The origin of scatter in the star formation rate - stellar mass relation

Observations have revealed that the star formation rate (SFR) and stellar mass (M$_{\rm star}$) of star-forming galaxies follow a tight relation known as the galaxy main sequence. However, what physical information is encoded in this relation is under debate. Here, we use the EAGLE cosmological hydrodynamical simulation to study the mass dependence, evolution and origin of scatter in the SFR-M$_{\rm star}$ relation. At $z=0$, we find that the scatter decreases slightly with stellar mass from 0.35 dex at M$_{\rm star} \approx 10^9$ M$_{\odot}$ to 0.30 dex at M$_{\rm star} \gtrsim 10^{10.5}$ M$_{\odot}$. The scatter decreases from $z=0$ to $z=5$ by 0.05 dex at M$_{\rm star} \gtrsim 10^{10}$ M$_{\odot}$ and by 0.15 dex for lower masses. We show that the scatter at $z=0.1$ originates from a combination of fluctuations on short time-scales (ranging from 0.2-2 Gyr) that are presumably associated with self-regulation from cooling, star formation and outflows, but is dominated by long time-scale ($\sim 10$ Gyr) variations related to differences in halo formation times. Shorter time-scale fluctuations are relatively more important for lower-mass galaxies. At high masses, differences in black hole formation efficiency cause additional scatter, but also diminish the scatter caused by different halo formation times. While individual galaxies cross the main sequence multiple times during their evolution, they fluctuate around tracks associated with their halo properties, i.e. galaxies above/below the main sequence at $z = 0.1$ tend to have been above/below the main sequence for $\gg1$ Gyr.