<p>The size of stars depends on the amount of non-hydrogen elements (&quot;metals&quot;) affecting the opacity of the gas that forms them. Metals make it easier to radiate away heat when a gas cloud is collapsing, making it easier for a large amount of gas to accrete (although <a href="https://academic.oup.com/mnras/article/363/2/363/1123406" rel="noreferrer">it may mainly act by increasing the minimum mass of stars that form</a>). There is a fair disagreement about whether the first stars (&quot;<a href="https://en.wikipedia.org/wiki/Stellar_population#Population_III_stars" rel="noreferrer">population III</a>&quot;) were <a href="https://ned.ipac.caltech.edu/level5/ESSAYS/Carr/carr.html" rel="noreferrer">very massive (hundreds of solar masses) or actually small</a>, but I think the rough consensus is that very massive stars were likely. <a href="https://iopscience.iop.org/article/10.1088/0004-637X/706/2/1184" rel="noreferrer">Once they emerged and died, they added metals to the interstellar medium</a> and star formation eventually became more like the present.</p>
<p>The expansion of the universe does not have much effect once gas become trapped in dark matter halos and start to form galaxies.</p>
<p>Once the star has formed opacity and mass determines its structure and luminosity. It turns out that <a href="https://arxiv.org/abs/astro-ph/9701131" rel="noreferrer">for increasing metallicity the maximum stable mass of a star decreases</a> (section B.2). For the eventual metallicity at the end of the stelliferous era Adams and Laughlin estimate a maximum mass star as only 30 solar masses.</p>

CC BY-SA 4.0
2020-12-04T19:07:04.420Z
2020-12-04T19:07:04.420Z
Anders Sandberg
<p>The first stars formed in the universe are likely to have a &quot;top-heavy&quot; mass function. There would be more high-mass stars (as a fraction of all stars) than in the present day and the most massive stars would be more massive than the most massive stars formed in the present day. On the contrary, there would be more low-mass stars formed in the present day than in the early universe.</p>
<p><strong>Details:</strong></p>
<p>The first stars formed from primoridal gas with no heavy elements, just hydrogen and helium produced in the big-bang. Such gas is very transparent to radiation. In the present day universe, some of this primordial material has been processed in previous stellar generations and so stars form from gas which has a small, enriched fraction (about 2% by mass) of heavier elements - mainly oxygen, iron, carbon, nitrogen and nickel.</p>
<p>This is an important difference. These additional chemical elements are more opaque to radiation. This for example prevents the formation of very massive stars in the present day. The reason is that the radiation generated in their hot interiors couples sufficiently well to their outer layers to prevent them collapsing to become stars. In the early universe, this restriction isn't present and very massive stars are able to form.</p>
<p>This is not the full story. In addition to preventing very massive stars from forming, the extra &quot;opacity&quot; of gas in the present-day universe makes it more likely that a collapsing gas cloud will fragment into smaller pieces as the collapse continues, because the same heavy elements are more effective at radiating away energy themselves. The <a href="https://en.wikipedia.org/wiki/Jeans_instability#:%7E:text=The%20Jeans%20mass%20is%20the,reintroduced%20in%20the%20end%20result." rel="nofollow noreferrer">Jeans mass</a>, which is the mass at which a cloud becomes unstable to collapse, is proportional to <span class="math-container">$T^{3/2} \rho^{-1/2}$</span>, where <span class="math-container">$T$</span> is the temperature and <span class="math-container">$\rho$</span> is the density. As collapse proceeds, the density goes up. Now compressing a gas makes it hotter. In fact if energy cannot escape (a so-called <a href="https://en.wikipedia.org/wiki/Adiabatic_process#Example_of_adiabatic_compression" rel="nofollow noreferrer">adiabatic compression</a>, much like in a petrol engine cylinder), then the temperature goes up so much that the collapse is halted because the Jeans mass rises and the cloud stabilises. However, if energy <em>can</em> escape, effectively radiated away by the heavy elements in the gas, then the temperature can remain constant and the Jeans mass can <em>go down</em> with increasing density. This leads to fragmentation of the cloud into smaller clumps and leads to the the production of smaller stars.</p>
<p>Thus the change in behaviour has little to do with the expansion of the universe. The characteristics of star formation are a local phenomenon driven by local conditions of density and temperature. These conditions (bar the heavy element fraction discussed above) will be broadly similar in collapsing gas clouds near the beginning of the universe, the present day or the future, because gravity acts to clump together material into the denisties required to initiate star formation.</p>

CC BY-SA 4.0
2020-12-04T19:47:14.700Z
2020-12-04T19:47:14.700Z
ProfRob
<p>Do stars made by universe getting smaller or larger in mass compared to stars made 180 million years after the Big Bang? If they are getting smaller, is this due to the fact that the universe is expanding and the interstellar mass that made stars is getting less denser?</p>

CC BY-SA 4.0
2020-12-04T13:35:59.890Z
Technically, that's a yes and a no. The Population III stars had masses over ~500 solar masses, while no such star exists today. So, it could be yes, but it is also no because there are still stars that are very massive but also ones that are very small.
WarpPrime
CC BY-SA 4.0
2020-12-04T16:53:51.360Z
I can't understand your question. Are you asking whether stars forming now are larger or smaller than stars that were formed in the early history of the universe? And by larger, do you mean in terms of mass, radius or both?
ProfRob
CC BY-SA 4.0
2020-12-04T17:07:59.597Z
I think you are looking for the time evolution of the "initial mass function" for stars
planetmaker
CC BY-SA 4.0
2020-12-04T18:39:50.477Z
...there are also stars do not exist *yet*, because there was no time yet to form. Afaik Sun will be such a star in its red giant phase. The long-term tendency is that stars will be smaller.
peterh
CC BY-SA 4.0
2020-12-05T01:18:50.037Z
@RobJeffries Thanks for pointing that out, I edited the question more specific now.
Jack the Ranger
<star><star-formation>
Do stars made by universe getting smaller or larger in mass?
Jack the Ranger
# Do stars made by universe getting smaller or larger in mass?

