4 Data reduction

In order to reveal calibration problems, the ISO-SWS data have to be reduced in a homogeneous way. For all the stars in our sample, at least one AOT01 observation (AOT = Astronomical Observation Template; AOT01 = a single up-down scan for each aperture with four possible scan speeds at degraded resolution) is available, some stars have also been observed using the AOT06 mode (=long up-down scan at full instrumental resolution). Since these AOT01 observations form a complete and consistent set, they were used as the basis for the research. In order to check potential calibration problems, the AOT06 data are used. The scanner speed of the highest-quality AOT01 observations was 3 or 4, resulting in a resolving power $\simeq$870 or $\simeq$1500, respectively (Leech et al. 2002). The appropriate resolving power of each sub-band was taken to be the most conservative theoretical resolving power as determined by Lorente in Leech et al. (2002), with the exception being band 1A for which this value has been changed from 1500 to 1300, as will be discussed in Sect. 6.2.

The ISO-SWS data were processed to a calibrated spectrum by using the same procedure as described in Paper I using the calibration files available in OLP6.0.

The band 2 (Si:Ga) detectors used in SWS "remember'' their previous illumination history. Going from low to high illumination, or vice versa, results in detectors asymptotically reaching their new output value. These are referred to as memory effects or transients. For sources with fluxes greater than about 100 Jy, memory effects cause the up and down scans in the SPD (=Standard Processed Data) to differ in response by up to 20% in band 2. Since an adapted version of the Fouks-Schubert model to correct for these memory effects in band 2 was still in development (Leech et al. 2002), this method could not be applied during our reduction procedure. Instead, we have used the down-scan data of our observation as a reference to do a correction of the flux level of the first scan (up-scan). This is justified since the memory effects appear to be less severe in the down-scan measurements, suggesting a more stabilised response to the flux level for the down-scan data.

Also the band 2 dark current subtraction is closely tied to the band 2 memory effect correction. The memory effect for Si:Ga detectors as described by the Fouks-Schubert model is an additive effect. As such, its proper correction will take place during the dark current subtraction. Since this correction tool was still not available, all dark currents were checked individually. When a dark current was corrupted too much by memory effects, its value was replaced by the value of a preceding or following dark-current not being affected. In this way, a small error can occur, which is, however, negligible due to the high flux level of our stellar sources.

 

 

Table 3: Factors used to multiply the sub-bands for the highest-quality AOT01 observation (denoted by its revolution number) of the selected stars in our sample are given. For each band the wavelength range $\lambda _{\rm b}$ - $\lambda _{\rm e}$ (in $\mu$m) and the (constant) resolving power for a speed-4 AOT01 observation are also noted. For a speed-3 AOT01 observation one has to multiply the average resolving power by $\sim$0.58. In the last two columns the pointing offset as estimated from known imperfections in the satellite attitude control system is given in arcsec, where the y-axis denotes the cross-dispersion direction for SWS and the z-axis the dispersion direction.

	1A	1B	1D	1E	2A	2B	2C	rev.	dy	dz
$\lambda / \Delta \lambda$	1300	1200	1500	1000	1200	800	800
$\lambda _{\rm b}$ [$\mu$m]	2.38	2.60	3.02	3.52	4.08	5.30	7.00
$\lambda _{\rm e}$ [$\mu$m]	2.60	3.02	3.52	4.08	5.30	7.00	12.00
$\alpha$ Lyr	1.06	1.06	1.00	1.00	1.00	0.97	+12Jy	178	-0.608	-1.179
$\alpha$ CMa	1.00	1.00	1.00	0.995	1.12	1.23	1.00	689	0.034	0.003
$\beta$ Leo	0.99	0.99	1.00	1.00	1.16	1.27	+3.5Jy	189	0.478	0.556
$\alpha$ Car	0.97	0.98	1.00	1.00	0.98	1.10	0.91	729	0.024	0.072
$\alpha$ Cen A	1.01	1.02	1.00	1.01	0.985	1.06	0.91	607	0.000	0.000
$\delta$ Dra	0.97	0.98	1.00	1.015	1.03	1.02	1.10	206	-0.422	1.480
$\xi$ Dra	0.99	0.99	1.00	0.99	1.12	1.15	1.05	314	1.286	-0.282
$\alpha$ Boo	0.995	1.01	1.00	1.005	0.95	1.05	1.00	452	0.000	0.000
$\alpha$ Tuc	1.005	1.02	1.00	1.01	1.05	1.00	1.00	866	0.000	0.000
$\beta$ UMi	1.00	1.015	1.00	1.01	0.91	0.885	1.00	182	-1.062	0.045
$\gamma$ Dra	0.995	1.005	1.00	1.005	0.935	0.98	0.91	377	-0.304	0.181
$\alpha$ Tau	1.00	1.01	1.00	1.00	1.00	1.045	1.00	636	0.000	0.000
H Sco	1.00	1.015	1.00	1.00	1.13	1.05	1.15	847	0.000	0.000
$\beta$ And	1.00	1.00	1.00	1.005	1.00	1.10	0.95	795	0.000	0.000
$\alpha$ Cet	0.985	1.00	1.00	1.01	0.935	1.03	0.91	797	0.000	0.000
$\beta$ Peg	1.00	1.015	1.00	1.005	0.935	1.03	0.935	551	0.017	0.095

