A 1-dimensional hydrodynamic model for accretion, cooling and heating of
  gas in dark matter halos from $z=6$ to $z=0$
  We study an idealized 1D model for the evolution of hot gas in dark matter
halos for redshifts $z=[0,6]$. We introduce a numerical setup incorporating
cosmological accretion of gas, along with the growth of the halo, based on the
Van den Bosch model for the average growth of halos as a function of cosmic
time. We evolve one-dimensional Lagrangian shells with radiative cooling of the
gas and heating due to feedback from the gas cooling and moving in toward the
center. A simple Bondi accretion model on to a central black hole is used to
include feedback heating. The setup captures some of the key characteristics of
spherically symmetric accretion onto the halos: formation of virial shocks
slightly outside $r_{200}$ and long-term thermal balance in the form of cooling
and heating cycles. The gas density outside our initial halos at $z=6$ is
constrained by requiring that the baryon fraction within the virial radius for
non-radiative evolution be equal to the universal value at almost all times.
The total mass in the cold phase (taken to be $\sim 10^4$ K) within $40$ kpc is
tracked as a function of the halo mass and redshift. We compare the evolution
of the cold gas mass to the observed stellar-mass versus halo mass relations,
following which, we can constrain the feedback energy required for different
halo masses and redshifts. We also compare and match the hot gas density and
temperature profiles for our most massive halo to those of clusters observed
upto redshift $2$. Our model is thus an improvement over the semi-analytic
models in which isothermal condition and $\rho \propto r^{-2}$ are assumed.
