What if the Sun was made of helium?
I like thinking about astronomical objects in universes like our own, but with a twist. For instance, in a universe with a lot of dark matter, how soon after the Big Bang can stars form? Or consider the Sun, late in its life; is there any way to turn it back into a main sequence star, and what would that mean for Earth? These aren’t questions that astronomers typically work on, but they’re questions I’ve thought about as I’ve gone about building my own universes. Sometimes they lead me to interesting places, and teach me something about our own universe in the process.
A worldbuilding puzzle I’ve been working on lately was inspired by a question on our sister site, Physics Stack Exchange. Most stars in our universe are composed primarily of hydrogen, with some helium thrown in, and a small amount of heavier elements for some added flavor. Say we have a gas cloud of pure helium — no hydrogen, carbon, oxygen, or anything else? Could it collapse to form a star that would support itself by fusing helium, rather than hydrogen?
The answer, it turns out, seems to be yes, thanks to some back-of-the-envelope calculations by Rob Jeffries. I’m going to talk about his reasoning, as well as my little problem: What happens if you have a gas cloud of pure carbon? Can it form a star? What about other common elements, like oxygen?
Star formation 101
Take a giant cloud of hydrogen gas, floating in outer space. If it’s massive enough, it will start to collapse in on itself, radiating away energy in the process. The temperature at the center of the cloud will start to increase, until, eventually, it becomes hot enough for hydrogen fusion to occur. Voila! You have a star.
This is a slightly simplified picture, of course, but it works well enough. However, there’s a problem. If the star isn’t that massive, it’s possible for it to reach conditions where electron degeneracy pressure — the pressure that comes from electrons being squeezed tightly together — will take over, converting the star into something similar to a white dwarf. This is a slight problem for our alternate universe!
Using an concept from the astrophysicist’s toolbox, the virial theorem, Rob came up with the following relation for a star creating energy by fusing a certain element:
Here, R is the star’s radius, M is its mass, T is its central temperature, and μ is something called the mean molecular mass. G and k are the gravitational constant and Boltzmann’s constant, respectively, and mᵤ is the mass of a proton. What we’re interested in is figuring out whether a star made of a certain element can reach temperatures high enough for nuclear fusion before degeneracy pressure takes over. The choice of element determines the mean molecular mass and the temperature at which fusion begins, so once we have that, we can put together a relation between radius and mass at that particular temperature.
Does it work?
In addition to the case of helium, which Rob investigated, I was interested in several other compositions: carbon, neon, oxygen, and silicon. I chose these because they’re all elements involved in fusion in very massive stars, at higher temperatures, and so we understand the conditions under which they fuse. Using some handy data from my textbook, Francis LeBlanc’s An Introduction to Stellar Astrophysics, I took the temperatures at which these elements begin to fuse, and used this to put together a plot of Rob’s mass-radius relations, as well as a simple mass-radius relation for a white dwarf. Here’s what I got:
Let’s break down this plot. On the vertical axis, we have a star’s radius; on the horizontal axis, we have a star’s mass. A star made of helium, carbon, etc. should lie somewhere on the correspondingly labeled line. Any parts of the curves under and to the left of the white dwarf curve is forbidden; a star of that composition, mass and radius would be dominated by degeneracy pressure — so no fusion.
I thought that these results were pretty interesting:
- The lower mass limit for pure helium stars is about 0.3 solar masses — around the mass of a normal white dwarf.
- A pure carbon star should be at least 1.0 solar masses; for neon, oxygen and silicon, this limit increases to a few solar masses.
- The heavier the element, the higher the temperature needed to fuse, and so the higher the minimum mass.
We’ve shown that it seems plausible that, if you could somehow get a large cloud of gas composed of one of these heavier elements, a star could form from it — assuming it was massive enough. Could this happen in our universe? It’s unlikely, given that hydrogen vastly outnumbers all the other elements. There are also plenty of simplifications and assumptions that we made, such as that the star will be stable for long periods of time, even though this isn’t necessarily the case for the heavy elements.
Want to play around with this a bit? Here’s the Python 3 code I used for my calculations and plotting:
