Dynamical properties and detectability of the magneto-thermal instability in the intracluster medium

Context. Amongst many plasma processes potentially relevant to the dynamics of the intracluster medium (ICM), turbulence driven at observable scales by internal magnetised buoyancy instabilities like the magneto-thermal instability (MTI) stand out in the ICM outskirt, where the background temperature decreases with radius. Aims. We characterise the statistical properties of MTI turbulence and assess whether such magnetised dynamics would be detectable with the future X-ray calorimeter X-IFU onboard ATHENA. Methods. We make use of scaling laws derived by Perrone & Latter (2022a,b) to estimate the observable turbulent saturation levels and injection length of MTI turbulence for different ICM thermodynamic profiles, and perform a numerical MHD simulation of the dynamics with Braginskii heat and momentum diffusion. As a prospective exercise, we use the simulation to virtually observe MTI turbulence through the X-IFU. Results. In bright enough regions amenable to X-ray observations, the MTI drives mild turbulence up to $\sim$ 5% and $\sim$ 100 km/s (rms temperature fluctuation and velocity). However, the measurable integrated temperature fluctuation and line-of-sight velocity fields, which is essentially the azimuthal velocity component in cluster haloes, hardly exceed 1% and 10 km/s respectively. We show that such moderate signals would be hard to detect with upcoming X-ray telescopes. MTI turbulence is anisotropic in the direction of the gravity. If the fluctuation intensities were to be stronger than the current theoretical estimates, MTI fluctuations may be detectable and their anisotropy discernible with the X-IFU. Conclusions. Finding direct signatures of magnetised dynamics in the ICM, even at observable scales typical of the MTI, remains challenging. This study is a first step in this direction. Several numerical and observational strategies are discussed to make further progress.