High Resolution Model

In order to determine the column density of $^{18}$OH in each absorbing cloud along the line of sight, the same method as used for $^{16}$OH was applied to the line. The resulting column densities and optical depths are shown in Table 7.6. For $^{18}$OH, the hyperfine structure did not affect the final line fit and column density found, so parameters averaged across the unresolved hyperfine transitions were used. In a similar way to the $^{16}$OH fit there were two components found with optical depth consistent with zero ($+31.4$ km s$^{-1}$ and $-51.9$ km s$^{-1}$), showing that they were not necessary to reproduce the line shape. Also, the errors on the components at $-44.04$ km s$^{-1}$ and $+52.78$ km s$^{-1}$ were very large (i.e. large changes in these components could be compensated for in the final line shape by small changes in the others). As with $^{16}$OH it is probably best to group the features with a similar galactocentric distance rather than results from individual clouds.

Figure 7.8: Co-added L03 data from the two $\Lambda$-doublet components of the $^{18}$OH $J=5/2\leftarrow 3/2$ transition. The data were binned at 1/4 resolution element and the errors represent the combined statistical and systematic uncertainty in each bin (see Chapter 5). The best fit model accounting for absorbing clouds in the line of sight is shown.

Table 7.6: Final parameters from the fit carried out to the co-added L03 spectrum of $^{18}$OH. Where errors are not shown they were too large to determine accurately (see text).

Velocity$^{(a)}$	FWHM$^{(a)}$	$\tau_{0}$	$N(\mathrm{OH})$	Identification
(km s$^{-1}$)	(km s$^{-1}$)		($10^{13}$ cm$^{-2}$)	(see Chapter 2)
$-107.6\pm1.9$	6.6$\pm$4.0	$0.07\pm0.05$	$0.7\pm0.6$	$<$1 kpc
$-81.7\pm4.2$	28.0$\pm$12.0	$0.05\pm0.01$	$2.0\pm1.0$	$<$1 kpc
$-51.9\pm5.7$	17.2$\pm$5.2	0.0001	0.003	?3-4 kpc arm
$-44.04\pm0.55$	7.5$\pm$2.4	0.044	0.5	3-4 kpc arm
$-24.39\pm0.81$	13.7$\pm$1.9	$0.10\pm0.03$	$2.1\pm0.7$	4.5-5 kpc arm
$+1.1\pm0.44$	18.7$\pm$1.2	$0.03\pm0.02$	$1.0\pm0.6$	local + Sgr B2
$+15.71\pm0.32$	7.3$\pm$1.0	$0.16\pm0.07$	$1.7\pm0.8$	?local
$+31.4\pm3.6$	20.7$\pm$13.9	0.0003	0.009	?Scutum arm
$+52.78\pm0.85$	11.1$\pm$2.4	0.019	0.3	Sgr B2
$+66.72\pm0.52$	16.2$\pm$1.0	$0.39\pm0.06$	$9.5\pm1.6$	Sgr B2

$(a)$ Gaussian fit parameters from Garwood & Dickey (1989)

The total column density of $^{18}$OH over the whole line of sight in this fit was 1.8$\times10^{14}$ cm$^{-2}$ with an error of approximately 0.2$\times10^{14}$ cm$^{-2}$. This is marginally consistent with the column density found by Lugten et al. (1986) of $\geq2\times10^{14}$ cm$^{-2}$. The column density in the fit for Sgr B2 itself was found to be $(9.8\pm1.6)\times10^{13}$ cm$^{-2}$ which is close to the value for Sgr B2 derived by Goicoechea & Cernicharo (2002) of $(6\pm2)\times10^{13}$ cm$^{-2}$. The final fit is shown in Figure 7.8. There appears to be some extra absorption at velocities greater than $+65$ km s$^{-1}$ which is not accounted for by the model (this is different to the discrepancy between components in Figure 7.7). This may be real but cannot be fitted because the HI measurements of Garwood & Dickey (1989) did not cover velocities above $+100$ km s$^{-1}$. In the fitting process, velocities above 88 km s$^{-1}$ were ignored for the calculation of $\chi ^{2}$ so that this extra absorption did not affect the velocity shift found by the fit. The errors on the final column densities were determined in the same way as for $^{16}$OH by examining the change in $\chi ^{2}$ when pairs of neighbouring optical depths were varied.

Table 7.7: Calculated $^{16}$OH/$^{18}$OH for each group of absorbing clouds in the line of sight using column densities given in Tables 7.6 and 7.3 (the Sgr B2 value was calculated from the $^{16}$OH fit carried out to the 53 $\mu$m line on its own).

Feature	Distance from Galactic Centre	$^{16}$OH/$^{18}$OH
	(kpc)
Galactic bar	$<$1	$370\pm220$
3-4 kpc arm	3.5	940$^{(a)}$
4.5-5 kpc arm	4.7	$220\pm90$
Local	8.5	$570\pm250$
Sgr B2	0.1	$390\pm140$

$(a)$ the error is at least 100% for this component.