3 Solar system object identification

Figure 3: Extraction procedure for ISOSS slew data to find SSO candidates, based only on pointings and timings of ISO slews and expected 170 $\mu$m fluxes. The flux preselection is described in the text.

The identification and separation of moving solar system targets from the Serendipity slews is difficult: the Serendipity slew data consist of very narrow stripes across the sky, lacking, to first approximation, any redundancy. Additionally, the colour information is missing and in the far-IR region the cirrus confusion is a serious problem. Therefore, the solar system object identification was done on basis of accurate ephemeris calculations and model flux estimates (see Müller 2001).

The Serendipity slew data consist of 11 847 slews with a total length of 141 411$^{\circ}$. The slews were cut in 4 232 525 individual pointings of approximately 2$^{\prime}$ length. Each of these pointings had to be checked against SSOs. On 20th of March 2000, the Minor Planet Center archive consisted of 68 840 asteroids (14 308 numbered, 24 598 unnumbered with multiple-opposition orbits and 29 934 unnumbered with single-opposition orbits) and 237 comets. Additionally, the outer planets and their satellites had to be included, leading to a total of approximately $3 \times 10^{11}$ ephemeris calculations. It was therefore necessary to preselect the number of SSOs considerably and to invent fast search procedures.

3.1 SSO preselection

To facilitate and speed up the search process, only SSOs which at maximum are brighter than the sensitivity limit of 1 Jy at 170 $\mu$m have been considered: the outer planets (Mars, Jupiter, Saturn, Uranus, Neptune and Pluto) and their satellites were included. The inner planets were not visible to the ISO. Due to the difficulties of predicting the brightness of active comets, no initial flux preselection was done for the 237 comets. The unnumbered single-apparition asteroids have not been considered because of possible large ephemeris uncertainties and generally too low brightness at 170 $\mu$m (except for a few Near-Earth asteroids which can reach this flux limit at extremely close encounters). The preselection of numbered and unnumbered multi-apparition asteroids was based on conservative flux calculations, using a simplified Standard Thermal Model (STM, Lebofsky et al. 1986, 1989) and assuming a non-rotating spherical object. The following conservative input values were used: $p_{\rm v} = 0.02$, G=-0.12, $\epsilon=1.0$, $\eta=0.7$. The input diameter was calculated using $p_{\rm v}$ and the absolute magnitude H with: $\log~p_{\rm v} = 6.259 - 2~\log~D_{{\rm eff}} - 0.4~H$. In Flux Preselection I, with a cut-off limit of 1.0 Jy, the object was assumed to be located at perihelion during opposition. This reduced the number of asteroids by 98% from 38 906 to 596. In Flux preselection II, with a cut limit of 0.5 Jy, the real calculated distances (r, $\Delta$) were used.

For the comets, we determined 36 "hits'' where the object was within 5$^{\prime}$ from the slew centre and with the comet being within 3 AU (for Hale-Bopp 5 AU) from the Sun. A simple flux estimate lowered the number to 16 possible candidates. The 170 $\mu$m flux estimate was based on an assumed dust albedo A=0.10 and a temperature of dust particles of T₀=330 K at the heliocentric distance of r=1 AU through the following formula:

$$% F_{\nu} = B(\lambda,T) \cdot f \cdot \frac{R^2}{4\Delta^2}$$ (1)

with the temperature $T=\sqrt[4]{T_0^4 \cdot (1-A)/r^2}$ and $\Delta$ the geocentric distance to the comet. We assumed a dense central coma of 10 000 km radius with a filling factor of f=10^-4 and 1/R brightness profile out to a distance of 50 000 km. The corresponding model predictions fitted nicely the published results by Campins et al. (1990) for comet P/Tempel 2 and by Hanner et al. (1994) for comet Mueller (1993a). This model was also used for initial flux estimates for the preparation of ISO comet observations (Grün, private communication).

3.2 Search radius

The search radius for each pointing had to be much bigger than the real $3^{\prime}\times3^{\prime}$ field of view of the detector for several reasons: 1) slew position uncertainties (up to 2$^{\prime}$, Stickel et al. 2000); 2) uncertainties of the 2-body unperturbed ephemeris, based on 200-day epoch orbital elements (up to a few arcmin); 3) the ISO parallax (up to 3$^{\prime}$ for close encounters at 0.5 AU). In the first iteration, the search radii were set to 8.1$^{\prime}$ for asteroids (3$^{\prime}$ for ephemeris uncertainties, 3$^{\prime}$ for ISO parallax, 2.1$^{\prime}$ for the centre-corner distance of the C200 array), to 30$^{\prime}$ for comets (to account for extended structures) and to 2$^{\circ}$ for the bright planets (to account for possible straylight influences). In the second iteration, after the ephemeris recalculation with an N-body programme and after parallax corrections, the search radius was uniformly set to 5$^{\prime}$. Additionally, all identified slews from the first iteration were marked, because of possible influences from bright SSOs.

3.3 Search procedure

Figure 3 summarizes the procedure in detail, giving also the input and output number of targets. With this procedure it was possible to reduce the initially estimated 10¹¹ ephemeris calculations to 10⁹ 2-body and 10⁴ N-body calculations. The final potential hits of 56 asteroids, 16 comets and 22 planets fulfilled the flux requirements at the actual time of the observation and were located within 5$^{\prime}$ of the slew. Note that we count each encounter of a slew with an SSO as "hit''. The actual numbers of different objects in this list are 21 asteroids, 7 comets and 2 planets. These results, based on pure pointing and timing information, are strongly influenced and biased by the unequal distribution of the slews in the sky, satellite visibility constraints and the ISO observing programme itself. The relatively large number of comets is due to the weak flux limit and it was clear that not all of them would be bright enough to be detected.