Results from hydrodynamical SPH simulations of galaxy clusters are used to investigate the dependence of the final cluster X-ray properties on the numerical resolution and the assumed models for the physical gas processes .
Two different spatially flat cosmological models have been considered : a low-density cold dark matter universe with a vacuum energy density \Omega _ { \Lambda } = 0.7 ( \Lambda CDM ) and a cold+hot dark matter model ( CHDM ) .
For each of these models two different clusters have been extracted from a cosmological N - body simulation .
A series of hydrodynamical simulations has then been performed for each of them using a TREESPH code .
These simulations first include radiative cooling and then also conversion of cold gas particles into stars ; because of supernova explosions these particles can release energy in the form of thermal energy to the surrounding intracluster gas .
For a specific treatment for the thermal state of the gas , simulation runs have been performed with different numerical resolutions .
This is in order to disentangle in the final results for the cluster profiles , the effects of the resolution from those due to the assumed model for the gas thermal evolution .
The numerical resolution of the simulation is controlled by the number of gas particles N _ { g } and the chosen value for the gas gravitational softening parameter \varepsilon _ { g } .
The latter is proportional to the minimum SPH smoothing length and therefore sets a maximum spatial resolution for the simulations .
For the cooling runs , final X-ray luminosities have been found to be diverging according to L _ { X } \propto 1 / \varepsilon _ { g } ^ { \sim 5 } .
The gas density profiles are also diverging at the cluster center .
This is in agreement with previous findings .
When cold gas particles are allowed to convert into stars , the divergences are removed .
The final gas profiles show a well defined core radius and the temperature profiles are nearly flat .
For the most massive test cluster in the \Lambda CDM model , these simulations show a prominent cooling flow in the cluster core .
This cluster was analyzed in detail , running simulations with different star formation methods and increasing numerical resolution .
A comparison between different runs shows that the results of simulations , based on star formation methods in which gas conversion into stars is controlled by an efficiency parameter c _ { \star } , are sensitive to the numerical resolution of the simulation .
In this respect star formation methods based instead on a local density threshold , as in Navarro and White ( 1993 ) , are shown to give more stable results .
Final X-ray luminosities are found to be numerically stable , with uncertainties of a factor \sim 2 .
These simulations are also in good agreement with observational data when the final results are compared with the observed star formation rate and the luminosity-temperature relation from cooling flow clusters .
Therefore I find that hydrodynamical simulations of cooling clusters can be used to give reliably predictions of the cluster X-ray properties .
For a given numerical resolution , the conversion of cool gas particles into stars as in Navarro and White should be preferred .