Introducing the TNG-Cluster simulation: Overview and the physical properties of the gaseous intracluster medium

We introduce the new TNG-Cluster project, an addition to the IllustrisTNG suite of cosmological magnetohydrodynamical simulations of galaxy formation. Our objective is to significantly increase the statistical sampling of the most massive and rare objects in the Universe: galaxy clusters with log(M-200c/M-circle dot) greater than or similar to 14.3 - 15.4 at z = 0. To do so, we re-simulate 352 cluster regions drawn from a 1 Gpc volume that is 36 times larger than TNG300, keeping the IllustrisTNG physical model entirely fixed as well as the numerical resolution. This new sample of hundreds of massive galaxy clusters enables studies of the assembly of high-mass ellipticals and their supermassive black holes (SMBHs), brightest cluster galaxies (BCGs), satellite galaxy evolution and environmental processes, jellyfish galaxies, intracluster medium (ICM) properties, cooling and active galactic nuclei (AGN) feedback, mergers and relaxedness, magnetic field amplification, chemical enrichment, and the galaxy-halo connection at the high-mass end, with observables from the optical to radio synchrotron and the Sunyaev-Zeldovich (SZ) effect, to X-ray emission, as well as their cosmological applications. We present an overview of the simulation, the cluster sample, select comparisons to data, and a first look at the diversity and physical properties of our simulated clusters and their hot ICM.