4 Calibration results

ISOSS observations of Uranus, Neptune and well known bright asteroids enabled us to improve and extend the existing ISOSS calibration (Method 1). They also allowed us to estabish the calibration of new source and flux extraction methods, namely Methods 2, 3a and 3b (see Sect. 2).

The Uranus and Neptune models are based on Griffin & Orton (1993) and Orton & Burgdorf (priv. comm.), respectively. For Ceres, Pallas, Juno and Vesta a thermophysical model (TPM) (Lagerros 1996, 1997, 1998) was used to predict their brightnesses at the times of the observations. The TPM and its input parameters are described in Müller & Lagerros (1998) and in Müller et al. (1999). The quality and final accuracy of TPM predictions are discussed in Müller & Lagerros (2002a). The general aspects of asteroids as calibration standards for IR projects are summarized in Müller & Lagerros (2002b).

Photometric measurements of different astronomical sources can be compared on the basis of colour corrected monochromatic fluxes at a certain wavelength or on the basis of band pass fluxes. In this calibration section all model fluxes have been modified by an "inverse colour correction'' in a way that they correspond to ISOSS band pass measurements of a constant energy spectrum ( $\nu F_{\nu } = const.$). This implied inverse colour correction terms of 1.09^-1 for Uranus and Neptune (both have temperatures at around 60 K at 170 $\mu$m) and 1.17^-1 for the bright main-belt asteroids (assumed far-IR temperature of 180-200 K), see also the colour correction tables in "The ISO Handbook, Volume V'', Laureijs et al. (2000).

   
4.1 Method 1

 

 

Table 1: Results for Method 1. The model fluxes are multiplied by 1.09 (planets) and by 1.17 (asteroids) to account for the spectral shape differences between $\nu F_{\nu } = {\rm const.}$ (assumed spectrum in the ISO calibration) and the real object spectrum. Column (4) contains the FCS calibrated fluxes.

TDT	Date/Time	SSO			/
No.			(Jy)	(Jy)
(1)	(2)	(3)	(4)	(5)	(6)
07881200	03-Feb.-96 09:46:42	(4) Vesta	28.9	39.6	0.73
10180400	26-Feb.-96 06:20:00	(4) Vesta	30.7	54.2	0.57
14080700	05-Apr.-96 15:39:10	Neptune	145.1	271.3	0.53
23080100	03-Jul.-96 20:15:13	(2) Pallas	15.2	27.5	0.55
32181100	03-Oct.-96 04:38:13	Neptune	153.2	279.8	0.55
42283300	11-Jan.-97 22:47:14	(3) Juno	12.6	12.0	1.05
34480700	26-Oct.-96 00:25:16	Neptune	159.1	272.7	0.58
69880600	13-Oct.-97 21:27:19	Neptune	160.7	277.6	0.58
70681100	22-Oct.-97 02:44:35	Neptune	158.0	274.9	0.57
71381000	29-Oct.-97 05:06:45	Neptune	168.3	272.7	0.62
71980500	03-Nov.-97 22:46:18	Neptune	149.9	271.3	0.55
72081500	05-Nov.-97 01:19:05	Uranus	395.7	672.8	0.59
72081600	05-Nov.-97 01:57:38	Neptune	156.1	270.5	0.58
76280400	16-Dec.-97 13:22:05	(1) Ceres	31.5	52.4	0.60
79781500	21-Jan.-98 00:30:12	(4) Vesta	24.2	23.9	1.01

ISOSS crossings over planets and asteroids, which were detected by the Automatic Point Source Extractor (Stickel et al. 2000), are listed in Table 1, where the columns are: (1) TDT number of the slew, (2) date and Universal Time at the moment of the SSO observation, (3) name of the solar system object, (4) observed flux density, (5) predicted flux density, (6) ratio between observed and modeled flux density (see also Fig. 4). The ISOSS results are the FCS calibrated band fluxes. The model predictions were modified by an inverse colour correction to make them comparable with the ISOSS measurements (see above). All list entries of Uranus, Neptune, Ceres, Pallas and Vesta give a ratio between observed and model flux of (0.58 $\pm$ 0.05), for fluxes larger than about 25 Jy. At fluxes below 25 Jy (only 2 cases) the ISOSS to model ratios are close to 1.0. This is in excellent agreement with the results of Stickel et al. (2000). They showed that ISOSS slew fluxes of 12 selected galaxies were systematically lower than fluxes derived from dedicated maps. To bring the fluxes from mapping and slewing into agreement ISOSS fluxes larger than $\approx$30 Jy were corrected with an estimated constant scaling factor of 2, while lower fluxes were scaled with a flux dependent correction function. Table 1 represents therefore the first direct flux calibration of the PHT Serendipity Mode as compared to the previously used indirect method of flux ratios between PHT22 raster maps and slew results.

