A general framework to test gravity using galaxy clusters VI: Realistic
  galaxy formation simulations to study clusters in modified gravity
  We present a retuning of the IllustrisTNG baryonic physics model which can be
used to run large-box realistic cosmological simulations with a lower
resolution. This new model employs a lowered gas density threshold for star
formation and reduced energy releases by stellar and black hole feedback. These
changes ensure that our simulations can produce sufficient star formation to
closely match the observed stellar and gas properties of galaxies and galaxy
clusters, despite having $\sim160$ times lower mass resolution than the
simulations used to tune the fiducial IllustrisTNG model. Using the retuned
model, we have simulated Hu-Sawicki $f(R)$ gravity within a $301.75h^{-1}{\rm
Mpc}$ box. This is, to date, the largest simulation that incorporates both
screened modified gravity and full baryonic physics, offering a large sample
($\sim500$) of galaxy clusters. We have reanalysed the effects of the $f(R)$
fifth force on the scaling relations between the cluster mass and four
observable proxies: the mass-weighted gas temperature, the Compton
$Y$-parameter of the thermal Sunyaev-Zel'dovich effect, the X-ray analogue of
the $Y$-parameter, and the X-ray luminosity. We show that a set of mappings
between the $f(R)$ scaling relations and their $\Lambda$CDM counterpart, which
have been tested in a previous work using a much smaller cosmological volume,
are accurate to within a few percent for the $Y$-parameters and $\lesssim7\%$
for the gas temperature for cluster-sized haloes ($10^{14}M_{\odot}\lesssim
M_{500}\lesssim10^{15}M_{\odot}$). These mappings will be important for
unbiased constraints of gravity using the data from ongoing and upcoming
cluster surveys.
