# Metal-rich star formation

While discussing star formation on cosmological scales with some classmates, we mentioned the breakdown between the different stellar populations via metallicity:

• Population III: $Z = [{\rm Fe/H}] \lesssim -5$
• Population II: $Z = [{\rm Fe/H}] \sim -1$
• Population I: $Z = [{\rm Fe/H}] \sim 0$

where $[{\rm Fe/H}]=\log_{10}\left[({\rm Fe/H})/({\rm Fe/H})_\odot\right]$ (the logarithm of the ratio of iron abundance to hydrogen abundance versus solar composition).

We wondered if there was a known maximum (analytical or computational) of metallicity in which stars can form. Binney & Merrifield's Galactic Astronomy briefly touches on the effect of low metallicity in star formation (see Section 5.1.5 of the text), but does not mention the other end of the spectrum.

There have been papers discussing the evolution of massive stars with high metallicity (e.g., Meynet, Mowlavi, & Maeder (2006) consider the case1 of $Z\sim1$). We also know that the metallicity will continue to increase (though Pop I stars are still at a low ~2% metals by mass, even after a few billion years of evolution), but I have not seen any mentioning of the effects of forming stars with the increased metallicity.

So my question is, is there such a maximum metallicity at which stars can no longer form?

1 They use the $X+Y+Z=1.0$ to define $Z$, with $X$ and $Y$ denoting the mass fractions of hydrogen & helium respectively (a fairly common definition). To convert to the definition I use above, use $[{\rm Fe/H}]\sim\log_{10}(Z/X)-\log_{10}(Z_\odot/X_\odot)$

• It's pretty standard notation for astronomers. – pela Mar 5 '15 at 12:40
• I'm looking forward to a good answer on this, but the answer must be 'yes'. Firstly, the more metals, the harder it becomes for the star to assemble, since more metals means more transitions, so radiation pressure counteracts the collapse. Secondly, in the limit of 100% metals, there isn't really any fuel for the star. I guess there are many stellar models available out there where you can punch your favorite values in and get masses, temperatures, and surface gravities, but they may have difficulties with "unrealistic" metallicities. – pela Mar 6 '15 at 8:21
• @Thriveth: Radiation pressure necessitates interaction of the radiation with the gas. If the blackbody radiation is surrounded by metal-free gas, there are only a few lines to absorb the spectrum, so most radiation (below the hydrogen ionization threshold) escapes. If it's full of metals, the gas creates a wall of lines, absorbing at all sorts of wavelengths (re-emitting in the IR). Wrt. a full metal jac… I mean star, you may be right. I assumed you needed hydrogen, but maybe not… – pela Jan 14 '16 at 21:22
• @pela Good point on the transitions. I wonder if that would prevent collapse, or simply slow it down and give stronger line emission and fainter continuum? I also don't know if hydrogen is actually needed, but carbon burning requires no H or He (actually produces a little bit), and same seems to be the case for Oxygen burning, and they are the dominant metals - and AFAIK, it is gravitational contraction that creates the temperatures needed to ignite it. – Thriveth Jan 15 '16 at 1:56
• @honeste: iron can fuse with helium (producing unstable Ni56), but I don't think there is a Fe+Fe process, so *pure * iron wouldn't work. AFAIK, one needs lighter elements for fusion to occur, but I'm not sure what the largest metal content would be while still able to form stars. – Kyle Kanos Jan 15 '16 at 19:33

No, I don't believe there is. Or, describing the scope of my answer, there is no maximum "metallicity" (for any normal mixture of metals) that could prevent a collapsing protostar becoming hot enough in its core to initiate nuclear fusion. (If your question is about the Jeans mass and metallicity, then you could clarify).

What determines whether fusion will ever commence is whether the contraction of the protostar is halted by electron degeneracy pressure before reaching a temperature sufficient for nuclear ignition.

For a solar composition protostar, the critical mass is about $$0.08M_{\odot}$$. Below this, the core does not attain a temperature of $$\sim 5\times 10^{6}$$ K that are required for nuclear fusion.

The calculation of this minimum mass depends on $$\mu_e$$, the number of mass units per electron in the core (which governs electron degeneracy pressure), and on $$\mu$$, the number of mass units per particle in the core (which governs perfect gas pressure). However, these dependencies are not extreme. In the core of the protosun, $$\mu_e \sim 1.2$$ and $$\mu \sim 0.6$$. If we made a metal rich star that had very little hydrogen by number and the rest say oxygen (a.k.a. a star made of water), then $$\mu_e \sim 1.8$$ and $$\mu \sim 1.6$$. The minimum mass for hydrogen fusion is given approximately by $$M_{\rm min} \simeq 0.08 \left( \frac{\mu}{0.5} \right)^{-3/2} \left(\frac{\mu_e}{1.2}\right)^{-1/2}$$

These different parameters would be enough to change the minimum mass (downwards actually) for hydrogen fusion to around $$0.012 M_{\odot}$$.

We could of course hypothesise a star that was wholly made of metals. A convenient estimate of the minimum mass for carbon fusion is already supplied by stellar evolution models. A $$>8M_{\odot}$$ star with a carbon core will initiate carbon fusion before it becomes degenerate. The mass is much higher than for H fusion because of the increased coulomb barrier between carbon nuclei. Of course the star also has a hydrogen/helium envelope, but if you replaced this with carbon, then the result will be little changed. Thus you could have a population of lower mass objects that do not become stable "stars". Those with masses of $$1.4 < M/M_{\odot} < 8$$ would presumably end up detonating as some kind of type Ia supernovae, because they will achieve a density/temperature combination where C can fuse, but in highly degenerate conditions. Lower than that and it becomes a stable white dwarf.

