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Using archival data from the 42-foot telescope at the Jodrell Bank Observatory, we produce daily stacks of aligned giant pulses for the Crab pulsar, to study changes to the daily profiles between 2012 April and 2016 December. From these, we identify echoes, where intervening material away from the line of sight causes pulsed emission to be redirected toward the observer, with delay corresponding to the increased distance of travel, resulting in additional profile components. These observations show that such echoes may be far more common than implied by the previous rate of detections. All the observed echoes are consistent with approaching zero delay at their closest approach to the normal giant pulse emission. This indicates that the structures responsible for producing these events must be highly anisotropic, with typical lengths greater than ∼4 au, typical widths on the sky of ∼0.1 au, and typical depths of ∼5 au, given the previously observed electron densities of the nebular filaments, on the order of 1000 cm ^−3 . This suggests that these inhomogeneities are likely to be offshoot substructure from the larger nebular filaments of the Crab nebula.

At 327 MHz, the observed emission of PSR B1937+21 is greatly affected by scattering in the interstellar medium, on a timescale of order the pulse period. We use the bright impulsive giant pulses emitted by the pulsar to measure the impulse response of the interstellar medium and then recover the intrinsic emission of the pulsar by deconvolution—revealing fine structure on timescales not normally observable. We find that the intrinsic widths of the main pulse and interpulse in the pulse profile are similar to those measured at higher frequencies. We detect 60,270 giant pulses, which typically appear as narrow, ∼100 ns bursts consisting of one to a few nanoshots with widths ≲ 10 ns. However, about 10% of the giant pulses exhibit multiple bursts that seem to be causally related to each other. We also report the first detection of giant micropulses in PSR B1937+21, primarily associated with the regular main pulse emission. These are distinct from giant pulses not only in the phases at which they occur, but also in their larger widths, of order a microsecond, and steeper energy distribution. These measurements place useful observational constraints on emission mechanisms for giant pulses as well as the regular radio emission of millisecond pulsars.

We use four observations with the European very long baseline interferometry (VLBI) network to measure the first precise radio parallax of the Crab Pulsar. We found two in-beam extragalactic sources just outside the Crab Nebula, with one bright enough to use as a background reference source in our data. We use the Crab Pulsar’s giant pulses to determine fringe and bandpass calibration solutions, which greatly improved the sensitivity and reliability of our images and allowed us to determine precise positional offsets between the pulsar and the background source. From those offsets, we determine a parallax of π = 0.53 ± 0.06 mas and proper motion of ( μ _α , μ _δ ) = (−11.34 ± 0.06, 2.65 ± 0.14) mas yr ^−1 , yielding a distance of $d={1.90}_{-0.18}^{+0.22}\,\mathrm{kpc}$ and transverse velocity of ${v}_{\perp }={104}_{-11}^{+13}\,\mathrm{km}\,{{\rm{s}}}^{-1}$ . These results are consistent with the Gaia 3 measurements, and open up the possibility of far more accurate astrometry with further VLBI observations.

The Crab Pulsar is the prime example of an emitter of giant pulses. These short, very bright pulses are thought to originate near the light cylinder, at ∼1600 km from the pulsar. The pulsar’s location inside the Crab Nebula offers an unusual opportunity to resolve the emission regions, using the nebula, which scatters radio waves, as a lens. We attempt to do this using a sample of 61,998 giant pulses found in coherently combined European VLBI network observations at 18 cm. These were taken at times of relatively strong scattering and hence good effective resolution. From correlations between pulse spectra, we show that the giant pulse emission regions are indeed resolved. We infer apparent diameters of ∼2000 and ∼2400 km for the main and interpulse components, respectively, and show that with these sizes the correlation amplitudes and decorrelation timescales and bandwidths can be understood quantitatively, both in our observations and in previous ones. Using pulse-spectra statistics and correlations between polarizations, we also show that the nebula resolves the nanoshots that comprise individual giant pulses. The implied diameters of ∼1100 km far exceed light-travel-time estimates, suggesting the emitting plasma is moving relativistically, with γ ≃ 10 ^4 , as inferred previously from drifting bands during the scattering tail of a giant pulse. If so, the emission happens over a region extended along the line of sight by ∼10 ^7 km. We conclude that relativistic motion likely is important for producing giant pulses, and may be similarly for other sources of short, bright radio emission, such as fast radio bursts.

In extreme scattering events, the brightness of a compact radio source drops significantly, as light is refracted out of the line of sight by foreground plasma lenses. Despite recent efforts, the nature of these lenses has remained a puzzle, because any roughly round lens would be so highly overpressurized relative to the interstellar medium that it could only exist for about a year. This, combined with a lack of constraints on distances and velocities, has led to a plethora of theoretical models. We present observations of a dramatic double-lensing event in pulsar PSR B0834+06 and use a novel phase-retrieval technique to show that the data can be reproduced remarkably well with a two-screen model: one screen with many small lenses and another with a single, strong one. We further show that the latter lens is so strong that it would inevitably cause extreme scattering events. Our observations show that the lens moves slowly and is highly elongated on the sky. If similarly elongated along the line of sight, as would arise naturally from a sheet of plasma viewed nearly edge-on, no large overpressure is required and hence the lens could be long-lived.

Giant pulses emitted by PSR B1937+21 are bright, intrinsically impulsive bursts. Thus, the observed signal from a giant pulse is a noisy but direct measurement of the impulse response from the ionized interstellar medium. We use this fact to detect 13,025 giant pulses directly in the baseband data of two observations of PSR B1937+21. Using the giant pulse signals, we model the time-varying impulse response with a sparse approximation method, in which the time dependence at each delay is decomposed in Fourier components, thus constructing a wavefield as a function of delay and differential Doppler shift. We find that the resulting wavefield has the expected parabolic shape with several diffuse structures within it, suggesting the presence of multiple scattering locations along the line of sight. We also detect an echo at a delay of about 2.4 ms, over 1.5 times the rotation period of the pulsar, which moves along the trajectory expected from geometry between the two observations. The structures in the wavefield are insufficiently sparse to produce a complete model of the system; hence, the model is not predictive across gaps larger than about the scintillation time. Nevertheless, within its range, it reproduces about 75% of the power of the impulse response, a fraction limited mostly by the signal-to-noise ratio of the observations. Furthermore, we show that by deconvolution, using the model impulse response, we can successfully recover the intrinsic pulsar emission from the observed signal.

We analyzed four epochs of beamformed European VLBI Network data of the Crab Pulsar at 1658.49 MHz. With the high sensitivity resulting from resolving out the Crab Nebula, we are able to detect even the faint high-frequency components in the folded profile. We also detect a total of 65,951 giant pulses, which we use to investigate the rates, fluence, phase, and arrival time distributions. We find that for the main pulse component, our giant pulses represent about 80% of the total flux. This suggests we have a nearly complete giant pulse energy distribution, although it is not obvious how the observed distribution could be extended to cover the remaining 20% of the flux without invoking large numbers of faint bursts for every rotation. Looking at the difference in arrival time between subsequent bursts in single rotations, we confirm that the likelihood of finding giant pulses close to each other is increased beyond that expected for randomly occurring bursts—some giant pulses consist of causally related microbursts, with typical separations of ∼30 μ s—but also find evidence that at separations ≳100 μ s the likelihood of finding another giant pulse is suppressed. In addition, our high sensitivity enabled us to detect weak echo features in the brightest pulses (at ∼0.4% of the peak giant pulse flux), which are delayed by up to ∼300 μ s.