Subsections

• 3.1 RSRF Change
• 3.2 Absolute Flux Calibration Change

3. Analysis

We have analyzed the systematic differences described, and have tried to disentangle systematic RSRF and flux calibration problems, systematic differences introduced by the post-pipeline processing of the data by the STARTYPE group (e.g. splicing together of the bands) and systematic memory effects that look the same on many of the sources used to produce Figure 1. It is clear that any update to the SWS calibration should avoid to correct for the latter two.

Based on the analysis in the following sections, we conclude that there is indeed room for improvement in the RSRF calibration of bands 2A and 2C and in the absolute flux calibration of band 2A.

3.1 RSRF Change

The Relative Spectral Response Function (RSRF) corrects for the different response at any wavelength within an AOT band to the response at the key wavelength of the band [8]. The base RSRF was observed in the laboratory (ILT data) with a fully extended absolutely calibrated black body. Inflight, a series of measurements were made on standard stars for which models and/or composites are available. This revealed important deficiencies in the RSRF as determined in the laboratory. The small-scale accuracy of the ILT RSRF in band 2 is limited by instrumental fringing, less resolved in the ILT RSRF measurements of an extended black body source in the lab than in in-orbit observations of point sources. This inaccuracy however is confined to about 1% in band 2. This is better than the accuracy any in-orbit observation and/or model, composite or template can yield.

The broad-band accuracy of the ILT RSRF is much worse. When we calibrate SWS observations of stellar standards with the ILT RSRF and compare the spectra to synthetic spectra, composites or templates, we see broadband differences of up to 40%. The reasons for this are uncertainties and drifts in the black-body temperature in the lab, laboratory setup filter leaks, etc. It is this deficiency in the ILT RSRF that we correct for based on in-orbit observations.

We determine a continuous, broad-band correction curve to multiply the ILT RSRF with. This guarantees that we keep the high frequency uncertainty of the RSRF as low as the 1% in the ILT RSRF while improving the RSRF broad-band accuracy to the limit imposed by the in-orbit observation noise and the model spectrum or composite uncertainties. Since the RSRF is different for every detector in every AOT-band, we need to determine these corrections separately per band and per detector.

If all models were perfect, and all the SWS observations of calibration stars were perfect (i.e. no noise. no pointing errors, no memory effects, etc), the division of the model by the SWS-observation calibrated with the ILT RSRF would be exactly the same for every calibration star. Figures 2-4 show that this is not the case. We show the SWS data from one detector for a selection of calibration stars divided by the flux densities expected from the corresponding synthetic spectrum (from now on, we refer to these divisions as 'residues').

The spread in the residues in band 2C (figure 2) amounts to about 10%-40%. In figure 2 we have plotted the residues of early-type and late-type stars separately. This shows a clear difference in the residues of stars later than K0 and earlier typesr:. in the SiO band region the residues of cool sources show a kink that goes 4% below and 4% above the hot star residues. This systematic difference is to a large extent caused by the less reliable depth of the SiO band in the synthetic spectra of the cool sources. For the OLP10 calibration, the correction curve (a smoothing spline, for details see Vandenbussche et al. 2001), was based on all the calibration sources. It is clear that here we gain RSRF accuracy when using the hot stars only. However, the noise in the residues at the red end of the band makes it important to have a large number of observations to get an acceptable accuracy in the correction for e.g. the 10 and 11 m features. We therefore use the hot sources (as listed above) only for the wavelength region till 9.8 m. For the rest of the band, we have kept the OLP 10 correction for the ILT RSRF. To avoid artifacts at 9.8 m we have imposed a continuity criterion in the second derivative of the last spline segment of the new correction spline for the blue end. The result can be seen in Figure 2 where the black curve is the correction curve determined to obtain cal25_2c_060. The calibration sources, observations and models used are the following :

Source	Type	Observation	Model
Sirius HR2491	A1 V	68901202	hr2491_m_ldecin
Vega HR7001	A0 V	17800601	hr7001_m_ldecin
Car HR2326	F0 II	72902207	hr2326_m_ldecin
Cen A	G2 V	60702006	alp-cen_m_ldecin
Dra HR7310	G9 III	20601232	hr7310_m_ldecin

Figure 2: Band 2C - det 18 : the residues (SED/SWS observation with ILT RSRF) for stars earlier than G9 (blue) and later than G9 (red). The black curve shows the correction smoothing spline used to obtain cal25_2c_060.

Figure 3: Band 2A - det 18 : the residues (SED/SWS observation with ILT RSRF) for stars earlier than G9 (blue) and later than G9 (red). The black curve shows the correction smoothing spline used to obtain cal25_2a_060.

Figure 3 shows the residues in band 2A of calibration stars cooler than G9 (red) and earlier than G9 (blue). In the wavelength region of the CO fundamental band there is a systematic difference between the hot and the cool star residues. It is clear that the SEDs of the K and M giants are less accurate in this wavelength region. These are also the sources which show the most discrepancy between the MARCS models and the Cohen composites and templates. The general correction applied to the ILT data RSRF is upto 40% for band 2A but there is still a clear difference of a few % between the hot star sample and the cool star sample. We confirm that we can improve the accuracy of the RSRF correction by a few percent if we correct for the hot star residues only. The black curve in figure 3 shows the correction curve determined for detector 18.

Figure 4 shows the residues for detector 18 in band 2B. No significant difference is seen between hot and cool stars, so we have not produced a new RSRF based on hot sources only.

3.2 Absolute Flux Calibration Change

The absolute flux calibration at the key wavelength shows a difference only for band 2A when calibrating purely against the hot stars (4%). For bands 2B and 2C no significant differences were found in the signal-to-flux ratios with respect to the OLP10 calibration. The three time dependent cal42 (114, 214, and 314) files have been updated accordingly.

We note here that SWS AOT bands are notoriously difficult to match at their overlap regions. There are two main reasons why the bands do not naturally line up. Slight satellite mis-pointings, on the order of 1.5", are enough to introduce uncertainties of 4% in absolute photometry of bands between 1A and 2C. Mis-pointings also make the relative photometry uncertain by 4% between AOT bands of different apertures (bands 1B-1D, 1E-2A, 2B-2C and 2C-3A). Secondly, a more elusive cause for band mis-matches is detector memory effects which can have significant influence on the band 2 overlap regions (bands 1E-2A, 2A-2B, 2B-2C and 2C-3A).

Figure 4: Band 2B - det 18 : the residues (SED/SWS observation with ILT RSRF) for stars earlier than G9 (blue) and later than G9 (red). No significant difference is seen between hot and cool stars. The black curve shows the correction smoothing spline used to obtain the OLP 10 RSRF.

Any code which combines all AOT bands of SWS to form a smooth final spectrum will necessarily re-calibrate every AOT band (except one) based on the data observed within the overlap regions.