tokens: described by a modified lognormal distribution (equation A7), whose parameters are given in Table 3 . The density PDF converges after the jet breaks out (jet head ≳ 3 kpc) and decouples from the ISM, proceeding along the cleared path. Figure 7. The evolution of the density PDF as the jet evolves with time and breaks out of the dense central region after a height of z ∼ 3 kpc. The density PDF converges after the jet breakout as the jet decouples from the ISM. Table 3. Coefficients of the fit to the density PDF in Fig. 7 following equation (A7). a Mean density for the PDF. b Standard deviation of variable ρ, which is related to the standard deviation in s = ln ρ as in equation (A8). c Volume-weighted mean of density for n > 10 cm −3 . This gives a measure of the mean density of the highdensity filaments. The duration of the flood-channel phase of the jet evolution depends on the mean density and filling factor of the ISM, as previously discussed in Wagner et al. ( 2012 ). Clouds with denser cores are less ablated and more efficiently impede the progress of the jet. In Fig. 8 , we present the density for Sim B (Table 2), where a jet of power 10 45 erg s −1 passes through a medium with a lower mean density ( n w 0 = 150 cm −3 ) compared to that of Sim A. We note that the jet breaks out of the warm dense gas much faster, in comparison to Sim A. Figure 8. Density {log [ n (cm −3 )]}in the x – z plane for Sim B. 4.2 Evolution of the energy bubble The confined jet creates a nearly homogeneous high-pressured energy bubble that sweeps through the ISM (see Fig. 6 ). The expanding bubble engulfs the dense filaments, driving shocks into them. The shocks become radiative, forming a skin of heated gas (∼10 5 K) surrounding the warm filaments at ∼10 4 K. The energy bubble also shears the filaments sweeping up the ablated gas to high velocities ≳1000 km s −1 . The dense filaments are themselves accelerated by the ram pressure from the bubble. However, the efficiency of acceleration depends on the density of the gas and injected mechanical power. For lower density (Sim B), the dense filaments are accelerated to speeds of ∼100 km s −1 , similar to earlier reported results of Wagner et al. ( 2012 ). In simulations with higher ISM density (Sim A) or lower jet power (Sim C and Sim D), the outward pressure from the bubble is not sufficient to overcome the inward gravitational acceleration. In Figs 10 and 11 , we show the evolution of the mean pressure inside the energy bubble and the volume of the bubble. Initially, the bubble pressure decreases more rapidly ( p ∼ t −1 ) than an adiabatic spherical bubble (with p ∼ t −0.8 ). This is likely the result of mixing with the ISM and cooling losses. Consistent with the lower pressure, the bubble expands less rapidly (volume ∼ t 1.5 ) than an adiabatic bubble (volume ∼ t 1.8 , see Appendix B). At later stages after the breakout from the confining dense ISM, the bubble expands more rapidly. 4.3 Evolution of the phase space
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