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Optical observations provide convincing evidence that the optical phase of the Crab pulsar follows the radio one closely. Since optical data do not depend on dispersion measure variations, they provide a robust and independent confirmation of the radio timing solution. The aim of this paper is to find a global mathematical description of Crab pulsars phase as a function of time for the complete set of published Jodrell Bank radio ephemerides (JBE) in the period 1988-2014. We apply the mathematical techniques developed for analyzing optical observations to the analysis of JBE. We break the whole period into a series of episodes and express the phase of the pulsar in each episode as the sum of two analytical functions. The first function is the best-fitting local braking index law, and the second function represents small residuals from this law with an amplitude of only a few turns, which rapidly relaxes to the local braking index law. From our analysis, we demonstrate that the power law index undergoes instantaneous changes at the time of observed jumps in rotational frequency (glitches). We find that the phase evolution of the Crab pulsar is dominated by a series of constant braking law episodes, with the braking index changing abruptly after each episode in the range of values between 2.1 and 2.6. Deviations from such a regular phase description behave as oscillations triggered by glitches and amount to fewer than 40 turns during the above period, in which the pulsar has made more than 2.0e10 turns. Our analysis does not favor the explanation that glitches are connected to phenomena occurring in the interior of the pulsar. On the contrary, timing irregularities and changes in slow down rate seem to point to electromagnetic interaction of the pulsar with the surrounding environment.
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We observed the Crab pulsar in October 2008 at the Copernico Telescope in Asiago - Cima Ekar with the optical photon counter Aqueye (the Asiago Quantum Eye) which has the best temporal resolution and accuracy ever achieved in the optical domain (hundreds of picoseconds). Our goal was to perform a detailed analysis of the optical period and phase drift of the main peak of the Crab pulsar and compare it with the Jodrell Bank ephemerides. We determined the position of the main peak using the steepest zero of the cross-correlation function between the pulsar signal and an accurate optical template. The pulsar rotational period and period derivative have been measured with great accuracy using observations covering only a 2 day time interval. The error on the period is 1.7 ps, limited only by the statistical uncertainty. Both the rotational frequency and its first derivative are in agreement with those from the Jodrell Bank radio ephemerides archive. We also found evidence of the optical peak leading the radio one by ~230 microseconds. The distribution of phase-residuals of the whole dataset is slightly wider than that of a synthetic signal generated as a sequence of pulses distributed in time with the probability proportional to the pulse shape, such as the average count rate and background level are those of the Crab pulsar observed with Aqueye. The counting statistics and quality of the data allowed us to determine the pulsar period and period derivative with great accuracy in 2 days only. The time of arrival of the optical peak of the Crab pulsar leads the radio one in agreement with what recently reported in the literature. The distribution of the phase residuals can be approximated with a Gaussian and is consistent with being completely caused by photon noise (for the best data sets).
We have carried out new, high-frequency, high-time-resolution observations of the Crab pulsar. Combining these with our previous data, we characterize bright single pulses associated with the Main Pulse, both the Low-Frequency and High-Frequency Interpulses, and the two High-Frequency Components. Our data include observations at frequencies ranging from 1 to 43 GHz with time resolution down to a fraction of a nanosecond. We find at least two types of emission physics are operating in this pulsar. Both Main Pulses and Low-Frequency Interpulses, up to about 10 GHz, are characterized by nanoshot emission - overlapping clumps of narrow-band nanoshots, each with its own polarization signature. High-Frequency Interpulses, between 5 and 30 GHz, are characterized by spectral band emission - linearly polarized emission containing about 30 proportionately spaced spectral bands. We cannot say whether the longer-duration High-Frequency Component pulses are due to a scattering process, or if they come from yet another type of emission physics.
Our high time resolution observations of individual pulses from the Crab pulsar show that the main pulse and interpulse differ in temporal behavior, spectral behavior, polarization and dispersion. The main pulse properties are consistent with one current model of pulsar radio emission, namely, soliton collapse in strong plasma turbulence. The high-frequency interpulse is quite another story. Its dynamic spectrum cannot easily be explained by any current emission model; its excess dispersion must come from propagation through the stars magnetosphere. We suspect the high-frequency interpulse does not follow the ``standard model, but rather comes from some unexpected region within the stars magnetosphere. Similar observations of other pulsars will reveal whether the radio emission mechanisms operating in the Crab pulsar are unique to that star, or can be identified in the general population.
We present statistical analysis of a fluence limited sample of over 1100 giant pulses from the Crab pulsar, with fluence > 130 Jy ms at ~1330 MHz. These were detected in ~260 hours of observation with the National Centre for Radio Astrophysics (NCRA)-15m radio telescope. We find that the pulse energy distribution follows a power law with index $alphaapprox$-3 at least up to a fluence of ~5 Jy s. The power law index agrees well with that found for lower energy pulses in the range 3-30 Jy ms. The fluence distribution of the Crab pulsar hence appears to follow a single power law over ~3 orders of magnitude in fluence. We do not see any evidence for the flattening at high fluences reported by earlier studies. We also find that at these fluence levels, the rate of giant-pulse emission varies by as much as a factor of ~5 on time-scales of a few days, although the power law index of the pulse-energy distribution remains unchanged. The slope of the fluence distribution for Crab giant pulses is similar to that recently determined for the repeating FRB 121102. We also find an anti-correlation between the pulse fluence and the pulse width, so that more energetic pulses are preferentially shorter.
Pulsars are well studied all over the electromagnetic spectrum, and the Crab pulsar may be the most studied object in the sky. Nevertheless, a high-quality optical to near-infrared spectrum of the Crab or any other pulsar has not been published to date. Obtaining a properly flux-calibrated spectrum enables us to measure the spectral index of the pulsar emission, without many of the caveats from previous studies. This was the main aim of this project, but we could also detect absorption and emission features from the pulsar and nebula over an unprecedentedly wide wavelength range. A spectrum was obtained with the X-shooter spectrograph on the Very Large Telescope. Particular care was given to the flux-calibration of these data. A high signal-to-noise spectrum of the Crab pulsar was obtained from 300 to 2400nm. The spectral index fitted to this spectrum is flat with alpha_nu=0.16 +- 0.07. For the emission lines we measure a maximum velocity of 1600 km/s, whereas the absorption lines from the material between us and the pulsar is unresolved at the 50 km/s resolution. A number of Diffuse Interstellar Bands and a few near-IR emission lines that have previously not been reported from the Crab are highlighted.
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