for the material residing in the outer regions, e.g., in the Homunculus and in the ISM, the same value as P09 used.

The three column density components and the total column density are plotted in Fig. \[fig:NH\]. The column density toward the hot component based on the spectrum above $5 \keV$, $N_H[>5 \keV]$, from H07 is also plotted.

Our model reproduces to within a factor of two the results of H07, and is with agreement with its qualitative behavior. This is done without any parameters fitting. Namely, we simply take the values of the different parameters as in our previous papers, where some parameters were adjusted to fit other observations of $\eta$ Car, such as the radio emission, some helium lines, and more.

Our results clearly shows that from our preferred line of sight ($\omega=90^\circ$,$i=42^\circ$) the column density hardly changes during most of the orbital cycle and can supply the required high column density, in accord with observations. When the system approaches periastron passage there is a fast increase of $N_{H,\rm{shock}}$ and $N_{Hi1}$, followed by a decrease after periastron passage.

One thing must be kept in mind. The ten-week X-ray minimum cannot be explained by the model. A different ingredient 