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We study an idealized 1D model for the evolution of hot gas in dark matterhalos for redshifts $z=[0,6]$. We introduce a numerical setup incorporatingcosmological accretion of gas, along with the growth of the halo, based on theVan den Bosch model for the average growth of halos as a function of cosmictime. We evolve one-dimensional Lagrangian shells with radiative cooling of thegas and heating due to feedback from the gas cooling and moving in toward thecenter. A simple Bondi accretion model on to a central black hole is used toinclude feedback heating. The setup captures some of the key characteristics ofspherically symmetric accretion onto the halos: formation of virial shocksslightly outside $r_{200}$ and long-term thermal balance in the form of coolingand heating cycles. The gas density outside our initial halos at $z=6$ isconstrained by requiring that the baryon fraction within the virial radius fornon-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 istracked as a function of the halo mass and redshift. We compare the evolutionof the cold gas mass to the observed stellar-mass versus halo mass relations,following which, we can constrain the feedback energy required for differenthalo masses and redshifts. We also compare and match the hot gas density andtemperature profiles for our most massive halo to those of clusters observedupto redshift $2$. Our model is thus an improvement over the semi-analyticmodels in which isothermal condition and $\rho \propto r^{-2}$ are assumed.

A 1-dimensional hydrodynamic model for accretion, cooling and heating of gas in dark matter halos from $z=6$ to $z=0$