Galaxy clusters are the traces of the formation of the largest structures in the Universe and so reliable tools to investigate structures formation and evolution. In principle, this is possible only if and when we have full knowledge of the properties of these objects. The total mass (i.e. the total amount of the dark matter (DM), the intracluster medium (ICM), and the stellar components) is an invaluable quantity when exploring the abundances of clusters along the redshift: a standard way to infer cosmological parameters such as the mean matter density Ωm and the amplitude of matter perturbations σ8(Planck Collaboration XIII 2016). Furthermore, under the assumption of a simple self-similar model (Kaiser 1986; Voit 2005), we could derive the total mass of the clusters from a few observables in optical, X-ray, or millimetre band (Giodini et al. 2013). This approach results in a few scaling relations valuable when we are interested to obtain averaged results based on some statistics. However, it is prone to the assumed simplified approximations: hydrostatic equilibrium and isothermal and spherical distribution for DM and ICM (Bryan & Norman 1998). It is well known that the hydrostatic equilibrium in haloes is not always satisfied, due to non-thermal pressure contributions from internal motions and turbulence (see e.g. Fang, Humphrey & Buote 2009; Lau, Kravtsov & Nagai 2009; Laganá, de Souza & Keller 2010; Rasia et al. 2012; Nelson, Lau & Nagai 2014; Yu, Nelson & Nagai 2015; Biffi et al. 2016; Eckert et al. 2019; Angelinelli et al. 2020; Ansarifard et al. 2020; Gianfagna et al. 2020; Green et al. 2020), pointing out the impact that the dynamical state of those large gravitational bounded objects should have. Several attempts have been made to infer clusters dynamical state, using both observational data and simulations, by analysing the images of the emission in optical (see e.g. Ribeiro, Lopes & Rembold 2013; Wen & Han 2013) and in the X-ray band (see e.g. Rasia, Meneghetti & Ettori 2013; Lovisari et al. 2017; Nurgaliev et al. 2017; Bartalucci et al. 2019; Cao, Barnes & Vogelsberger 2020; Yuan & Han 2020) or of the diffusion of the cosmic microwave background (CMB) photons by thermal Sunyaev–Zel’dovich (tSZ) effect in the millimetre band (Cialone et al. 2018; De Luca et al. 2020, hereafter DL20), or a combination of some of them (see e.g. Mann & Ebeling 2012; Molnar, Ueda & Umetsu 2020; Ricci et al. 2020; The CHEX-MATE Collaboration 2020; Zenteno et al. 2020). Among the possibilities, we have to mention the studies of the clusters morphology in X-ray and tSZ maps. Several indicators are commonly used, such as asymmetry parameter (Schade et al. 1995), light concentration (Santos et al. 2008), third-order power ratio (Buote & Tsai 1995; Weißmann et al. 2013), centroid shift (Mohr, Fabricant & Geller 1993; O’Hara et al. 2006), strip parameter, Gaussian fit parameter (Cialone et al. 2018), and so on. They exploit the maps with different apertures and efficiencies and are applied individually or combined together, even with different weights (see e.g. Böhringer et al. 2010; Nurgaliev et al. 2013; Rasia et al. 2013; Weißmann et al. 2013; Mantz et al. 2015; Cui et al. 2016; Lovisari et al. 2017; Cialone et al. 2018; Cao et al. 2020; DL20; Yuan & Han 2020). A complementary approach is by applying thresholds on specific thermodynamic variables. Among the others, the central electron gas density and the core entropy are fairly reliable (Hudson et al. 2010). The azimuthal scatter in radial profiles of gas density, temperature, entropy, or surface brightness (Vazza et al. 2011) is also used as a proxy of the ICM inhomogeneities and correlated to the clusters dynamical state (see e.g. Roncarelli et al. 2013; Ansarifard et al. 2020). Alternatively, the projected sky separations between key positions in the images are resulting in reliable estimators of the dynamical state. Interestingly, the offsets between the bright central galaxy (BCG) and the peaks and/or the centroids of X-ray or tSZ maps are an indication of how much the relaxation condition is satisfied, with different efficiency (see e.g. Jones & Forman 1984; Katayama et al. 2003; Lin & Mohr 2004; Sanderson, Edge & Smith 2009; Mann & Ebeling 2012; Rossetti et al. 2016; Lopes et al. 2018; DL20; Ricci et al. 2020; Zenteno et al. 2020). To be mentioned also other approaches based on wavelets analysis (Pierre & Starck 1998), on the Minkowski functionals (Beisbart, Valdarnini & Buchert 2001), or on machine learning (see e.g. Cohn & Battaglia 2019; Green et al. 2019; Gupta & Reichardt 2020).
Citation: Lovisari et al. 2017
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Citation: Lovisari et al. 2017
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