Subsections

• 5.7.1 Astronomical Calibration Sources (ACS)
• 5.7.2 Photometric calibration accuracy

5.7 Signal to Flux Conversion

Calculation of the conversion factors, $G_{c}$, from $\mu$V/s to Jy is based purely on observations of the standards listed in Table 5.2. For each band roughly 50 corrected observations at the key wavelengths are compared with model SEDs. Each observation is a measurement of the signal to flux conversion. The final S/F conversion (stored in Cal-G 42) is the average ratio of measured signal to expected flux for each standard at the key wavelength.

For the purpose of filtering out poor quality data, a number of conditions had to be met by the observations for them to be considered for the calibration. The first condition is that the reconstructed pointing had to be within 1 arcsecond of the intended coordinates. The second condition is that an observation was usable, only if it had high quality data in all the elements of the calibration group. For calibration purposes only, the bands are divided into 4 groups. Group 1 consisted of the short wavelength (SW) section of SWS (bands 1A, 1B, 1D, 1E, 2A, 2B and 2C). Group 2, consisted of bands 3A, 3C and 3D. Group 3 is just band 3E and group 4 is just band 4. The reason for creating these groups is that if and observation failed in any one part of a group, it is suspect in all the others. The final condition is that all points marked as glitches are thrown out. Unfortunately, this filter will not get the glitch tails seen in band 4 (see Section 7.2.8).

5.7.1 Astronomical Calibration Sources (ACS)

Table 5.2 gives an overview of the ACSs used for the photometric calibration of the pipeline products. The table indicates the source name, type of object, and bands which made use of the ACS.

The last 4 columns illustrate the diversity and distribution of observations used for the photometric calibration of the various bands. For each ACS, the number of observations going into the photometric calibration is given. In the last columns, there are 4 numbers per ACS indicating 4 different band groups. The first group combines bands 1A through 2C, the second group combines bands 3A through 3D, and the last two groups are the bands 3E and 4 respectively. For wavelengths shorter than 12 $\mu$m, the SEDs for the ACS were updated with stellar atmospheric models described in Decin 2000, [4]. The absolute calibration of these SEDs is based on the photometry used for the absolutely calibrated composite observed spectra described by Cohen et al. 1992a, [2]. For wavelengths longer that 12 $\mu$m the stellar composites themselves are used (Cohen et al. 1992a, [2]). The photometry and composites used for SWS are directly traceable to the published calibrated spectra of Sirius and Vega (Cohen et al. 1992b, [3]).

The stellar calibration sources span a wide range in spectral types from A0V to M0III with the bulk of the sources being K giants. Within each of the SW bands the SEDs cover more than 2 decades in flux. The diversity of the ACSs and the wide flux range increases the reliability of the photometric calibration and reduces the sensitivity to any one object or model.

For bands 3E and 4, models of Ceres (T. Müller, private communication) and Uranus (E. Lellouch, private communication) were used. These models can be obtained from the ISO Data Centre.

As can be seen in Table 5.2, the star, $\gamma$ Dra, was heavily used. The photometric calibration was checked with and without the inclusion of $\gamma$ Dra to ensure this one source was not skewing the photometric calibration.

Table 5.2: Summary of SWS astronomical calibration standards

Source	Alias	Spectral	Number Obs.
ID		Type	SW$^a$	3$^b$	3E	4
HR7001	Vega	A0V	5	0	0	0
HR2491	Sirius	A1V	5	5	0	0
HR4534	$\beta$ Leo	A3Vv	2	0	0	0
HR5459	$\alpha$ Cen A	G2V	1	1	1	1
HR7310	$\delta$ Dra	G9III	2	0	0	0
HR6688	$\xi$ Dra	K2III	4	0	0	0
HR5340	$\alpha$ Boo	K2IIIp	8	9	9	9
HR5563	$\beta$ UMi	K4III	2	0	0	0
HR1457	$\alpha$ Tau	K5III	6	6	6	6
HR6166	HD 149447	K5III	1	0	0	0
HR6705	$\gamma$ Dra	K5III	24	37	29	0
HR337	$\beta$ And	M0III	4	4	4	2
HR911	$\alpha$ Cet	M2III	2	2	2	0
HR8775	$\beta$ Peg	M2.5III	0	7	7	7
HR4763	$\gamma$ Cru	M4III	0	6	6	6
NML Cyg	IRC+10448	M6IIIe	0	4	3	3
Ceres	210001	Asteroid	0	0	1	1
Uranus		Planet	0	0	1	1

Notes:

$^a$

SW indicates the short wavelength section of the SWS grating: bands 1A to 2C covering wavelengths from 2.4 to 12 $\mu m$. Stellar photosphere models provided by L. Decin (private communication).

