Gas Cooling in Hydrodynamic Simulations with An Exact Time Integration Scheme

We implement and test the exact time integration method proposed by Townsend 2009 for gas cooling in cosmological hydrodynamic simulations. The errors using this time integrator for the internal energy are limited by the resolution of the cooling tables and are insensitive to the size of the timestep, improving accuracy relative to explicit or implicit schemes when the cooling time is short. We compare results with different time integrators for gas cooling in cosmological hydrodynamic simulations. We find that the temperature of the gas in filaments before accreting into dark matter halos to form stars, obtained with the exact cooling integration, lies close to the equilibrium where radiative cooling balances heating from the UV background. For comparison, the gas temperature without the exact integrator shows substantial deviations from the equilibrium relation. Galaxy stellar masses with the exact cooling technique agree reasonably well, but are systematically lower than the results obtained by the other integration schemes, reducing the need for feedback to suppress star formation. Our implementation of the exact cooling technique is provided and can be easily incorporated into any hydrodynamic code.