On the Reliability of Photometric and Spectroscopic Tracers of Halo Relaxation

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.