rich outer atmosphere left over after the star dies. For higher mass stars, even more of the mass goes into the (ejected at high speed) envelope than goes into the remaining neutron star. These high mass stars are much rarer though; most of the Milky Way's stars are faint, cool M dwarfs.

Answer 2

I think you've answered your own question.

if 1st and 2nd stars generation burned hydrogen to helium and more heavier elements, then should it be like 90% of all universe hydrogen already converted to helium and something else? If yes, then there should not be enough hydrogen to make the Sun.

Clearly the Sun does have enough Hydrogen to form and the universe is not 90% Helium and heavier elements (it is in fact ~74% Hydrogen, ~24% Helium, and a fraction of heavier elements). That means the first and second generations of stars have not burned up most of the Hydrogen and your basic assumptions are wrong.

Your main incorrect assumption comes from the statement

[A] star dies when there is no hydrogen left.

A more correct statement would be "A star dies when there is no hydrogen left in its core"¹. Once the core runs out of hydrogen for fusing, it generally can't support the gravitational pressure trying to compact it and it begins the stages of death. However, the outer shell around the core, which can make up 50-70% of a star's mass, never gets fused, thus remaining Hydrogen.

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¹ Technically its more complicated than that, and the notion of a when a star "dies" isn't well demarcated. But that's another question for another day.

Answer 3

The question is if 1st and 2nd stars generation burned hydrogen to helium and more heavier elements, then should it be like 90% of all universe hydrogen already converted to helium and something else?

Only a tiny portion of the primordial hydrogen has been converted to helium or something else. The explanation is fourfold.

1. Most of the universe's primordial hydrogen lies between galaxies. Some of this intergalactic gas might become captured by a galaxy, but much of it probably never will.
2. Most of the hydrogen within a galaxy is in the form of the warm to hot interstellar medium. Some of this interstellar gas might condense to form an interstellar gas cloud, but as is the case with the intergalactic medium, much of this interstellar medium probably never will be incorporated into a star.
3. While some of the gas in an interstellar gas cloud does collapse to form stars and planets, this process is incredibly inefficient. Well over 90% of the gas in a gas cloud gets ejected into the interstellar medium during the star formation process.
4. While some of the hydrogen in a star is indeed converted to helium or more massive elements, this burning is incomplete. Stars between roughly 1/2 to 5 solar masses eject a lot of hydrogen during their death throes.

That said, star formation in our galaxy is now drastically reduced compared to what it was at its peak. The reason isn't that hydrogen has been converted to helium and more massive elements. The reason is instead that a lot of the hydrogen is now locked up in low mass stars. The lifetime of a half solar mass star is several times the current age of the universe, and this lifetime grows as star mass decreases. All of the low mass stars that have ever formed are still stars, and that makes for a lot of locked-up hydrogen.