The POINT-AGAPE survey - II. An unrestricted search for microlensing events towards M31

An automated search is carried out for microlensing events using a catalogue of 44 554 variable superpixel light curves derived from our 3-yr monitoring programme of M31. Each step of our candidate selection is objective and reproducible by a computer. Our search is unrestricted, in the sense that it has no explicit time-scale cut. So, it must overcome the awkward problem of distinguishing long time-scale microlensing events from long-period stellar variables. The basis of the selection algorithm is the fitting of the superpixel light curves to two different theoretical models, using variable star and blended microlensing templates. Only if microlensing is preferred is an event retained as a possible candidate. Further cuts are made with regard to: (i) sampling, (ii) goodness of fit of the peak to a Paczyński curve, (iii) consistency of the microlensing hypothesis with the absence of a resolved source, (iv) achromaticity, (v) position in the colour-magnitude diagram and (vi) signal-to-noise ratio. Our results are reported in terms of first-level candidates, which are the most trustworthy, and second-level candidates, which are possible microlensing events but have a lower signal-to-noise ratio and are more questionable. The pipeline leaves just three first-level candidates, all of which have very short full-width at half-maximum time-scales (t1/2 < 5 d) and three second-level candidates, which have time-scales of t1/2 = 31, 36 and 51 d. We also show 16 third-level light curves, as an illustration of the events that just fail the threshold for designation as microlensing candidates. They are almost certainly mainly variable stars. Two of the three first-level candidates correspond to known events (PA 00-S3 and 00-S4) already reported by the POINT-AGAPE project. The remaining first-level candidate is new. This algorithm does not find short time-scale events that are contaminated with flux from nearby variable stars (such as PA 99-N1