3.1 Handling of the confirmed attributions

The attributions, even if confirmed by a successful least squares fit with low RMS of the residuals, cannot always be considered certain. To assess the reality of a proposed attribution we have to take into account, besides the RMS and the other fit parameters discussed in Section 2.3, the presence of systematic signatures and/or outliers in the residuals and the length of both observed arcs. Although our three stages filtering procedure is sophisticated, it can only provide a necessary condition for identification. At present, the intervention of an experienced human is still essential, and in many cases the residuals have to be inspected visually to decide if there is some signature suggesting an erroneous identification. The main criterion to assess the likelihood of an identification is the length of the two observed arcs (and the number of observations). As an example, for asteroids already observed at multiple apparitions, a good fit for an attributed arc is reliable even when this second arc is short, e.g., a one night stand. In contrast, when both arcs are short, an ostensibly good fit could be deceiving. It is therefore a fact that some proposed attributions can be rated neither true nor false, but have to remain as ``possible'', in some cases even ``probable'', but cannot be considered certain. The MPC is presently using a cautious policy, which appears sensible, trying to publish only identifications that appear almost certain, to minimize the number of ``erroneous identifications''. The others are left ``pending'', either because they have been submitted to the MPC and not published, or because they have been rated too uncertain and therefore not been submitted by us. This pending status could be better formalized. There is one way to remove a proposed identification from this pending status and that is to find other observations that could belong to the same object. As a matter of principle one could propagate the best fitting orbit resulting from the identification, predict observability conditions and then use a telescope (and/or a plate archive search) to either confirm or contradict the reality of the identification (contradiction requires a procedure of negative observation, as discussed in [Milani et al. 2000b]). In practice, nowadays this method can be applied only for especially important cases, such as Near Earth Asteroids; in the future, with better automation, it could be used more extensively. For most proposed attributions to an orbit computed with the data of a single apparition and with the second arc of short duration, e.g., a one night stand, a certain confirmation can come only with a serendipitous rediscovery. Thus it is essential, whenever a possible attribution is found, to restart the same procedure of Section 2 looking for additional attributions. Since a single apparition orbit can be substantially changed by the addition of an attribution to the fit, the new orbit might pick up new attributions. This argument applies to all new orbits computed as a result of a proposed identification, both with the attribution algorithm and with the orbit identification one. In a few cases this procedure, applied recursively, gives spectacular results, with many arcs identified at once. Our record is

$$1998{\rm\ SP}_{61} = 2000{\rm\ CK}_{108} = 1972{\rm\ LH} = 19... ... HF}_2 = 1986{\rm\ VQ}_6 = 1988{\rm\ GL}_1 = 1990{\rm\ UQ}_1,$$

in which the first identification was found with the orbit identification algorithm, the other 5 as attributions to the new multi-opposition orbit. For this reason, Table 2 has four columns containing: the attributions to orbits computed on the basis of the already known identifications, the attributions to the orbits recomputed after finding a new attribution, the orbit identifications and the attributions to the orbits recomputed after finding a new orbit identification. Thus the procedure to process the orbit-attributable pairs selected by the differential correction stage needs to include the search for these additional attributions, and those which are found are relevant to the credibility of the proposed attribution. After some experimenting, we have decided as a standard procedure to submit to the MPC:

• all the orbit identifications with a good fit;
• all the attributions to multi-apparition orbits;
• all the attributions of arcs spanning more than one night;
• the attributions of one night stands to single apparition orbits only if we can find an additional attribution.

All the other attributions proposed by our algorithm remain in the pending status, because they are one night attributions to single apparition orbits for which no additional attribution has been found so far. After the May 2000 update, we have 2,219 possible attributions pending (and not submitted to the MPC), all fulfilling the criteria discussed in Section 2.3. This pending status can change only in two ways: either the identification is contradicted by one of the asteroids in the pair being identified with a different one, or it is confirmed by finding another attribution in a later monthly update. Table 2 lists for each monthly update the identifications submitted by us to the MPC and those published by the MPC. Note we are not including in the table the identifications we have sometimes proposed and that had already been published, even only the previous day. It is understandable that the different groups of identification hunters, even by using different methods, can end up proposing lists of identifications partially overlapping and hence the credit goes to the fastest. We are now, before submitting, removing ourselves all the identifications published up to the same day. It is clear from such a table that only a small fraction of the identifications we propose are not accepted, especially since Dec. 1999 when we adopted the more restrictive protocol for submission described above.