  We characterize the relaxation state of galaxy systems by providing an
assessment of the reliability of the photometric and spectroscopic probe via
the semi-analytic galaxy evolution model.
  We quantify the correlations between the dynamical age of simulated galaxy
groups and popular proxies of halo relaxation in observation, which are mainly
either spectroscopic or photometric. We find the photometric indicators
demonstrate a stronger correlation with the dynamical relaxation of galaxy
groups compared to the spectroscopic probes.
  We take advantage of the Anderson Darling statistic ($A^2$) and the
velocity-segregation ($\bar{\Delta V}$) as our spectroscopic indicators, and
use the luminosity gap ($\Delta m_{12}$) and the luminosity de-centring
($D_{\mathrm{off-set}}$) as photometric ones. Firstly, we find that a
combination of $\Delta m_{12}$ and $D_{\mathrm{off-set}}$ evaluated by a
bivariant relation ($\mathrm{B} = 0.04 \times \Delta m_{12} - 0.11 \times
Log(D_{off-set}) + 0.28$), shows a good correlation with the dynamical age
compared to all other indicators.
  Secondly, by using the observational X-ray surface brightness map, we show
that the bivariant relation brings about some acceptable correlations with
X-ray proxies. These correlations are as well as the correlations between $A^2$
and X-ray proxies, offering reliable yet fast and economical method of
quantifying the relaxation of galaxy systems.
  This study demonstrates that using photometric data to determine the
relaxation status of a group will lead to some promising results that are
comparable with the more expensive spectroscopic counterpart.
