the critical point in the phase diagram. The Jacobi matrix of equation (\[integ eq\]) around the critical point becomes infinite. Thus, there is no solution passing the critical point smoothly. In order to obtain infinite extent solution, shock front is required. Solutions with shock front are described in Appendix \[app:shock\]. We call this type of solutions “C-c” solution, where “C-c” means solutions connecting the CNM and the critical point.

[*C-C Solutions.*]{} For much larger mass flux case $j=1500j_\mathrm{ZP}$, since the solution passes the equilibrium curve before arriving at the critical point, the solution becomes the infinite extent solution connecting the CNM and CNM (see figure \[fig:large\_flux\_sonic\]). We call this type of solutions C-C solutions, where ‘C-C’ means solutions connecting the CNM and CNM.

![ Classification diagram of obtained solutions in parameter space $(P_\mathrm{c},j)$. The white dashed line corresponds to $j_\mathrm{ZP}$. The solid line indicates the critical mass flux $j_\mathrm{crit}(P_\mathrm{c})$. The black area where $|j|<|j_\mathrm{ZP}|$ is not focused in this paper. []{data-label="fig:sol_diag_lowpre"}](fig5.eps){width="8.0cm"}

Figure \[fig:sol\_diag\_lowpre\] shows classification of solutions in the parameter space $(P_\mathrm{c},j)$ for $P_\mathrm{min}<P_\mathrm{c}<P_\mathrm{max}$. The white dashed line corresponds to $j=j_\mathrm{ZP}(P_\mathrm{c})$ on which the ZP solutions exist. The black area where $|j|<|j_\mathrm{ZP}|$ is not focused in this paper. From figure 