<p>One can make a <em>theoretical</em> upper bound by considering the most short-lived star possible <span class="math-container">$\tau_{short}$</span>, and a large supply of initial hydrogen <span class="math-container">$M_H$</span>. Then one could calculate the fraction hydrogen that is recycled <span class="math-container">$r$</span> after the star ends (with a supernova), and get a total number of generations as <span class="math-container">$ \log (M_{star}/M_H)/\log(r)$</span>. If one uses the solar-mass <span class="math-container">$r\approx 0.5$</span> and a galaxy mass of gas <span class="math-container">$M_H=10^{10}M_\odot$</span> one could get 33 generations.
One could of course try tweaking this <a href="https://en.wikipedia.org/wiki/Pair-instability_supernova#/media/File:Supernovae_as_initial_mass-metallicity.svg" rel="noreferrer">by using heavier stars that recycle better yet are not affected by the growing metallicity of the medium</a>, but it would be rather wasted effort: it is not a realistic model.</p>
<p>The overlap between generations is growing: stars are made today from mixed gas recycled from all previous generations. They also last very different lengths of time depending on mass, so the gas reservoir does not conveniently fill up for the next generation to be created, but rather is topped up while star formation is ongoing. So speaking of generations becomes less and less useful, and instead it makes sense to mainly speak of when a star formed or how much metals it had at the start due to a highly evolved gas reservoir.</p>
<p>One can simulate star formation and recycling by using models of each, but <a href="https://academic.oup.com/mnras/article/456/2/1235/1059677" rel="noreferrer">it quickly turns rather complex</a> and worse, dependent on assumptions about how much intra-cluster gas will fall in the future, something that is weakly constrained. Current trends in star formation suggest that we are close to peak star number and that peak star formation was in the past, so relatively few stars will form in the future until the gas levels go below a critical surface density and shuts off (see <a href="https://arxiv.org/abs/astro-ph/9701131" rel="noreferrer">section D in this paper</a>). But if intra-cluster gas cools and rains down slowly that may prolong things a fair bit. Still, in about <span class="math-container">$10^{14}$</span> years normal star formation will have ceased.</p>

CC BY-SA 4.0
2020-12-30T10:02:46.880Z
2020-12-30T10:02:46.880Z
Anders Sandberg
<p>As in general case, stars are formed from nebula which in some case itself is the result of a supernova.</p>
<p>Also stars need hydrogen to become a star (to do nuclear fusion), but stars consume hydrogen in their lifecycle. Thus, less and less hydrogen is left for the future generation and <a href="https://astronomy.stackexchange.com/a/6399/35031">more heavy elements take that place</a>.</p>
<p>How many generation of stars can be formed until there is no more enough hydrogen left to create new stars?</p>

CC BY-SA 4.0
2020-12-30T09:07:47.177Z
See https://astronomy.stackexchange.com/questions/1414/will-new-stars-stop-forming-at-some-point-of-time and https://astronomy.stackexchange.com/questions/16311/how-can-there-be-1-000-stellar-ancestors-before-our-sun/16313#16313 and https://astronomy.stackexchange.com/questions/16380/is-the-composition-of-stars-in-future-made-of-more-and-more-heavy-elements
ProfRob
CC BY-SA 4.0
2020-12-30T09:14:31.917Z
And also https://astronomy.stackexchange.com/questions/27180/where-did-the-sun-get-hydrogen-to-work-with-if-it-is-in-the-3rd-generation-of-st
ProfRob
CC BY-SA 4.0
2020-12-30T12:12:55.167Z
And https://astronomy.stackexchange.com/questions/31782/when-will-the-number-of-stars-be-a-maximum/31786#31786
ProfRob
CC BY-SA 4.0
2020-12-30T13:35:25.737Z
Does this answer your question? [How can there be 1,000 stellar ancestors before our Sun?](https://astronomy.stackexchange.com/questions/16311/how-can-there-be-1-000-stellar-ancestors-before-our-sun)
WarpPrime
CC BY-SA 4.0
2020-12-30T22:46:39.970Z
*I think it is not a dupe*, it was only not very well formulated. The orig candidate asks for the precursors of the Sun. This question asks for the count of generations in the stelliferous era. I tried to fix it.
peterh
CC BY-SA 4.0
2020-12-30T22:48:30.460Z
@aDEp I did not unterstand your last some sentences, but your question was imho clear even without them. In order to fix your question, I deleted them. You can roll back any time if you wish to in the page history. I suggest to not do it, instead if it was some type of a "secondary question", then ask it as a different question.
peterh
<the-sun><star-formation><hydrogen>
How many generations of stars can be formed in the Stelliferous Era?
aDEp
# How many generations of stars can be formed in the Stelliferous Era?

