To define a framework for the formation and evolution of the cooling cores in X-ray galaxy clusters , we study how the physical properties change as function of the cosmic time in the inner regions of a 4 keV and 8 keV galaxy cluster under the action of radiative cooling and gravity only .
The cooling radius , R _ { cool } , defined as the radius at which the cooling time equals the Universe age at given redshift , evolves from \sim 0.01 R _ { 200 } at z > 2 , where the structures begin their evolution , to \sim 0.05 R _ { 200 } at z = 0 .
The values measured at 0.01 R _ { 200 } show an increase of about 15-20 per cent per Gyr in the gas density and surface brightness and a decrease with a mean rate of 10 per cent per Gyr in the gas temperature .
The emission-weighted temperature diminishes by about 25 per cent and the bolometric X-ray luminosity rises by a factor \sim 2 after 10 Gyrs when all the cluster emission is considered in the computation .
On the contrary , when the core region within 0.15 R _ { 500 } is excluded , the gas temperature value does not change and the X-ray luminosity varies by 10 - 20 per cent only .
The cooling time and gas entropy radial profiles are well represented by power-law functions , t _ { cool } = t _ { 0 } + t _ { 0.01 } ( r / 0.01 R _ { 200 } ) ^ { \gamma } and K = K _ { 0 } + K _ { 0.1 } ( r / 0.1 R _ { 200 } ) ^ { \alpha } , with t _ { 0 } and K _ { 0 } that decrease with time from 13.4 Gyrs and 270 keV cm ^ { 2 } in the hot system ( 8.6 Gyr and 120 keV cm ^ { 2 } in the cool one ) and reach zero after about 8 ( 3 ) Gyrs .
The slopes vary slightly with the age , with \gamma \approx 1.3 and \alpha \approx 1.1 .
The behaviour of the inner slopes of the gas temperature and density profiles are the most sensitive and unambiguous tracers of an evolving cooling core .
Their values after 10 Gyrs of radiative losses , T _ { gas } \propto r ^ { 0.4 } and n _ { gas } \propto r ^ { -1.2 } , are remarkably in agreement with the observational constraints available for nearby X-ray luminous cooling core clusters .
Because our simulations do not consider any AGN heating , they imply that the feedback process does not greatly alter the gas density and temperature profiles as generated by radiative cooling alone .