# Gas Cooling in Hydrodynamic Simulations with An Exact Time Integration Scheme

## TL;DR

This paper implements and tests an exact time integration method for gas cooling in cosmological simulations, demonstrating improved accuracy and more realistic gas temperature and star formation results compared to traditional schemes.

## Contribution

The authors adapt Townsend's exact cooling integration method for cosmological hydrodynamics, showing it enhances accuracy and reduces the need for feedback in galaxy formation models.

## Key findings

- Gas temperature near equilibrium with radiative cooling and UV heating is accurately captured.
- The exact integrator produces systematically lower stellar masses, reducing feedback dependence.
- Errors are limited by cooling table resolution and are insensitive to timestep size.

## Abstract

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.