Thermal conduction has been suggested as a possible mechanism by which sufficient energy is supplied to the central regions of galaxy clusters to balance the effect of radiative cooling. Recent high resolution observations of the nearby Virgo cluster make it an ideal subject for an attempt to reproduce the properties of the cluster by numerical simulations, since most of the defining parameters are comparatively well known. Here we present the results of a simulated high-resolution, 3-d Virgo cluster for different values of thermal conductivity (1, 1/10, 1/100, 0 times the full Spitzer value). Starting from an initially isothermal cluster atmosphere we allow the cluster to evolve freely over timescales of roughly 1.3?4.7×109 yrs. Our results show that thermal conductivity at the Spitzer value can increase the central ICM radiative cooling time by a factor of roughly 3.6. In addition, for larger values of thermal conductvity the simulated temperature and density profiles match the observations significantly better than for the lower values. However, no physically meaningful value of thermal conductivity was able to postpone the cooling catastrophe (characterised by a rapid increase in the central density) for longer than a fraction of the Hubble time nor explain the absence of a strong cooling flow in the Virgo cluster today. We also calculate the effective adiabatic index of the cluster gas for both simulation and observational data and compare the values with theoretical expectations. Using this method it appears that the Virgo cluster is being heated in the cluster centre by a mechanism other than thermal conductivity. Based on this and our simulations it is also likely that the thermal conductvity is suppressed by a factor of at least 10 and probably more. Thus, we suggest that thermal conductvity, if present at all, has the effect of slowing down the evolution of the ICM, by radiative cooling, but only by a factor of a few
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