astrophysics - 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 $[{\rm Fe/H}]\sim\log_{10}(Z/X)-\log_{10}(Z_\odot/X_\odot)$}

Answer

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.