Molecular Gas in the Galactic Center Region II. Gas mass and N(H_2)/I(^12CO) conversion based on a C^18O(J = 1 -> 0) Survey

The large scale structure and physics of molecular gas in the Galactic center region is discussed based on the analysis of a 9' resolution survey of the Galactic center region in the J=1->0 line of C^18O. Emphasis is placed on the comparison with ^12CO(1--0) data. The line shapes of C^18O(1--0) and ^12CO(1--0) differ significantly. The ratio of the intensities of the two isotopomers in the Galactic center region is generally higher than the value of ~15 expected from the ``Standard Conversion Factor'' (SCF) of ^12CO integrated line intensity to H_2 column density. In our data, this ratio is in the range from 30 to 200, mostly ~60 to 80. From LVG calculations, we estimate that the large scale ^12CO(1--0) emission in the Galactic center region is of moderate or low optical depth. Higher optical depths are restricted to very limited regions. We estimate H_2 densities and kinetic temperatures for different ranges of intensity ratios. A considerable amount of molecular mass is in a widespread molecular gas component with low densities and high kinetic temperatures. The total molecular mass is found to be (3^+2_-1) 10^7 M_{sun}. We show that the SCF is not valid toward the Galactic bulge. It overestimates the H_2 column density by an order of magnitude because the assumptions required for this factor are not fulfilled for a significant fraction of the molecular gas. Therefore, also one cannot apply a modified conversion factor to the Galactic center region since the N(H_2)/I(^12CO) ratio is highly variable and cannot be represented by a universal constant. Results from external galaxies indicate that the ^12CO emission is generally not a suitable tracer of H_2 masses in galactic bulges.