  We study non-parametric morphologies of mergers events in a cosmological
context, using the Illustris project. We produce mock g-band images comparable
to observational surveys from the publicly available Illustris simulation
idealized mock images at $z=0$. We then measure non parametric indicators:
asymmetry, Gini, $M_{20}$, clumpiness and concentration for a set of galaxies
with $M_* >10^{10}$ M$_\odot$. We correlate these automatic statistics with the
recent merger history of galaxies and with the presence of close companions.
Our main contribution is to assess in a cosmological framework, the empirically
derived non-parametric demarcation line and average time-scales used to
determine the merger rate observationally. We found that 98 per cent of
galaxies above the demarcation line have a close companion or have experienced
a recent merger event. On average, merger signatures obtained from the
$G-M_{20}$ criteria anticorrelate clearly with the elapsing time to the last
merger event. We also find that the asymmetry correlates with galaxy pair
separation and relative velocity, exhibiting the larger enhancements for those
systems with pair separations $d < 50$ h$^{-1}$ kpc and relative velocities $V
< 350$ km s$^{-1}$. We find that the $G-M_{20}$ is most sensitive to recent
mergers ($\sim0.14$ Gyr) and to ongoing mergers with stellar mass ratios
greater than 0.1. For this indicator, we compute a merger average observability
time-scale of $\sim0.2$ Gyr, in agreement with previous results and demonstrate
that the morphologically derived merger rate recovers the intrinsic total
merger rate of the simulation and the merger rate as a function of stellar
mass.
