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 \times 10 ^ { 9 } 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 .