Thermodynamic evolution of the $z=1.75$ galaxy cluster IDCS J1426.5+3508
  We present resolved thermodynamic profiles out to 500 kpc, about $r_{500}$,
of the $z=1.75$ galaxy cluster IDCS J1426.5+3508 with 40 kpc resolution. Thanks
to the combination of Sunyaev-Zel'dovich and X-ray datasets, IDCS J1426.5+3508
becomes the most distant cluster with resolved thermodynamic profiles. These
are derived assuming a non-parametric pressure profile and a very flexible
model for the electron density profile. The shape of the pressure profile is
flatter than the universal pressure profile. The IDCS J1426.5+3508 temperature
profile is increasing radially out to 500 kpc. To identify the possible future
evolution of IDCS J1426.5+3508 , we compared it with its local descendants that
numerical simulations show to be $0.65\pm0.12$ dex more massive. We found no
evolution at 30 kpc, indicating a fine tuning between cooling and heating at
small radii. At $30<r<300$ kpc, our observations show that entropy and heat
must be deposited with little net gas transfer, while at 500 kpc the gas need
to be replaced by a large amount of cold, lower entropy gas, consistent with
theoretical expectation of a filamentary gas stream, which brings low entropy
gas to 500 kpc and energy at even smaller radii. At $r \gtrsim 400$ kpc the
polytropic index takes a low value, which indicates the presence of a large
amount of non-thermal pressure. Our work also introduces a new definition of
the evolutionary rate, which uses unscaled radii, unscaled thermodynamic
quantities, and different masses at different redshifts to compare ancestors
and descendants. It has the advantage of separating cluster evolution,
dependence on mass, pseudo-evolution and returns a number with unique
interpretation, unlike other definitions used in literature.
