How can a Population III star have a mass of several hundred solar masses? Normally the limit is about 100 solar masses.
[Physics] How to a Population III star be so massive
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The oldest Population I stars are about 10 billion years old. Those stars have 0.1 times the metal abundance of the Sun (source).
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 $$ M_{\rm min} \simeq 0.08 \left( \frac{\mu}{0.5} \right)^{-3/2} \left(\frac{\mu_e}{1.2}\right)^{-1/2}$$ (e.g., see here).
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.
Best Answer
I think there are really three questions that need to be answered for this to make sense:
An answer to the first question is tricky. We expect large stars to be rare, and the largest stars to be the rarest. On top of this, they'll lead the shortest lives. Getting observational constraints has thus been tricky. There might be a limit to the amount of mass that is available to turn into stars when they form. As for the "normal" limits on the masses of stars, most (as far as I know) involve around pulsational instability. But the recent discovery of massive stars in and near the cluster R136a suggests that stars with masses over 150 solar can form even in material that has a non-negligible metal content. So whether there is a "normal" limit is open question.
The second question is much better understood, thanks to a lot of numerical work. Tom Abel recently wrote an article for Physics Today that summarizes current understanding of pop III star formation. Basically, the smallest amount of gas unstable to collapse under its own gravity, the Jeans Mass, increases with temperature (like T3/2). So the cooler the gas can become, the smaller the fragments we expect to see. What determines how cool the gas can become? The atoms and molecules that radiate within it, and whether this radiation can escape. In metal-polluted gas, various molecular and atomic lines allow the gas to cool to tens of K. In metal-free material, the most effective coolant (in terms of the low temperatures it can achieve) is molecular hydrogen, which will only cool to around 200 K. This is a higher temperature, so we expect more massive fragments. This is a gross simplification! The situation really involves complex dynamics, shock formation, and all sorts of other stuff. Even the question of whether or not molecular hydrogen can form is contested.
Finally, if a massive pop III star formed, would it keep its mass? We know that the some massive stars in the local universe, like Eta Carinae, are violent beasts. This kind of episodic, pulsational mass loss could be present in Pop III stars, but since such mass loss is so poorly understood, this is often ignored. More generally, we expect that the metals in the atmospheres of massive stars absorb enough of the radiation created inside the star to be driven away in a wind. Again, there aren't any metals in metal-free gas, so we expect this effect to be much smaller in Pop III stars.
So, we expect Pop III stars to be larger because there is more gas available, because the gas fragments less owing to its higher temperature, and because we don't think the stars lose as much mass as modern stars do. And, we aren't even sure that there's a limit on how massive stars can be in the first place!