We conduct two-dimensional hydrodynamical simulations of jets expanding in the intra-cluster medium ( ICM ) .
We find that for a fat , i.e .
more or less spherical , bubble attached to the center to be formed the jet should have high momentum flux and a large opening angle .
Typically , the half opening angle should be \alpha \gtrsim 50 ^ { \circ } , and the large momentum flux requires a jet speed of v _ { j } \sim 10 ^ { 4 } { ~ { } km } { ~ { } s } ^ { -1 } .
The inflation process involves vortices and local instabilities which mix some ICM with the hot bubble .
These results predict that most of the gas inside the bubble has a temperature of 3 \times 10 ^ { 8 } \lesssim T _ { b } \lesssim 3 \times 10 ^ { 9 } { ~ { } K } , and that large quantities of the cooling gas in cooling flow clusters are expelled back to the intra-cluster medium , and heated up .
The magnetic fields and relativistic electrons that produce the synchrotron radio emission might be formed in the shock wave of the jet .