(Asked by: username_0 on 2020-12-04)

Do stars made by universe getting smaller or larger in mass compared to stars made 180 million years after the Big Bang? If they are getting smaller, is this due to the fact that the universe is expanding and the interstellar mass that made stars is getting less denser?

**Tags:** star, star-formation

> **Comments:**
> **username_1**: Technically, that's a yes and a no. The Population III stars had masses over ~500 solar masses, while no such star exists today. So, it could be yes, but it is also no because there are still stars that are very massive but also ones that are very small.  
> **username_2**: I can't understand your question. Are you asking whether stars forming now are larger or smaller than stars that were formed in the early history of the universe? And by larger, do you mean in terms of mass, radius or both?  
> **username_3**: I think you are looking for the time evolution of the "initial mass function" for stars  
> **username_4**: ...there are also stars do not exist *yet*, because there was no time yet to form. Afaik Sun will be such a star in its red giant phase. The long-term tendency is that stars will be smaller.  
> **username_0**: @RobJeffries Thanks for pointing that out, I edited the question more specific now.  

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## 2 answers

### Answer by username_5 on 2020-12-04. Score: 6 | Accepted answer

The size of stars depends on the amount of non-hydrogen elements ("metals") affecting the opacity of the gas that forms them. Metals make it easier to radiate away heat when a gas cloud is collapsing, making it easier for a large amount of gas to accrete (although [it may mainly act by increasing the minimum mass of stars that form](https://academic.oup.com/mnras/article/363/2/363/1123406)). There is a fair disagreement about whether the first stars ("[population III](https://en.wikipedia.org/wiki/Stellar_population#Population_III_stars)") were [very massive (hundreds of solar masses) or actually small](https://ned.ipac.caltech.edu/level5/ESSAYS/Carr/carr.html), but I think the rough consensus is that very massive stars were likely. [Once they emerged and died, they added metals to the interstellar medium](https://iopscience.iop.org/article/10.1088/0004-637X/706/2/1184) and star formation eventually became more like the present.

The expansion of the universe does not have much effect once gas become trapped in dark matter halos and start to form galaxies.

Once the star has formed opacity and mass determines its structure and luminosity. It turns out that [for increasing metallicity the maximum stable mass of a star decreases](https://arxiv.org/abs/astro-ph/9701131) (section B.2). For the eventual metallicity at the end of the stelliferous era Adams and Laughlin estimate a maximum mass star as only 30 solar masses.


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### Answer by username_2 on 2020-12-04. Score: 4

The first stars formed in the universe are likely to have a "top-heavy" mass function. There would be more high-mass stars (as a fraction of all stars) than in the present day and the most massive stars would be more massive than the most massive stars formed in the present day. On the contrary, there would be more low-mass stars formed in the present day than in the early universe.

**Details:**

The first stars formed from primoridal gas with no heavy elements, just hydrogen and helium produced in the big-bang. Such gas is very transparent to radiation. In the present day universe, some of this primordial material has been processed in previous stellar generations and so stars form from gas which has a small, enriched fraction (about 2% by mass) of heavier elements - mainly oxygen, iron, carbon, nitrogen and nickel.

This is an important difference. These additional chemical elements are more opaque to radiation. This for example prevents the formation of very massive stars in the present day. The reason is that the radiation generated in their hot interiors couples sufficiently well to their outer layers to prevent them collapsing to become stars. In the early universe, this restriction isn't present and very massive stars are able to form.

This is not the full story. In addition to preventing very massive stars from forming, the extra "opacity" of gas in the present-day universe makes it more likely that a collapsing gas cloud will fragment into smaller pieces as the collapse continues, because the same heavy elements are more effective at radiating away energy themselves. The [Jeans mass](https://en.wikipedia.org/wiki/Jeans_instability#:%7E:text=The%20Jeans%20mass%20is%20the,reintroduced%20in%20the%20end%20result.), which is the mass at which a cloud becomes unstable to collapse, is proportional to $T^{3/2} \rho^{-1/2}$, where $T$ is the temperature and $\rho$ is the density. As collapse proceeds, the density goes up. Now compressing a gas makes it hotter. In fact if energy cannot escape (a so-called [adiabatic compression](https://en.wikipedia.org/wiki/Adiabatic_process#Example_of_adiabatic_compression), much like in a petrol engine cylinder), then the temperature goes up so much that the collapse is halted because the Jeans mass rises and the cloud stabilises. However, if energy *can* escape, effectively radiated away by the heavy elements in the gas, then the temperature can remain constant and the Jeans mass can *go down* with increasing density. This leads to fragmentation of the cloud into smaller clumps and leads to the the production of smaller stars.

Thus the change in behaviour has little to do with the expansion of the universe. The characteristics of star formation are a local phenomenon driven by local conditions of density and temperature. These conditions (bar the heavy element fraction discussed above) will be broadly similar in collapsing gas clouds near the beginning of the universe, the present day or the future, because gravity acts to clump together material into the denisties required to initiate star formation.


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