Figure 4: The ratio of Serendipity slew flux densities and model predictions for reliable Uranus, Neptune, Ceres, Pallas, Juno and Vesta observations. For bright sources, the Serendipity slews miss some flux.

Figure 4 shows the ratios between the flux densities derived from ISOSS and the 170 $\mu$m model predictions. The stars represent the results from dedicated calibration measurements (Stickel et al. 2000), the filled circles are values from Table 1. Uranus, Neptune, Ceres, Pallas, Juno and Vesta, serendipitously seen by ISOSS, provide now a reliable calibration at higher flux densities.

   
4.2 Method 2

Table 2 summarizes the values which were derived from the solar system far-IR standards for slow slewing speeds, saturated measurements and sources outside the slews. These measurements were rejected by the source extraction procedures of Method 1. The table columns are: (1-6) same as in Table 1, (7) slew speed category at the moment of the SSO observation, (8) additional remarks.

   

Table 2: Results for Method 2. The model fluxes are multiplied by 1.09 (planets) and by 1.17 (asteroids) to account for the spectral shape differences between $\nu F_{\nu } = const.$ (assumed spectrum in the ISO calibration) and the real object spectrum. The values in Col. (4) are already corrected for the individual pixel point-spread function ( $F_{\rm psf}=0.64$).

TDT	Date/Time	SSO			/	Slew speed	Remarks
No.			(Jy)	(Jy)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
09380600	18-Feb.-96 15:10:15	(1) Ceres	>46	73.8	>0.62	slow	ok
29280600	04-Sep.-96 00:31:59	(1) Ceres	>54	67.2	>0.80	slow	very high bgd.
32880600	09-Oct.-96 23:11:09	Neptune	>155	277.8	>0.56	slow	ok
36381700	14-Nov.-96 04:34:23	Neptune	$\gg$50	267.2	$\gg$0.19	moderate	outside
54480800	13-May.-97 12:58:55	Uranus	$\gg$236	700.1	$\gg$0.34	moderate	saturated
55280300	21-May.-97 06:17:09	Uranus	$\gg$70	709.5	$\gg$0.10	stop	outside
69880200	13-Oct.-97 17:39:49	Uranus	$\gg$265	700.1	$\gg$0.38	moderate	saturated
69880500	13-Oct.-97 20:48:47	Uranus	$\gg$245	700.1	$\gg$0.35	moderate	saturated
71480300	29-Oct.-97 23:34:32	Uranus	$\gg$202	680.8	$\gg$0.30	moderate	saturated
87481000	07-Apr.-98 14:36:41	Uranus	$\gg$232	652.0	$\gg$0.36	moderate	saturated

The results from Method 2 show that also difficult slew data with either saturated pixels, objects slightly outside the array or slow speeds can be used to derive useful lower limits for interesting sources. As the satellite still moves the flux loss corrections from Method 1 have to be applied to get the best lower limits. In fact, for the 2 unproblematic hits (TDT 9380600 and 32880600) with neither saturated signals nor large impact parameters, the flux loss correction brings the ISOSS fluxes within 10% of the model predictions.

   
4.3 Method 3

At the slewend, when the satellite does not move anymore, the ISOSS data can in principle be treated as normal C200 photometric data. Two ideal cases - source centred on the array (Method 3a) and source centred on one pixel (Method 3b) - can be distinguished. The results on the bright sources for both methods are summarized in Table 3, where the columns are the same as in Table 1. The uncertainties in the table, given in brackets, are statistical errors of weighted results from all 4 pixels. The results of Method 3 are compared with the model predictions in Fig. 5.

Figure 5: The ratio of Serendipity flux densities from Method 3a and model predictions for Neptune, Ceres, Pallas, Juno and Vesta observations. Error bars are statistical errors from the individual pixel results. Circles encompass data points from slews which had to be calibrated with the default calibration; in these cases, the true uncertainties exceed the given statistical errors. A flux dependency similar as in Fig. 4 (Method 1) can be seen.

 

 

Table 3: Results for Method 3 (upper part: 3a, lower part 3b). The model fluxes are multiplied by 1.09 (planets) and by 1.17 (asteroids) to account for the spectral shape differences between $\nu F_{\nu } = {\rm const.}$ (assumed spectrum in the ISO calibration) and the real object spectrum. The uncertainties in the table, given in brackets, are statistical errors of weighted results from all 4 pixels.

