4 Discussion and conclusions

These upper limits for the dust mass around pulsars $M_{\rm cr}$/$M_{\odot}$, suggest that none of them are surrounded by a sufficiently massive disc in which planets are likely to form. It is generally agreed that the suitable protoplanetary disc has at least 0.01 $M_{\odot}$ of gas and dust in Keplerian orbit around a solar-mass protostar (Boss 2000). The dust mass found in T Tauri discs is typically $10^{-3}~M_{\odot}$ (Beckwith et al. 1990); protoplanetary discs with masses in the range of 0.01 to 0.1 $M_{\odot}$ are commonly found in orbit around young stars (Zuckerman 2001). When stars reach ages of about 10⁷ yr, the evidence of planet-forming discs disappears (Boss 2000). Evidence of debris discs has been found, e.g. around Beta Pictoris with about $10^{-6}~M_{\odot}$ (Artymowicz 1994). One caveat is that these estimates are very dependent on the properties of the dust grains and do not provide a good estimate for the total amount of gas and dust because the dust to gas ratio is undetermined. These estimates could be quite different for circumpulsar discs with very non-solar composition. This negative result is perhaps not so surprising, since planets around pulsars do not appear to be common observationally (Konacki et al. 1999), certainly much rarer than planets around normal-type stars. This also suggests that planet formation around pulsars is not a natural consequence of the pulsar-formation process (whether it is the formation of the neutron star in a supernova or the recycling of the pulsar in a binary). This is rather different from planet formation around normal-type stars, which appears to be an ubiquitous by-product of the star-formation process.

Acknowledgements

We warmly thank the ISO project and the ISOCAM and ISOPHOT Teams in Villafranca, Saclay and Heidelberg. This research has made use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We express our thanks to the anonymous referee for very helpful comments.