Astronomers who simulate galaxies do not always get the same result, even when they start from identical conditions. New research from Leiden University shows that this is not a flaw, but a consequence of how galaxies behave - and how they are modelled.
The findings offer, for the first time, a way to address a long‑standing question: how chaotic is a galaxy like the Milky Way really? The computer simulations by Tetsuro Asano and Simon Portegies Zwart (Leiden Observatory) will soon be published in Astronomy & Astrophysics.
The researchers created hundreds of models of Milky Way‑like galaxies: flat discs of stars, embedded in a large, invisible cloud of dark matter that holds the system together. In each experiment, they ran two almost identical simulations, differing by just one tiny detail - for instance, a small shift in the position of a single star. Over time, that slight difference grows into visible structural changes: spiral arms develop differently and the central bar rotates in another way.

Small causes, big effects
This resembles the well-known butterfly effect, where small causes can lead to large consequences. In astronomy, that idea clashes with a traditional view. A galaxy contains hundreds of billions of stars, so it is often assumed to behave like a smooth system in which small disturbances average out. This study shows that the opposite is true: small disturbances can grow into noticeable differences. 'It's quite remarkable that the Milky Way, with so many stars that you would expect it to behave smoothly, still turns out to be so chaotic,' says Portegies Zwart.
This tension has led to conflicting results in previous research. Some simulations suggested that galaxies become more chaotic as more stars are included, while others found the reverse. The new work by Asano and Portegies Zwart explains where this difference comes from. In many simulations, gravity at very small distances is 'softened' to keep calculations stable and manageable. As a result, stars are treated as small clouds rather than as precise points, and the strong, close interactions that drive chaos are effectively smoothed out. By systematically varying how much this 'softening' is applied, the researchers show when a simulation accurately reflects a real galaxy, and when it does not.
''The Milky Way becomes unpredictable after about a million years.'
An unpredictable Milky Way
This leads to an important practical insight: not all simulations are equally reliable when it comes to understanding the fine details of a galaxy. Some features always appear, such as the formation of a central 'bar' of stars, which emerges at roughly the same time in all simulations. Other properties - such as the exact shape of that bar or the structure of spiral arms - turn out to depend strongly on tiny differences. 'In fact, the Milky Way becomes unpredictable after about a million years,' says Portegies Zwart.
That is extremely short compared with the age of the Milky Way (about ten billion years) - roughly the equivalent of a single second in a human lifetime.
'We have now quantified how choices in a simulation determine how much of that chaos you see.'
A paradox resolved
At the same time, the study shows that these small differences do not keep growing indefinitely; the butterfly effect has its limits. Two simulations may end up looking different - with different spiral arms or a differently oriented bar - but both still remain recognisable as spiral galaxies.
'This resolves the paradox that galaxies can behave both smoothly and chaotically at the same time,' says Portegies Zwart. 'We have now quantified how choices in a simulation determine how much of that chaos you see. That not only explains how a single star can reshape an entire galaxy, but also how we can model this reliably.'
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