A Symphony of Echoes in the Crab Nebula

The radio emission of the Crab Pulsar occasionally features plasma lensing events known as echoes, during which new persistent components appear delayed relative to the primary emission. This delay decreases as the pulsar approaches the lensing material and increases as it recedes from it. To study these echoes, we search archival Jodrell Bank observations of the Crab (at $610{\rm\,MHz}$), producing daily profile averages by aligning individual pulses to correct for intrinsic phase variations. We then expand on this by producing our own archive of daily Crab pulses with the Canadian Hydrogen Intensity Mapping Experiment (CHIME, between $400$ and $800{\rm\,MHz}$). These aligned stacks result in less smeared average profiles than typical methods, and as a result we clearly identify a large number of echoes in both data sets, concluding that they are far more common than previously thought. We see that echoes are produced in clusters which evolve in delay at similar rates, and that echoes demonstrate a wide variety in their time and frequency evolution. From our observations and the previously observed electron densities in the nebula, we infer that echoes are produced by sheet-like structures seen at grazing incidence, with typical on-sky widths of $\sim\!0.1 {\rm\,au}$ and column depths of $\sim\!5{\rm\,au}$. In the CHIME dataset, we identify the first echoes seen with nonzero minimum delays, produced by structures which never directly intersect the pulsar's proper motion. From the low observation rate of these events, we infer that the echo structures must be highly anisotropic, with lengths $\gtrsim\!10{\rm\,au}$. From these observations, we model echoes as the product of cylinders of dense, neutral material with a thin and smooth ionized skin. The simulated delays closely match those observed, and this model reproduces a wider variety of characteristics than prior modelling attempts. However, the model fails to reproduce magnifications quantitatively, which we attribute to the smoothness of the modelled skin. Overall, our results strongly suggest that echoes are produced by unresolved small-scale filamentary structures which fill the nebula, and that these may themselves be substructure of the larger filaments seen in optical and infrared images.

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