SWS Observations of H$_2$ Rotational Lines

The absence of dipole rotational and vibrational transitions in H$_2$ means that it must be observed via its weak quadrupole lines. As both nuclei are identical, only one combination of nuclear spins is possible for each rotational level (for a review of H$_2$ properties see Shull & Beckwith, 1982) and so the selection rule for transitions in the ground vibrational state is $\Delta J=\pm2$, where $J$ is the total angular momentum quantum number. In levels with odd $J$, H$_2$ has a nuclear triplet state and the statistical weight of each level is given by $g=3(2J+1)$. For levels with even $J$, it has a nuclear singlet state with $g=(2J+1)$. The triplet state is known as ortho-H$_2$ and the singlet state as para-H$_2$. Transitions between levels within each state occur between 3 and 28 $\mu$m. These have small probabilities for spontaneous transition which means that opacities are small even in lines of sight through dense clouds. Many such H$_{2}$ ro-vibrational lines have been observed in emission towards the Orion Peak 1 outflow using the ISO Short Wavelength Spectrometer (SWS) (Rosenthal et al., 2000). These were used to determine the excitation conditions in the outflow and to determine the total column density of warm H$_{2}$ for comparison with HD measurements (Ramsay Howat et al., 2002; Bertoldi et al., 1999).

The ISO SWS was used to observe Sgr B2 in its SWS06 mode over the range 2.4-45 $\mu$m. This mode used the SWS grating to observe wide ranges in wavelength (Leech et al., 2002). The observation carried out on 1996 August 30 (TDT 28702002) was downloaded from the ISO Data Archive^F.1. Calibration was carried out with the SWS OLP pipeline version 10. The only interactive calibration applied in addition to this was the removal of glitches using ISAP (further interactive calibration would have improved the quality of the data but based on the results obtained this was not justified - see below). The SWS resolving power over this range varied between 900 and 2800 for extended sources (Lutz et al., 2000) and this is lower than the theoretical resolution obtained for point sources (Valentijn et al., 1996). The SWS beam was centred at $\alpha=17^{\mathrm{h}}47^{\mathrm{m}}21.80^{\mathrm{s}}$, $\delta=-28\hbox{$^\circ$}23\hbox{$^\prime$}14.0\hbox{$^{\prime\prime}$}$ (J2000) with aperture sizes given in Table 6.2.

The continuum spectrum of Sgr B2 falls sharply over the range 45 $\mu$m to 20 $\mu$m and at wavelengths shorter than 20 $\mu$m the flux is consistent with zero at the signal to noise in the SWS06 spectrum. However, the two lowest energy H$_2$ lines were detected in emission. For most practical purposes it is adequate to assume that the SWS instrumental profile has a Gaussian shape with FWHM equal to the resolution element (Lutz et al., 2000) and so each detected line was fitted with a Gaussian of fixed width using the ISAP line fitting routine. The final flux values are shown in Table 6.2. Detection limits (2$\sigma$) for a further two lines were determined in the same way as for the HD 56 $\mu$m line. The S(0) 28 $\mu$m line was observed in both SWS bands 3E and 4 with a difference of approximately a factor of two between the continuum in each. This may be due to the extended nature of the source as the SWS calibration was only strictly applicable to point sources. A correction was not applied to account for this effect and a final value for the flux in the line was obtained by averaging the two measurements weighted by their statistical and systematic errors. The error in the fluxes given in Table 6.2 was determined from the fit. Further systematic errors in the flux in each band are given in the SWS Handbook (Leech et al., 2002) and are in the range 10-23% for point sources.

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