# How long will the Universe's hydrogen reserves last for?

I recently became really interested in learning about physics and cosmology, but I still know very little. Hopefully someone with more knowledge will be able to shed some light on my questions.

Here are my presumptions (please correct me if I'm mistaken):

• $t_{0}$: Big Bang.
• The Universe expands (and thus cools) sufficiently to allow the formation of atoms.
• The early Universe mostly consists of Hydrogen and is not uniform in its geometry.
• Gravity pushes lumps of matter together until their density (temperature) is so high that nuclear fusion kicks off. The first giant stars are born.
• Some heavy elements are created in these stars and when they explode, sufficient temperatures are reached to form heavier elements still.
• All of the successive stars and planets are the product of these original stars.

My questions:

• If the amount of Hydrogen is finite in the Universe and each successive generation of stars use up most of their Hydrogen, what is the theoretical maximum number of generations of stars that our Universe can support? A ballpark figure in terms of years is fine too. ;)

• Are there some special physical processes that occur in the Universe on a large enough scale that are able to break up heavy elements (i.e., Helium) into lighter elements (i.e., Hydrogen)? Kind of like a cosmic recycling operation.

• If we discount the possibility of a Big Crunch, is the Universe pretty much headed into a time when there will be no more stars and only a bunch of black holes, planets, and other debris?

• You might want to make the title more specific. For example, "How many generations of stars will exist before the universe's nuclear fuel is depleted?" – Mark Eichenlaub Dec 29 '10 at 23:11
• These questions are pretty independent so you might consider asking them separately. Although the answers to 2. and 3. are AFAIK "no" and "yes" respectively (barring Big Crunch, Brane-worlds and other speculative scenarios) and the answer for 1. will be easy multiplication if you could find the number of stars, average life-time of a star and few other numbers :-) – Marek Dec 29 '10 at 23:29
• See arxiv.org/abs/astro-ph/9701131 and the very accessible papers by Dyson referenced therein (which are what I was looking for as I have read those...). It's not clear to be that the preprint discusses the fate of intelligent life, which the 1979 Dyson paper Time Without End does. Also that reference is slightly dated now. – dmckee --- ex-moderator kitten Dec 29 '10 at 23:32
• Here's a link to Dyson's paper in the Review of Modern Physics which you can probably download at your local university. Or the text is available in various other places on-line. Ah... a link which doesn't require a subscription to an expensive jaurnal. – dmckee --- ex-moderator kitten Dec 29 '10 at 23:40
• @dmckee: Thanks also, I'll try to read it, but I'm pretty sure it'll be over my head at this point. ;) – plslick Dec 29 '10 at 23:49

Tis, a good question. Two related questions arise from it. The first one is, will the hydrogen all be used up in finite time? The second related one is, will star formation completely stop in finite time? They sound related, but the first result doesn't necessarily imply the same result for the second, or vice versa. I.E. a low but nonzero gas density might possibly not allow further star formation, and maybe we could have no hydrogen, but have other types of gas (or even solid objects) still collect into stellar mass objects.

I don't know for sure the answers. The rate of star formation (and hydrogen consumption) could decline slowly enough as to never formally reach zero. Or not.

We do know that a lot of gas gets blown out of galaxies by massive stars, supernova, and black hole activity, and becomes intergalactic gas -usually staying within the galaxy cluster. On a long time scale this should eventually fall back into the cluster's galaxies. So I would think the star formation rate would have a very long tail.

• Any ideas as to how much longer stars will be able to be formed? I'm trying to understand the scale of our ~14 billion years in comparison to the life expectancy of the Universe. Are we zygotes, infants, children, teenagers, ..., elderly? – plslick Dec 30 '10 at 4:13
• @plslick: In an open universe we would be very young indeed. – dmckee --- ex-moderator kitten Dec 30 '10 at 4:48
• plslick: I've heard the claim that 90% of the stars that will ever be have already been formed. So it one sense we are near retirement age (like me). In another sense, I think, since I don't really study these things, that the long tail of slow rate star formation ought to be several times longer than the current age of the universe. – Omega Centauri Dec 30 '10 at 20:41

The vast majority of hydrogen in the universe is in hot gas in galaxy clusters, or cold, extremely diffuse atomic hydrogen in the intergalactic medium (Lyman alpha absorbers). Neither population is likely to ever form stars, so I think the safe answer is "forever."

