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

We study an idealized one-dimensional model for the evolution of hot gas in dark matter haloes for redshifts z = [0, 6]. We introduce a numerical set-up incorporating cosmological accretion of gas, along with the growth of the halo, based on the Van den Bosch model for the average growth of haloes 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 towards the centre. A simple Bondi accretion model on to a central black hole is used to include feedback heating. The set-up captures some of the key characteristics of spherically symmetric accretion on to the haloes: formation of virial shocks slightly outside r₂₀₀ and long-term thermal balance in the form of cooling and heating cycles. The gas density outside our initial haloes 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 ∼10⁴ 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 ρ ∝ r^-2 are assumed.