(Asked by: username_0 on 2020-12-30)

As in general case, stars are formed from nebula which in some case itself is the result of a supernova.

Also stars need hydrogen to become a star (to do nuclear fusion), but stars consume hydrogen in their lifecycle. Thus, less and less hydrogen is left for the future generation and [more heavy elements take that place](https://astronomy.stackexchange.com/a/6399/35031).

How many generation of stars can be formed until there is no more enough hydrogen left to create new stars?

**Tags:** the-sun, star-formation, hydrogen

> **Comments:**
> **username_1**: See https://astronomy.stackexchange.com/questions/1414/will-new-stars-stop-forming-at-some-point-of-time and https://astronomy.stackexchange.com/questions/16311/how-can-there-be-1-000-stellar-ancestors-before-our-sun/16313#16313 and https://astronomy.stackexchange.com/questions/16380/is-the-composition-of-stars-in-future-made-of-more-and-more-heavy-elements  
> **username_1**: And also https://astronomy.stackexchange.com/questions/27180/where-did-the-sun-get-hydrogen-to-work-with-if-it-is-in-the-3rd-generation-of-st  
> **username_1**: And https://astronomy.stackexchange.com/questions/31782/when-will-the-number-of-stars-be-a-maximum/31786#31786  
> **username_2**: Does this answer your question? [How can there be 1,000 stellar ancestors before our Sun?](https://astronomy.stackexchange.com/questions/16311/how-can-there-be-1-000-stellar-ancestors-before-our-sun)  
> **username_3**: *I think it is not a dupe*, it was only not very well formulated. The orig candidate asks for the precursors of the Sun. This question asks for the count of generations in the stelliferous era. I tried to fix it.  
> **username_3**: @username_0 I did not unterstand your last some sentences, but your question was imho clear even without them. In order to fix your question, I deleted them. You can roll back any time if you wish to in the page history. I suggest to not do it, instead if it was some type of a "secondary question", then ask it as a different question.  

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## 1 answers

### Answer by username_4 on 2020-12-30. Score: 9

One can make a *theoretical* upper bound by considering the most short-lived star possible $\tau\_{short}$, and a large supply of initial hydrogen $M\_H$. Then one could calculate the fraction hydrogen that is recycled $r$ after the star ends (with a supernova), and get a total number of generations as $ \log (M\_{star}/M\_H)/\log(r)$. If one uses the solar-mass $r\approx 0.5$ and a galaxy mass of gas $M\_H=10^{10}M\_\odot$ one could get 33 generations.
One could of course try tweaking this [by using heavier stars that recycle better yet are not affected by the growing metallicity of the medium](https://en.wikipedia.org/wiki/Pair-instability_supernova#/media/File:Supernovae_as_initial_mass-metallicity.svg), but it would be rather wasted effort: it is not a realistic model.

The overlap between generations is growing: stars are made today from mixed gas recycled from all previous generations. They also last very different lengths of time depending on mass, so the gas reservoir does not conveniently fill up for the next generation to be created, but rather is topped up while star formation is ongoing. So speaking of generations becomes less and less useful, and instead it makes sense to mainly speak of when a star formed or how much metals it had at the start due to a highly evolved gas reservoir.

One can simulate star formation and recycling by using models of each, but [it quickly turns rather complex](https://academic.oup.com/mnras/article/456/2/1235/1059677) and worse, dependent on assumptions about how much intra-cluster gas will fall in the future, something that is weakly constrained. Current trends in star formation suggest that we are close to peak star number and that peak star formation was in the past, so relatively few stars will form in the future until the gas levels go below a critical surface density and shuts off (see [section D in this paper](https://arxiv.org/abs/astro-ph/9701131)). But if intra-cluster gas cools and rains down slowly that may prolong things a fair bit. Still, in about $10^{14}$ years normal star formation will have ceased.


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