Temporal Self-Organization in Galaxy Formation

We report on the discovery of a relation between the number of star formation (SF) peaks per unit time, $\nu_{\rm peak}$, and the size of the temporal smoothing window function, $\Delta t$, used to define the peaks: $\nu_{\rm peak}\propto\Delta t^{1-\phi}$ ($\phi\sim 1.618$). This relation holds over the range of $\Delta t=10$ to $1000$Myr that can be reliably computed, using a large sample of galaxies obtained from a state-of-the-art cosmological hydrodynamic simulation. This means that the temporal distribution of SF peaks in galaxies as a population is fractal with a Hausdorff fractal dimension equal to $\phi-1$. This finding reveals, for the first time, that the superficially chaotic process of galaxy formation is underlined by a temporal self-organization up to at least one gigayear. It is tempting to suggest that, given the known existence of spatial fractals (such as the power-law two-point function of galaxies), there is a joint spatio-temporal self-organization in galaxy formation. From an observational perspective, it will be urgent to devise diagnostics to probe SF histories of galaxies with good temporal resolution to facilitate a test of this prediction. If confirmed, it would provide unambiguous evidence for a new picture of galaxy formation that is interaction driven, cooperative and coherent in and between time and space. Unravelling its origin may hold the key to understanding galaxy formation.