TDT	Date/Time	SSO			/
No.			(Jy)	(Jy)
(1)	(2)	(3)	(4)	(5)	(6)
09380500	18-Feb.-96 07:11:04	(1) Ceres	70.1(6.9)	74.4	0.94
15480200	19-Apr.-96 03:42:10	Neptune	269(11.1)	275.3	0.98
23781000	11-Jul.-96 04:13:16	(3) Juno	12.9(2.6)	9.5	1.35
25180400	24-Jul.-96 23:47:09	(2) Pallas	26.4(2.0)	22.3	1.18
26580800	08-Aug.-96 02:50:48	(2) Pallas	25.1(2.4)	19.5	1.29
27580200	18-Aug.-96 02:17:46	(1) Ceres	85.2(10.2)	79.4	1.07
32880500	09-Oct.-96 21:54:26	Neptune	236(18.3)	277.8	0.85
35680200	06-Nov.-96 20:07:37	Neptune	267(16.1)	269.3	0.99
38781200	07-Dec.-96 23:52:44	(3) Juno	22.4(5.4)	15.6	1.44
41980900	08-Jan.-97 18:53:29	(3) Juno	16.3(0.5)	12.5	1.30
51080600	09-Apr.-97 10:54:42	(2) Pallas	14.1(2.1)	10.8	1.30
51080800	09-Apr.-97 15:19:52	(2) Pallas	16.1(1.3)	10.5	1.53
51380100	12-Apr.-97 04:33:19	(2) Pallas	16.7(3.9)	11.5	1.45
53980100	08-May-97 03:39:36	Neptune	282(70.4)	280.8	1.00
53980300	08-May-97 11:11:10	Neptune	278(31.1)	280.8	0.99
54581400	14-May-97 10:49:26	(1) Ceres	67.2(4.3)	55.5	1.21
57581500	13-Jun.-97 13:53:04	(4) Vesta	32.5(2.9)	24.6	1.32
74881000	03-Dec.-97 02:21:54	(1) Ceres	67.1(3.5)	58.3	1.15
53880300	07-May-97 07:54:19	(1) Ceres	43.8(4.9)	52.5	0.83
61580800	23-Jul.-97 02:07:07	(4) Vesta	31.1(1.2)	34.4	0.91

The 5 Neptune measurements (Method 3a) agree nicely with the model predictions (Observation/Model: 0.96 $\pm$ 0.09). For the fainter asteroids the Method 3a overestimates the flux systematically by 10-50%, depending on the brightness level (see Fig. 5). The discrepancy between bright and faint sources is probably due to detector nonlinearities, which are not corrected in the OLP 7 Serendipity Mode data, and which could be responsible for the flux dependency of the scaling factor (see Sect. 4.1). A comparison of Fig. 5 with Fig. 4 supports this explanation, as both diagrams show a decrease in the detector signals for bright sources. The fast slewing on the other hand, which affects Method 1 but not Method 3, could be responsible for the generally too low ISOSS fluxes in Fig. 4.

Both options of Methods 3 open a powerful new possibility to evaluate the 170 $\mu$m fluxes of many scientific ISO targets, which are quite often covered in the end of slews before the intended science programme starts.

   
4.4 Pointing comparison

The N-body ephemeris calculations for our SSOs included a transformation from geocentric to ISOcentric frame. The maximal geo-/ISOcentric parallax corrections were: 737.7 $^{\prime \prime}$ for the Apollo asteroid (7822) 1991 CS, 336.6 $^{\prime \prime}$ comet P/Encke and 61.2 $^{\prime \prime}$ for Mars. The final accuracy of the ISOcentric SSO ephemeris has been estimated to about 1-2 $^{\prime \prime}$.

The ISOSS signal pattern, i.e. the relative signals of the 4 pixels, is a very sensitive indicator of the exact position of the source within the detector array. All close encounters have been checked by eye for discrepancies between predicted slew offsets and the signal patterns. No disagreement was found, which implies that the predicted SSO positions and the slew positions agree with each other within 30 $^{\prime \prime}$, corresponding to 1/3 pixel width. In case of non-detections, the SSOs were either too faint, or they were actually just outside the slew. This high pointing accuracy allowed us to give upper limits (depending on the background) in cases when the source was crossed by the slew but no signal was detected (see also Sect. 2.2.2). In slew direction the position accuracy is better than 1$^{\prime}$, limited by fast slewing in combination with the detector read-out frequency.