dotted line), 3000(the dot-dashed line). The CNM pressure is set to $P_\mathrm{c}=3000k_\mathrm{B}$ K cm$^{-3}$. The filled circle shows the state at $x=\infty$. []{data-label="fig:large_flux"}](fig3.eps){width="8.0cm"}

![ Trajectories of solutions for $j/j_\mathrm{ZP}=300$(the solid line), 500(the dashed line), 1000(the dotted line), 1500(the dot-dashed line). The CNM pressure is set to $P_\mathrm{c}=4000k_\mathrm{B}$ K cm$^{-3}$. The filled circle shows the state at $x=\infty$. []{data-label="fig:large_flux_sonic"}](fig4.eps){width="8.0cm"}

[*C-c Solutions.*]{} Figure \[fig:large\_flux\_sonic\] shows the solutions for $j/j_\mathrm{ZP}=300$, 500, 1000, and 1500. Here, we set $P_\mathrm{c}/k_\mathrm{B}=4000$ K cm$^{-3}$. The corresponding mass flux is $j_\mathrm{ZP}=-2.15\times10^{-2}m_\mathrm{H}$ km s$^{-1}$. The solution for $j=300j_\mathrm{ZP}$ belongs to the C-U solution. For larger mass flux $j=500j_\mathrm{ZP}$, the solution truncates at a certain point before arriving at the equilibrium state. This critical point corresponds to $T=T_\mathrm{crit}=M^2/(4{\cal R}j^2)$ above which solutions do not exist (see equation (\[rho\])-(\[P\])). The physical variables at the critical point is denoted by using the subscript of ‘crit’. From equations (\[const\]) and (\[const mom\]), the condition $T=T_\mathrm{crit}$ is equivalent to $$|v_\mathrm{crit}| = \sqrt{P_\mathrm{crit}/\rho_\mathrm{crit}}.
        \label{vcrit}$$ Note that equation (\[vcrit\]) is slightly smaller than the adiabatic sound speed $\sqrt{\gamma P_\mathrm{crit}
/\rho_\mathrm{crit}}$. These critical velocity and temperature are also seen in the steady state structure of the shock front with heat conduction without physical viscosity [^2][@ZR67]. At the 