The origin of scatter in the stellar mass - halo mass relation of   central galaxies in the EAGLE simulation
  We use the hydrodynamical EAGLE simulation to study the magnitude and origin of the scatter in the stellar mass - halo mass relation for central galaxies. We separate cause and effect by correlating stellar masses in the baryonic simulation with halo properties in a matched dark matter only (DMO) simulation. The scatter in stellar mass increases with redshift and decreases with halo mass. At $z = 0.1$ it declines from 0.25 dex at $M_{200, \rm DMO} \approx 10^{11}$ 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 to scatter in the halo concentration. At fixed halo mass, a larger stellar mass corresponds to a more concentrated halo. This is likely because higher concentrations imply earlier formation times and hence more time for accretion and star formation, and/or because feedback is less efficient in haloes with higher binding energies. The maximum circular velocity, $V_{\rm max, DMO}$, and binding energy are therefore more fundamental properties than halo mass, meaning that they are more accurate predictors of stellar mass, and we provide fitting formulae for their relations with stellar mass. However, concentration alone 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 are also not responsible for the remaining scatter, which thus could be due to more complex halo properties or non-linear/stochastic baryonic effects. 
Jorryt Matthee, Joop Schaye, Robert A. Crain, Matthieu Schaller,   Richard Bower, Tom Theuns
astro-ph.GA astro-ph.CO