Limits on Planet Formation Around Young Pulsars and Implications for Supernova Fallback Disks

We have searched a sample of 151 young, energetic pulsars for periodic variation in pulse time-of-arrival arising from the influence of planetary companions. We are sensitive to objects with masses two orders of magnitude lower than those detectable with optical transit timing, but we find no compelling evidence for pulsar planets. For the older pulsars most likely to host planets, we can rule out Mercury analogues in one third of our sample and planets with masses $>0.4 M_{\oplus}$ and periods $P_b<1$ yr in all but 5% of such systems. If pulsar planets form primarily from supernova fallback disks, these limits imply that such disks do not form, are confined to $<0.1$ AU radii, are disrupted, or form planets more slowly ($>2$ Myr) than their protoplanetary counterparts.