Do cooling and heating functions actually exist?
  Cooling and heating functions describe how radiative processes impact the
thermal state of the gas as a function of its temperature and other physical
properties. In a most general case they depend on the detailed distributions of
level populations of numerous ionic species and on the radiation spectrum.
Hence, these functions may vary on a very wide range of spatial and temporal
scales. In this paper, we explore cooling and heating functions between $5\leq
z \leq10$ in simulated galaxies from the Cosmic Reionization On Computers
(CROC) project. We find that the actual cooling (heating) rates experienced by
the gas at different temperatures in the simulations do not correspond to any
single cooling (heating) function. Gas about $T \gtrsim 10^{4}$ K has
sufficiently different combinations of density, metallicity, and
photoionization rates than colder gas such that, if the hot gas were suddenly
cooler, it would still cool and heat more efficiently than $T \lesssim 10^{4}$
K gas. In other words, the thermodynamics of the gas in the simulations cannot
be described by a single set of a cooling plus a heating function that could be
computed with common tools, such as Cloudy.