• Isn't this intergalactic gas being prevented from falling into the clusters galaxies because it is millions of degrees -this gas is seen as diffuse X-ray glow. In any case to maintain that high temp requires an energy source. As stars die out, this gas should cool, and rain down into the local gravity wells, the galaxies mainly. So much of this gas should be available for late stage star formation in the by then very ancient galaxies. I don't know what fraction will do this, some must be lost to the voids between clusters, but it should keep star formation going for a long time. – Omega Centauri Dec 31 '10 at 1:41

This is really a comment but is too long.

A simpler, but related question is "How much of the primordial hydrogen has been used up so far?" or "Can we measure a difference between the percentage of primordial hydrogen (~75% H-1) or the percentage of primordial Helium (~25% He-4) and the percentages today. Short answer - no.

Well, how about a gradient of helium-4 from the galactic center to the outer arms. I think the answer is yes but it's hard for me to tell. Well, can we see a metallicity gradient (all elements heavier than He)? Yes, we can. See http://nedwww.ipac.caltech.edu/level5/Sept04/Henry/Henry2_1.html, fig 1.

Conclusion, you have asked an experimental question in astronomy, and I would like to see astronomical evidence in any answer given.

• The primordial He abundance and how it has changed with time have indeed been estimated. – ProfRob Jul 23 '18 at 21:12
• $\Delta Y/\Delta Z$ has been calibrated to be of order 1-2. i.e. For a present day metallicity of the ISM of $\sim 0.02$ then 2% of the initial H has been converted into He AND injected back into the ISM. – ProfRob Jul 25 '18 at 17:23

One can estimate the primordial abundance of He by using the Planck/WMAP parameters to get the baryon/photon ratio and a standard big-bang nucleosynthesis model. The result can be checked by estimating the He abundance in very low-metallicity galaxies and there is reasonable concordance between the two (see for example Why is hydrogen the most abundant element in the Universe? ).

Next you can estimate how the He mass-fraction $Y$ varies as a function of the increase in metallicity $Z$(elements heavier than He) as the pristine gas is processed through stars. One can also cross-calibrate this with an estimate for the initial He abundance of the Sun and Galactic chemical evolution models (see Serenelli & Basu 2010) to infer that $\Delta Y/\Delta Z \simeq 2$. That is for every (absolute) 1% increase by mass in heavy elements, we deduce an absolute increase of 2% in the He mass fraction.

The current metallicity of the Galactic disk interstellar medium is $Z \sim 0.015$, indicating that the mass fraction of He (in our Galaxy) has increased from about 25% after the big bang, to 28% now. The mass fraction of H has therefore decreased from about 75% after the big bang, to $100-28-1.5 = 70.5$%. In other words a relative fraction of 6% of the initial hydrogen has been processed inside stars, been converted into heavier elements and been returned to the ISM. A further $\sim 20-30$% of the hydrogen atoms in our Galaxy are still locked inside (low-mass) stars.

However, we cannot conclude from this that $\sim 40$% of the hydrogen has been used up or captured in stars. It is estimated that only 10% of hydrogen is actually in stars. The vast majority is expected to exist in the form of ionised protons in the intergalactic or intracluster medium (e.g. see the second slide of this presentation).

In conclusion, about 10% of the H is incorporated into stars and if our Galaxy is a typical residing place for those stars then only about 4% of the hydrogen has actually been processed into heavier elements.

What happens in the future depends on the (uncertain) future star formation rate. This is already in steep decline in our own Galaxy and in the universe in general. However, if gas continues to cool radiatively and fall into potential wells and is not re-energised by new supernovae explosions, then we might expect it to eventually form stars. The cooling time for hot intracluster gas as sparse as the average H atom density in the universe is about $10^{11}$ years (see here) and this is also about the freefall timescale of a large cluster of galaxies (even larger structures will likely be pulled apart by the accelerating cosmic expansion). After a few of these timescales then it is likely that most hydrogen will have cooled, collapsed and been recycled to heavier elements or incorporated into long-lived low-mass stars.