(This page is currently incomplete – sorry!)

In 2016, I started a PhD in astronomy. After around a year of trying out projects and eventually diving fully into one, I decided that the overall topic of my thesis would be the evolution of triple stars. My supervisor, Dr Rob Izzard’s research focussed on binary stars, and he had spent much of his academic career developing binary_c, a piece of software that simulate binary stars at very high speeds (billions of years of evolution in less than a second) that is used to (among other things) study the evolution of populations of stars.

I’ll make a copy of my thesis available here once the corrected version has been resubmitted and approved.

Chapter 1: Binary Bondi-Hoyle-Lyttleton accretion

This was the original topic which got me into studying triples. We (roughly) know how stars accrete material from nearby – with the right assumptions, you can solve it with pen and paper. However, adding a second star to the mix makes everything more complicated. This will become a recurring theme for the following few years of my life.

We simulated a series of binary systems flying through a uniform cloud of gas, using the code GANDALF on the Dirac supercomputer, which was a lot of fun. Varying the binary’s properties allowed us to measure the effect, and interpolate the results. The figure above shows a few snapshots from our simulation runs.

In binary stars, this kind of accretion happens when one star is producing a wind, which its companion flies through. In some scenarios, the accretion is sufficient to significantly increase the companion’s mass or alter its chemical composition. Of course, if you add another star, you get a triple, which typifies the setup we used in the paper. Just as the regular BHLA formalism could be applied to single stars moving through a cloud of gas, the binary version applies to a binary moving through gas. This could be important in particular environments – particularly near the galactic centre, for example.

The results of the paper are essentially just numerical data, but we identified some broad qualitative points: mainly that the form the accretion takes mostly depends on the orbital separation of the stars in the binary. If they’re close together, they behave more like a single star which scoops up gas, then shares between the two stars; if they’re far apart, they essentially accrete individually and do not affect each other. The interesting stuff happens in the intermediate range, but if you want the results, you’ll have to read the paper.

Chapter 2: Triple common envelope evolution

Unfortunately, this project produced many fewer pretty figures than the last – it’s difficult to beat hydrodynamical simulations in that aspect.

In binary systems, there’s an interesting evolutionary stage which can occur when one star becomes large enough to actually engulf the other, called common envelope evolution. A lot of research has been (and continues to be) done on this topic because it is interesting, important, and not fully understood. However, the broad strokes are generally agreed upon, even if the specifics are not.

Common envelope evolution consists of these stages:

  1. Plunge and Inspiral. Friction between the stars and the gaseous envelope shrinks the orbit, making it speed up (if that sounds weird, it’s just how orbits work – think of the stars falling towards each other)
  2. Circularization. As angular momentum is transferred to the envelope it begins to spin up, until the friction between the stars and envelope is reduced to zero. At this point, the binary orbit stops contracting.
  3. Ejection. Shrinking the orbit released a lot of gravitational potential energy (and angular momentum), which has to go somewhere. The only possible recipient is the envelope, which reacts to this by expanding too fast for the stars to hang on to, meaning it it almost completely ejected from the system. There may be other sources of energy at play, but the envelope is ejected either way – this matches observations.

Unsurprisingly, triples make it complicated. We studied the possible evolution by considering each of the above steps, but with an extra star along for the ride.

  1. Plunge and Inspiral aren’t too different; the main thing to keep track of is that there are two orbits to shrink (see the figure above). We found that in almost all realistic cases, the big triple orbit shrinks much faster then the small binary orbit.
  2. Circularization doesn’t really happen at all. Triples require a decent difference of orbital separations to remain stable. Since the triple orbit shrinks too quickly during the inspiral, the triple eventually becomes unstable.
  3. Ejection in this case doesn’t just refer to ejection of the envelope. As the triple approaches instability, it’ll undergo a chaotic three-body interaction, which culminates in the complete ejection of one of the stars, while the resulting binary recoils in the opposite direction. The speeds of this ejection are so fast, that all three stars shoot out of the envelope, leaving it behind. Without the stars gravity to hold it together, the envelope simply dissipates.

At the end of the paper, we outline an algorithm you could use if you wanted to quickly estimate the outcome of the triple common envelope. Which would be useful if, say, you wanted to write a triple star evolution code.

Chapter 3: Evolution of triple stars

This is the bit which ties the rest together. Using the results from the previous chapters, plus a lot more from the pre-existing literature, I set about modifying binary_c to simulate triple stars.