Since the different sub-band spectra can show jumps in flux at the band-edges, several sub-bands had to be multiplied by a small factor to construct a smooth spectrum. Three causes for the observed shift factors between different sub-bands of an observation and between different observations of a given stellar source can be reported: 1. pointing errors, 2. problems with the RSRF correction, and 3. a problematic dark current subtraction, from which the pointing errors are believed to have the largest impact. The pointing errors as well as the RSRF correction causes a decrease in flux by a gain factor, while the dark current subtraction can lower the flux level by an offset. As the effects of the pointing errors are estimated to have the biggest effect, and since the stars in our sample have a high flux level so that the dark current subtraction only plays a marginal role, the individual sub-bands were multiplied with a factor - rather than shifted with an offset - in order to obtain a smooth spectrum. These factors (see Table 3) were determined by using the overlap regions of the different sub-bands and by studying the other SWS observations. The band-1D data were taken as reference data, due to the absence of strong molecular absorption in this wavelength range which may cause a higher standard deviation in the bins obtained when rebinning the oversampled spectrum, and - most importantly - due to the low systematic errors in this band, caused by e.g. errors in the curve of the RSRF, detector noise, uncertainties in the conversion factors from $\mu$V/s to Jy, ... (Leech et al. 2002). Using the total absolute uncertainty values - which have accumulated factors from each of the calibration steps plus estimated contributions from processes which were unprobed or uncorrected - as given in Table 5.3 in Leech et al. (2002), the estimated 1 $\sigma$ uncertainty on these factors is 10%. As is clearly visible from Table 3, these factors do not show any trend with spectral type or flux-level. This is displayed in Fig. 1, where the band-border ratios between 1A-1B, 1B-1D and 1D-1E are plotted in function of the flux at 2.60, 3.02 and 3.52 $\mu$m respectively. For this plot, all the observations of the cool stars in our sample, discussed in the Appendix of Paper IV of this series, are used. In band 1, the band-border ratios of 1A-1B and 1D-1E are from bands within the same aperture. Going from band 1B to band 1D, the aperture changes. Satellite mispointings can have a pernicious impact on this band-border ratio: the mean deviation of the band-border ratios w.r.t. 1 is significantly larger for 1B-1D (=0.015) than for 1A-1B and 1D-1E (being respectively 0.009 and 0.005). Due to the problems with memory effects in band 2 (4.08-12 $\mu$m), the factors of each sub-band of band 2 were determined by use of the corresponding spectral data of Cohen (Cohen et al. 1992, 1995, 1996; Witteborn et al. 1999): for Vega and Sirius Cohen has constructed a calibrated model spectrum; a composite spectrum (i.e. various observed spectra have been spliced to each other using photometric data) is available for $\alpha$ Cen A, $\alpha$ Boo, $\gamma$ Dra, $\alpha$ Tau, $\beta$ And, $\alpha$ Cet, and $\beta$ Peg; a template spectrum (i.e. a spectrum made by using photometric data of the star itself and the shape of a "template'' star) is built for $\delta$ Dra (template: $\beta$ Gem: K0 III), $\xi$ Dra (template: $\alpha$ Boo: K2 IIIp), $\alpha$ Tuc (template: $\alpha$ Hya: K3 II-III) and H Sco (template: $\alpha$ Tau: K5 III). When no template was available (for $\beta$ Leo, $\alpha$ Car and $\beta$ UMi), the synthetic spectrum showing the best agreement with the band-1 data was used as reference. This does not imply that we are trapped in a circular argument, since the stellar parameters for the synthetic spectrum were determined from the band-1 data only. Moreover, the maximum difference in the correction factors for band 2 obtained when using the synthetic spectra instead of a Cohen template for the 13 stars common in the sample is 7%, which is well within the photometric absolute flux uncertainties claimed by Leech et al. (2002). Note that all shift factors are in within the AOT01 band border ratios as derived in Figs. 5.33 and 5.34 in Leech et al. (2002). Using the overlap regions in band 2 can have quite a big effect on the final composed spectrum: focussing on $\beta$ UMi, we note that by using these overlap regions band 2A (and consequently bands 2B and 2C) should be shifted downwards by a factor 1.04; in order then to match the shifted band 2B and band 2C, band 2C should be once more shifted downwards by a factor 1.12. In general, the error in the absolute flux could increase to $\sim$20% at the end of band 2C when this method would be used.

For a more elaborate discussion on the SWS error budget, we would like to refer to Leech et al. (2002).

Figure 1: Flux ratios between the different sub-bands of band 1 at the wavelengths of overlap. The mean deviation w.r.t. 1 is given for the different band borders at the right corner of the figure.