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"Four Measures of the Intracluster Medium Temperature and their Relation to a Cluster's Dynamical State" (Introduction) by Mathiesen & Evrard, Astrophysical Journal v. 546, 2001.

Galaxy clusters are the youngest and largest organized structures in the universe, and as such provide us with a wealth of cosmological information. The most massive clusters draw their substance from cosmologically significant volumes of linear scale ≈ 10 h-1 Mpc. No known coherent process can compete against gravity on such large scales, so the contents of rich clusters are thought to comprise a fair sample of the universe's ingredients (White et al. 1993). Because clusters are rare nonlinear excursions of the cosmic density field, the statistical properties of their population are quite sensitive to both cosmological model and the slope of the primordial fluctuation spectrum. Unfortunately, their relative youth can also make interesting physical properties difficult to measure. About 50% of the local population bears evidence of ongoing mergers, and the canonical "relaxed" cluster is a relatively rare beast.

Nearly all interesting cosmological tests depend on accurate measurement of cluster virial masses. Observations of the intracluster medium (ICM) have shown promise in this regard: the ICM's high X–ray luminosity and large spatial extent make it possible to probe the content and structure of clusters in great detail. Bulk properties of the ICM such as luminosity, temperature, mass, and gas density profile shape have been found to display highly significant correlations with each other (Edge & Stewart 1991; David et al. 1993; Mohr & Evrard 1997; Mushotzky & Scharf 1997; Markevitch 1998; Allen & Fabian 1998; Mohr, Mathiesen & Evrard 1999; Arnaud & Evrard 1999). In contrast to the noisy correlations of early X–ray data (see Sarazin 1986 and references therein) many correlations now display scatter at the 10-20% level, indicating that a high degree of physical uniformity exists even in this structurally diverse population. Hydrodynamic simulations of cluster evolution predict tight relationships between observable quantities and between those quantities and the cluster binding mass (Evrard 1990; Kang et al. 1994; Navarro, Frenk & White 1995; Evrard et al. 1996; Bryan & Norman 1998), even when some members of the sample are far from dynamical equilibrium. The existence of both observed and theoretical correlations implies that the prevalence of cluster substructure is not a fundamental barrier to interpreting the properties of the population.

However, moderate biases caused by the presence of substructure are likely to be present, and we explore the role of substructure in temperature measurements of the ICM in this paper. A previous paper (Mathiesen, Evrard & Mohr 1999) demonstrated that ICM clumping leads to a modest (~ 15%) overestimate of ICM masses derived under the typical assumptions of spherical symmetry and isothermality. As the X–ray data improve, the limits of simplifying assumptions such as these become clearer. High-resolution X–ray images reveal secondary peaks and strong asphericities in many clusters and X–ray spectra indicate the presence of multiple temperature components within the cores of many clusters (Fabian et al. 1994, Holzapfel et al. 1997, Allen et al. 2000). The Chandra and XMM satellite missions will provide the most detailed maps of the ICM emission and temperature structure yet obtained, and will allow more precise definition of the limitations of the current models.

Three-dimensional hydrodynamical simulations of cluster formation can help bridge the gap between the new generation of data and traditional methods and results. While simulated clusters often do not include many processes thought to be important to ICM evolution (e.g. radiative cooling and galactic winds), they excel at the creation of populations with realistic merger histories (Mohr et al. 1995; Tsai & Buote 1996). Ensembles of simulated clusters can therefore be used to investigate the effects of accretion events, major mergers, clumping, and substructure on measurements of the ICM. In this paper, we analyze the spectral properties of an ensemble of 24 simulated clusters using a realistic plasma emission model and assuming a uniform metallicity 0.3 times the solar abundance. We find that even minor accretion events can significantly bias our measurements of the mean, mass-weighted cluster temperature, and that clusters undergoing a major merger can sometimes be identified as extreme examples of this bias.

Section 2 of this paper describes the simulations, the cluster ensemble, and the process of creating our spectral images. Section 3 discusses the various measures of cluster temperature which have seen frequent use and explores the relationships between them. In particular, we explore the relationship between spectrally determined temperatures and the mass-weighted mean temperature. The latter is found in simulations to follow most closely the virial relationship. Section 4 then delves into cluster dynamics, investigating the effects of a major merger on the ICM and looking for observable signatures of the merging process. Finally, section 5 summarizes our conclusions.