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We study the chaotic-like behavior of cosmological simulations by quantifyinghow minute perturbations grow over time and manifest as macroscopic differencesin galaxy properties. When we run pairs of 'shadow' simulations that areidentical except for random minute initial displacements to particle positions(e.g. of order 1e-7pc), the results diverge from each other at the individualgalaxy level (while the statistical properties of the ensemble of galaxies areunchanged). After cosmological times, the global properties of pairs of'shadow' galaxies that are matched between the simulations differ from eachother generally at a level of ~2-25%, depending on the considered physicalquantity. We perform these experiments using cosmological volumes of(25-50Mpc/h)^3 evolved either purely with dark matter, or with baryons andstar-formation but no feedback, or using the full feedback model of theIllustrisTNG project. The runs cover four resolution levels spanning a factorof 512 in mass. We find that without feedback the differences between shadowgalaxies generally become smaller as the resolution increases, but with theIllustrisTNG model the results are mostly converging towards a 'floor'. Thishints at the role of feedback in setting the chaotic properties of galaxyformation. Importantly, we compare the macroscopic differences between shadowgalaxies to the overall scatter in various galaxy scaling relations, andconclude that for the star formation-mass and the Tully-Fisher relations thebutterfly effect in our simulations contributes significantly to the overallscatter. We find that our results are robust to whether random numbers are usedin the sub-grid models or not. We discuss the implications for galaxy formationtheory in general and for cosmological simulations in particular.

A Quantification of the Butterfly Effect in Cosmological Simulations and Implications for Galaxy Scaling Relations