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We use the hydrodynamical EAGLE simulation to study the magnitude and originof the scatter in the stellar mass - halo mass relation for central galaxies.We separate cause and effect by correlating stellar masses in the baryonicsimulation with halo properties in a matched dark matter only (DMO) simulation.The scatter in stellar mass increases with redshift and decreases with halomass. At $z = 0.1$ it declines from 0.25 dex at $M_{200, \rm DMO} \approx10^{11}$ M$_{\odot}$ to 0.12 dex at $M_{200, \rm DMO} \approx 10^{13}$M$_{\odot}$, but the trend is weak above $10^{12}$ M$_{\odot}$. For $M_{200,\rm DMO} < 10^{12.5}$ M$_{\odot}$ up to 0.04 dex of the scatter is due toscatter in the halo concentration. At fixed halo mass, a larger stellar masscorresponds to a more concentrated halo. This is likely because higherconcentrations imply earlier formation times and hence more time for accretionand star formation, and/or because feedback is less efficient in haloes withhigher binding energies. The maximum circular velocity, $V_{\rm max, DMO}$, andbinding energy are therefore more fundamental properties than halo mass,meaning that they are more accurate predictors of stellar mass, and we providefitting formulae for their relations with stellar mass. However, concentrationalone cannot explain the total scatter in the $M_{\rm star} - M_{200, \rm DMO}$relation, and it does not explain the scatter in $M_{\rm star} -V_{\rm max,DMO}$. Halo spin, sphericity, triaxiality, substructure and environment arealso not responsible for the remaining scatter, which thus could be due to morecomplex halo properties or non-linear/stochastic baryonic effects.

The origin of scatter in the stellar mass - halo mass relation of central galaxies in the EAGLE simulation