$^b$

3 indicates bands 3A, 3C and 3D covering wavelengths 12 to 27 $\mu m$. All stellar photosphere composites covering 12 to 35 $\mu$m are from Cohen et al. 1992a, [2].

5.7.2 Photometric calibration accuracy

An overview of the SWS in-flight photometric calibration for point sources is given in Shipman et al. 2001, [35], from which this section is a summary. The standard processing corrects the observed raw signal for dark current, responsivity changes (monitored with the internal calibrator), RSRF, and flat-fielding. The final step is to convert the signal at all wavelengths from instrumental units ($\mu$V/s) to astronomical units (Jy) based on observations of the Astronomical Calibration Sources.

Table 5.3 lists the $1\sigma$ uncertainties in the measured signal to flux conversion factors. For each grating band the table lists the key wavelength of the band, the bandpass used around the key wavelength, the $1\sigma$ accuracy at the key wavelength, and the $1\sigma$ worst accuracy within the band which is usually at the edges of the band. As calculated, the uncertainty is the total absolute uncertainty which has accumulated factors from each of the calibration steps plus estimated contributions from processes which were unprobed or uncorrected. Some examples of these additional uncertainties are, uncorrected memory effects in band 4, higher order memory effects in band 2, and pointing effects. See Section 5.9 for a complete description of the uncertainties in the SWS data.

Table 5.3: Photometric Accuracies for pipeline products

	Key $\lambda$	Bandpass	Accuracy	Worst	$\lambda$
Band	[$\mu m$]	[$\mu m$]	1 $\sigma$ [%]	1 $\sigma$ [%]	of worst
1A	2.48	0.05	4	7	edges
1B	2.87	0.07	4	5	edges
1D	3.08	0.07	4	5	edges
1E	3.80	0.10	4	5	edges
2A	4.50	0.10	7	10	6 $\mu m$
2B	5.90	0.20	7	9	edges
2C	7.70	0.20	7	8	edges
3A	14.0	0.30	12	14	12$\mu m$
3C	17.0	0.30	10	13	edges
3D	24.0	0.60	13	16	19.5$\mu m$
3E	28.5	0.60	17	21	edges
4	32.0	0.60	22	23	edges
5A	11.8	0.01	23	23
5B	14.0	0.01	23	23
5C	17.0	0.01	23	23
5D	24.0	0.01	24	24
6	27.0	0.01	30	30

The accuracies listed in Table 5.3 are entirely consistent with our current knowledge of SWS and the ISO satellite. A pointing accuracy of 1.5-2" (1$\sigma$) will produce more than half of the uncertainty in photometry for bands 1 and 3 and contribute up to half of the uncertainty in bands 2 and 4.

The accuracy expected on the flux calibration of the Fabry-Pérot are the same as that on the grating, but an extra 20% uncertainty needs to be added due to wavelength dependent leakage.

Figures 5.30 to 5.32 show examples of fully calibrated spectra for $\alpha$ Boo. Each spectral segment is made up of 12 detectors. The signal from these 12 detectors is kept separate to demonstrate the flat-fielding. The SED for $\alpha$ Boo is overlaid in red. In Figure 5.31, the up and down scans are shown separately to show the influence of residual memory effects. Figure 5.32 shows bands 3 and 4. In this figure radiation hits (glitches) are quite prevalent in band 4. The residual memory effect introduced by a radiation hit can artificially increase the signal. Also listed in the figures are the ratios of the data to the model at the key wavelength for each of the bands.

Figure 5.30: The SWS data are in blue and the SEDs are overplotted in red. The data here are direct pipeline products without flat-fielding or rebinning.

Figure 5.31: Band 2 for $\alpha$ Boo. Up and Down scans are shown in separate colours (blue and green) while the SEDs are shown in red. The ratio of the observation to SED is indicated. The residual memory effects are clearly seen in this figure as a mismatch between the up and the down scan.

Figure 5.32: Bands 3 and 4 for $\alpha$ Boo. Note the extreme number of radiation hits in band 4. The band 3D leakage can also be seen around 27 $\mu$m)