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 semianalytic galaxy evolution model. We quantify the correlations between the dynamical age of simuglated 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 (A²) and the velocity segregation ( $\overline{{\rm{\Delta }}V}$ ) as our spectroscopic indicators, and use the luminosity gap (Δm₁₂) and the luminosity decentering (D_offset) as photometric ones. First, we find that a combination of Δm₁₂ and D_offset evaluated by a bivariant relation ( ${\rm{B}}=0.04\times {\rm{\Delta }}{m}_{12}-0.11\times \mathrm{Log}({D}_{\mathrm{off}-\mathrm{set}})+0.28$ ) shows a good correlation with the dynamical age compared to all other indicators. Second, 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 A² and X-ray proxies, offering a 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.