Of course your metal rich "star" could just be a ball of iron, in which case nuclear fusion isn't going to happen and if it is more than $$\sim 1.2M_{\odot}$$ it will collapse directly to a neutron star or black hole, possibly via some sort of supernova. Lower than that and it becomes a stable iron white dwarf.

I would say the answer depends on what you mean by a star. A lot of places require that there be fusion in there somewhere to call it a star, but this is a bit tricky because we still call things stars that are either pre-fusion, or post-fusion. What's more, all but the highest mass stars are finished any process we might want to call "star formation" long before they ever start fusing anything, and we might even say the star formation process is totally independent from the fusion process. So I think we have two rather separate issues where, one is, how does metallicity affect star "formation", and the other is, whether or not what is "forming" ever ends up fusing much. The answer to the first question is, metallicity only affects the scales on which the star formation occurs-- how long it takes, how much mass and angular momentum ends up in the star, and what is the status of binarity, it doesn't change the inevitability of the star-forming process which is really just a story of gravity and heat loss. The answer to the second question deals more with how fusion works, and the important fact that iron cannot be fused into anything that releases heat, but fusion can be made to occur by the energy release of gravitational collapse. So I would tend to divorce the complex fusion issues from the simple "formation" issues, and answer that metallicity alters the formation process, moreso than it allows or prevents it.

• You are inventing a new question ("what is a star") that I didn't ask, then answering that question and haphazardly ignoring the actual question I asked. Your last half of a sentence is the closest you come to answering my actual question, but you basically state what I've given evidence for in my question. – Kyle Kanos Sep 3 '16 at 16:35
• Apparently you feel it is possible to ask when a star can form, without saying what you mean by a star. What I was trying to point you to is the difference between the questions "what physical processes led to the generation of an object in our solar system that contained a solar mass of gas", and "what physical processes had to occur such that fusion could originate in that solar mass of gas." If you see that those are two quite different questions, then you will see what I was saying. If you cannot, then you won't. – Ken G Sep 3 '16 at 17:52
• Actually, if you read the actual question I posed, I am not at all asking about when a star can form. My question is seeking the maximum metallicity of a material (i.e., gas cloud) that can form a star (which does have a more definite definition than you seem to suggest it does have). – Kyle Kanos Sep 3 '16 at 18:30
• If you look at the literature of "star formation" in astronomy, you will find no mention of fusion physics anywhere. Yet some answers you have received have mentioned fusion, because the definition of "what is a star" often includes fusion somewhere. So are you asking about metallicity effects on fusion physics (like, what is the minimum mass a star needs in order to ever accomplish fusion, which does depend on metallicity but has nothing to do with "star formation" physics), or about the metallicity effects of forming large bright balls of hot gas, which has nothing to do with fusion? – Ken G Sep 3 '16 at 19:42
• That depends on your answer to this: if a ball of gas forms that is as bright as the Sun, but is made of metals that never produce fusion, would you say that a star has formed, or would you say that a star has not formed? Until you clarify that, no one can know how to answer your question. – Ken G Sep 3 '16 at 20:04

It makes sense that there would be a maximum metallicity for fusion. At high enough metallicity, hydrogen atoms are separated mostly from each other by metal atoms, stopping fusion and causing collapse until fusion occurs OR degeneracy pressure supports the star. So if the metallicity is very high, the way I see it, fusion cannot occur due the low concentration of reactant.

• Do you have any references or calculations to back this up? Otherwise, this isn't that much different from pela's comment (third comment to the question). – Kyle Kanos Aug 16 '16 at 11:50
• Yes, I do have more reasoning. The temperature at which fusion can occur is determined by the frequency of the quantum tunnelling reaction which causes it, which decreases very rapidly with increasing tunneling distance. So fusion would require a fairly high density of reactant, otherwise the reaction would not occur, the core would collapse and it would heat up, lowering the density required. If the temperature reached the point of iron fusion, then the metal would become unstable and photodisintegrate in the temperature, causing collapse. – Temsia-Carrolla Aug 16 '16 at 12:35
• Again, that's basically the same thing as what Pela's comment says. Have you a real computation (not intuition) or a resource that does the computation? – Kyle Kanos Aug 16 '16 at 13:02

Technically, the tempretures necessary for star formation is directly proportional to the general heaviness of the atoms in the gas cloud forming it. in other words, stars can be formed out of any kind of atom, notwithstanding how metallic it is, as long as They can reach the high enough temperatures necessary to begin fusion. As we know that stars form when a gas cloud collapses under its own gravity, and the atoms heat up due to friction. Hence, it is theoretically possible for the temperature to keep increasing as the cloud contracts. I do not know if there is a limit to the radius a gas cloud is able to shrink to, but the limit that is necessary here is on temperature. The temperature at which the laws of physics as we know it, begin to break down is the Planck temperature. so, since the general heaviness of the atoms in a forming star is directly proportioinal to the temperature needed to begin fusion, the maximum temperature attainable within the laws of physics must set a limit on the heaviest atom that can be fused in a star. So, yes, there is a limit. What, i do not know.