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We present a detailed study of an estimator of the HI column density, basedon a combination of HI 21cm absorption and HI 21cm emission spectroscopy. This"isothermal" estimate is given by $N_{\rm HI,ISO} = 1.823 \times 10^{18} \int\left[ \tau_{\rm tot} \times {\rm T_B} \right] / \left[ 1 - e^{-\tau_{\rm tot}}\right] {\rm dV}$, where $\tau_{\rm tot}$ is the total HI 21cm optical depthalong the sightline and ${\rm T_B}$ is the measured brightness temperature. Wehave used a Monte Carlo simulation to quantify the accuracy of the isothermalestimate by comparing the derived $N_{\rm HI,ISO}$ with the true HI columndensity $N_{\rm HI}$. The simulation was carried out for a wide range ofsightlines, including gas in different temperature phases and random locationsalong the path. We find that the results are statistically insensitive to theassumed gas temperature distribution and the positions of different phasesalong the line of sight. The median value of the ratio of the true H{\sc i}column density to the isothermal estimate, $N_{\rm HI}/{N_{\rm HI, ISO}}$, iswithin a factor of 2 of unity while the 68.2% confidence intervals are within afactor of $\approx 3$ of unity, out to high HI column densities, $\le 5 \times10^{23}$\,cm$^{-2}$ per 1 km s$^{-1}$ channel, and high total optical depths,$\le 1000$. The isothermal estimator thus provides a significantly bettermeasure of the HI column density than other methods, within a factor of a fewof the true value even at the highest columns, and should allow us to directlyprobe the existence of high HI column density gas in the Milky Way.

Accurate measurement of the HI column density from HI 21cm absorption-emission spectroscopy