2 Observations and data reduction

The ISO observations presented here have been carried out between February and October 1997 with two different detectors of the instrument ISOPHOT: PHT-P and PHT-S.

In Table 1 the observational aspect data of the observed asteroids are listed. The background measurements (indicated in the Table as "off'') have been carried out at the same sky position, but 1 or 2 days later when the asteroid was outside the field of view. Davida and Palisana have no dedicated background measurements of the PHT-S observations. The second PHT-P Davida measurement was intended to be taken off-source, but by error done again on-source.

2.1 PHT-P data

Multi-filter photometry was carried by PHT-P with all 3 detector subsystems at wavelengths of 10, 12, 25 and 60 $\mu$m. The apertures used were 23 $^{\prime \prime}$ diameter (10 and 12 $\mu$m), 52 $^{\prime \prime}$(25 $\mu$m) and 99 $^{\prime \prime}$ (60 $\mu$m). The integration times were: 64 s at 10 $\mu$m and 32 s at 12 $\mu$m (P1-detector); 32 s at 25 $\mu$m (P2-detector); 32 s at 60 $\mu$m (P3-detector).

ISOPHOT Interactive Analysis (PIA) V9.0.1(e) was used for the standard data reduction up to signal level, including linear ramp fitting, deglitching on ramp and signal level and orbit dependent dark signal subtraction (Gabriel et al. 1997). Unfortunatly the integration time was in many cases not long enough to obtain stabilized signals. In these cases (P1-detector, 10 and 12 $\mu$m) the internal reference measurements were replaced by the "default'' detector responsivity. Additionally the used non-default apertures caused problems in terms of absolute calibration of the background photometry (in comparison with COBE-DIRBE values by Hauser et al. 1998). For these reasons, all background measurements were replaced by COBE-DIRBE values (weekly maps, color corrected, PHT-P aperture size corrected).

All source measurements have been background subtracted and color corrected. The following color correction values have been used: 10 $\mu$m: 0.99; 12 $\mu$m: 0.91; 25 and 60 $\mu$m: 1.07. These values correspond to temperatures between 200 and 300 K.

The analysis of similar measurements on calibration targets in the same apertures revealed that the internal calibration source of ISOPHOT (the Fine Calibration Source, FCS) leads in some cases to a flux overestimation up to 20% (P2-detector, 25 $\mu$m) and a flux underestimation up to 20% (P3-detector, 60 $\mu$m). This is reflected in the asymmetric uncertainties in the values. In case of strong signal transients the error values have been increased accordingly.

2.2 PHT-S data

PHT-S, which consists of two low-resolution grating spectrometers, covered the wavelength ranges 2.5-4.9 $\mu$m (PHT-SS) and 5.8-11.6 $\mu$m (PHT-SL). The obtained spectra have a resolution $\lambda/\Delta\lambda$ of about 85 for PHT-SS and of about 95 for PHT-SL. All PHT-S observations have been performed in staring mode with a default of 32 s dark exposure at the beginning of the measurement. The integration time was of 1024 s for 77 Frigga, 114 Kassandra, 308 Polyxo, 914 Palisana, and 512 s for 511 Davida.

PIA V8.2(e) was used for the standard data reduction up to signal level, including linear ramp fitting, deglitching on ramp and signal level and orbit dependent dark signal subtraction (Gabriel et al. 1997). The flux calibration is done with the dynamic response method (Laureijs et al. 2002) by taking the ratio between the signals from the target and the calibrators along the observing time and then deriving the mean and median values, which are scaled by the known flux from the chosen calibrators. The dark current subtraction was performed before the dynamic calibration application.

Figure 1: PHT-S background measurements at the positions of the asteroids Frigga, Kassandra and Polyxo. The fitted blackbody curve (solid line) and the corresponding COBE-DIRBE value (box) are also shown.

The on-source measurements have been background subtracted in the following way: 1) cross check of the absolute background level with COBE-DIRBE data (weekly maps, color corrected, PHT-S beam size corrected) for the 3 dedicated background spectra (see Fig. 1); 2) fit of a blackbody curve to the observed background spectra (blackbody temperatures taken from Ábrahám et al. 1999); 3) for Davida and Palisana the blackbody fit was done directly to the COBE-DIRBE values since no dedicated background measurements exist; 4) subtraction of the blackbody fits from the on-source measurements. This procedure avoids the noise introduction from the background subtraction. Figure 1 shows the PHT-S background spectra of Frigga, Kassandra, and Polyxo together with the fitted blackbody curve and the corresponding COBE-DIRBE values.

The uncertainties from the signal processing by PIA are 3-5%, which reflect also the relative accuracy from pixel to pixel. The absolute uncertainty is generally stated better than 30% (Klaas et al. 1997). Since we used an interactive analysis with improved calibration we believe that the absolute calibration is better than 15% for Frigga, Kassandra and Palisana and better then 10% for Polyxo and Davida. This is also in agreement with our cross-calibration experiences between different ISO instruments and with stellar models. The PHT-SS 2.5-4.9 $\mu$m part of the asteroid spectra is at a very low signal level, close to the detection limit. Therefore we exclude in this paper this part of the spectrum.

In Fig. 2 the low-resolution PHT-S spectra between 5.8 and 11.6 $\mu$m together with the PHT-P data are shown with the uncertainties produced by the signal processing procedure.

Figure 2: PHT-S spectra between 5.8 and 11.6 $\mu$m and PHT-P data (box).