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The steady state of free jets are considered in the phase space, composed of pressure $p$, density $\rho$, and the ratio of velocity angle from the axis over radial distance $A$, where trajectories of fluids in a jet form a leaf structure. To simpify the problem, elementary thermal processes of cooling and heating are assumed. Cooling is due to free-free emission and heating depends only on density in the power law of $\rho^n$. The state of the jet is characterised by three parameters: Mach number $M_0$, effective coefficients of cooling $c_0$ and heating $h_0$, which are normalized quantities at the orifice. The numerical calculations are performed mainly for the case of $M_0=10$, by using the characteristic method in axially symmetric configuration. In the adiabatic case of $c_0=h_0=0$, the free jet expands at the rate of the asymptotically saturated magnitude of $A$, which is proportional to $M_0$. On-the-other-hand, in the case where cooling is in action, the pressure is affected to decrease. However, the density does not change much.
When heating is effective to halt the pressure and temperature decreasing, the difference of power $n$ on heating brings the following features.
1) The case of $n<0.5$: A thermal instability is seen on the axial region of jets where the parameters $c_0$ and $h_0$ satisfy the restricted condition. This is the bifurcation phenomena of structural stability occuring at the critical pin-point in the phase space. In the unstable region, density is growing, but pressure and temperature are decreasing. On the other side, the temperature is rising in the outer rarefied region.
2) The case of $n>0.5$: The jets are quite stable. Slender jets are formed under the restricted condition; e.g. $h_0 < 0.3 c_0$, in the case of $n=1$, where both of the inner and outer regions keep a constant temperature.
Investigations on the above phase space help us to construct models for various types of astrophysical jets such as Cyg A and 3C273.
