Four measures of the intracluster medium temperature and their relation to a cluster's dynamical state

We employ an ensemble of 24 hydrodynamic cluster simulations to create spatially and spectrally resolved images of quality comparable to Chandra's expected performance. Emission from simulation mass elements is represented using the XSPEC "MEKAL" program assuming 0.3 solar metallicity and the resulting spectra are fitted with a single-temperature model. Despite significant departures from isothermality in the cluster gas, single-temperature models produce acceptable fits to 20,000 source photon spectra. The spectral fit temperature T-s is generally lower than the mass-weighted average temperature T-m due to the influence of soft line emission from cooler gas being accreted as part of the hierarchical clustering process. The nature of this deviation depends on the bandpass used for spectral fitting. In a Chandra-like bandpass of 0.5 to 9.5 keV we find a nearly uniform fractional bias of (T-m - T-s)/T-s similar or equal to 20%, although smaller clusters sometimes demonstrate much greater deviations. If the minimum energy threshold is raised to 2 keV, however, the effect of line emission on the spectrum is greatly decreased and T-s becomes a nearly unbiased estimator of for smaller clusters. The fractional deviation in T-s relative to T-m is scale-dependent in this bandpass and follows the approximate relation (T-m - T-s)/T-s = 0.2 log(10) T-m. This results in an observed M-ICM-T-s relationship for the simulations with slope of about 1.6, intermediate between the virial relation M proportional to T-m(3/2) and the observed relation M-ICM proportional to T-2. Tracking each cluster in the ensemble at 16 epochs in its evolutionary history, we catalog merger events with mass ratios exceeding 10% in order to investigate the relationship between spectral temperature and proximity to a major merger event. Clusters that are very cool relative to the mean mass-temperature relationship lie preferentially close to a major merger, suggesting a viable observational method to cull a subset of dynamically young clusters from the general population.