Crab Pulsar Research Articles

Frequency steering of spaceborne clocks based on XPNAV-1 observations

Due to high stable rotations, timing of pulsars provides a natural tool to correct the frequency deviation of spaceborne atomic clocks. Based on processing the observational data about a year of Crab pulsar given by XPNAV-1 satellite, we study the possibility of correcting the frequency deviation of spaceborne atomic clocks using pulsar timing. According to the observational data in X-ray band and the timing model parameters from radio observations, the pre-fit timing residuals with a level of 67.66 µs are obtained. By fitting the slope of the timing residuals affected by the faked frequency-biased reference clock, we estimated successfully the relative frequency deviation of the reference clock. For a satellite clock with frequency deviation of the order about 10−12, a calibration accuracy with relative error of about 2% can be obtained from the Crab pulsar’s data for one year. The stability of the time scale based on Crab pulsar is about 10−12 for an interval of one year.

Resolving the Emission Regions of the Crab Pulsar’s Giant Pulses. II. Evidence for Relativistic Motion

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 ≃ 104, 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 ∼107 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.

A Decade of Linear and Circular Polarimetry with the POLISH2 Polarimeter

The POLISH2 optical polarimeter has been in operation at the Lick Observatory 3 m Shane telescope since 2011, and it was commissioned at the Gemini North 8 m in 2016. This instrument primarily targets exoplanets, asteroids, and the Crab Pulsar, but it has also been used for a wide variety of planetary, galactic, and supernova science. POLISH2's photoelastic modulators, employed instead of rotating wave plates or ferroelectric liquid crystal modulators, offer the unprecedented ability to achieve sensitivity and accuracy of order 1 ppm (0.0001%), which are difficult to obtain with conventional polarimeters. Additionally, POLISH2 simultaneously measures the intensity (Stokes I), linear polarization (Stokes Q and U), and circular polarization (Stokes V), which fully describe the polarization state of incident light. We document our laboratory and on-sky calibration methodology and our archival on-sky database, and we demonstrate the conclusive detection of circular polarization of certain objects.

Synchrotron Pair Production Equilibrium in Relativistic Magnetic Reconnection

Magnetic reconnection is ubiquitous in astrophysical systems, and in many such systems the plasma suffers from significant cooling due to synchrotron radiation. We study relativistic magnetic reconnection in the presence of strong synchrotron cooling, where the ambient magnetization, σ, is high and the magnetic compactness, ℓ B , of the system is of order unity. In this regime, e± pair production from synchrotron photons is inevitable, and this process can regulate the magnetization σ surrounding the current sheet. We investigate this self-regulation analytically and find a self-consistent steady state for a given magnetic compactness of the system and initial magnetization. This result helps estimate the self-consistent upstream magnetization in systems where plasma density is poorly constrained, and can be useful for a variety of astrophysical systems. As illustrative examples, we apply it to study the properties of reconnecting current sheets near the supermassive black hole of M87, as well as the equatorial current sheet outside the light cylinder of the Crab pulsar.

Bounding the photon mass with the dedispersed pulses of the Crab pulsar and FRB 180916B

Tight limits on the photon mass have been set through analyzing the arrival time differences of photons with differentfrequencies originating from the same astrophysical source. However, all these constraints have relied on usingthe first-order Taylor expansion of the dispersion due to a nonzero photon mass. In this work, we present an analysisof the nonzero photon mass dispersion with the second-order derivative of Taylor series. If the arrival time delay correctedfor all known effects (including the first-order delay time due to the plasma and photon mass effects) is assumed to bedominated by the second-order term of the nonzero photon mass dispersion, a conservative upper limit on the photon mass can be estimated. Here we show that the dedispersed pulses with the second-order time delays from the Crab pulsar andthe fast radio burst FRB 180916B pose strict limits on the photon mass, i.e.,mγ,2 ≤ 5.7 × 10-46 kg ≃ 3.2 × 10-10 eV/c 2and mγ,2 ≤ 6.0 × 10-47 kg ≃ 3.4 × 10-11 eV/c 2, respectively.This is the first time to study the possible second-order photon mass effect.

Pulsars in AstroSat-CZTI: detection in sub-MeV bands and estimation of spectral index from hardness ratios

The Cadmium Zinc Telluride Imager (CZTI) onboard AstroSat, an open detector above \(\sim \)100 keV, is a promising tool for the investigation of hard X-ray characteristics of \(\gamma \)-ray pulsars. A custom algorithm has been developed to detect pulsars from long integration (\(\sim \)years) of archival data, as reported by us earlier. Here, we extend this method in the analysis to include additional \(\sim \)20% of the CZTI pixels that were earlier ignored due to their lower gain values. Recent efforts have provided better and more secure calibration of these pixels, demonstrating their higher thresholds and extended energy range up to \(\sim \)1 MeV. Here, we use the additional information provided by these pixels, enabling the construction of pulse profiles over a larger energy range. We compare the profiles of the Crab pulsar at different sub-bands and show that the behavior is consistent with the extended energy coverage. As detailed spectroscopy over this full band remains difficult due to the limited count rate, we construct hardness ratios which, together with AstroSat mass model simulations, are able to constrain the power-law index of the radiation spectrum. We present our results for the phase-resolved spectrum of PSR J0534\(+\)2200 and for the total pulsed emission of PSR J1513−5908. The recovered photon indices are found to be accurate within \({\sim }20\)%.

Scattering variability detected from the circumsource medium of FRB 20190520B

ABSTRACT Fast radio bursts (FRBs) are millisecond-time-scale radio transients, the origins of which are predominantly extragalactic and likely involve highly magnetized compact objects. FRBs undergo multipath propagation, or scattering, from electron density fluctuations on sub-parsec scales in ionized gas along the line of sight. Scattering observations have located plasma structures within FRB host galaxies, probed Galactic and extragalactic turbulence, and constrained FRB redshifts. Scattering also inhibits FRB detection and biases the observed FRB population. We report the detection of scattering times from the repeating FRB 20190520B that vary by up to a factor of 2 or more on minutes to days-long time-scales. In one notable case, the scattering time varied from 7.9 ± 0.4 ms to less than 3.1 ms ($95{{\ \rm per\ cent}}$ confidence) over 2.9 min at 1.45 GHz. The scattering times appear to be uncorrelated between bursts or with dispersion and rotation measure variations. Scattering variations are attributable to dynamic, inhomogeneous plasma in the circumsource medium, and analogous variations have been observed from the Crab pulsar. Under such circumstances, the frequency dependence of scattering can deviate from the typical power law used to measure scattering. Similar variations may therefore be detectable from other FRBs, even those with inconspicuous scattering, providing a unique probe of small-scale processes within FRB environments.

Evolution of Spin Period and Magnetic Field of the Crab Pulsar: Decay of the Braking Index by the Particle Wind Flow Torque

The evolutions of a neutron star’s rotation and magnetic field (B-field) have remained unsolved puzzles for over half a century. We ascribe the rotational braking torques of pulsar to both components, the standard magnetic dipole radiation (MDR) and particle wind flow (MDR + Wind, hereafter named MDRW), which we apply to the Crab pulsar (B0531 + 21), the only source with a known age and long-term continuous monitoring by radio telescope. Based on the above presumed simple spin-down torques, we obtain the exact analytic solution on the rotation evolution of the Crab pulsar, together with the related outcomes as described below: (1) unlike the constant characteristic B-field suggested by the MDR model, this value for the Crab pulsar increases by a hundred times in 50 kyr while its real B-field has no change; (2) the rotational braking index evolves from ∼3 to 1 in the long-term, however, it drops from 2.51 to 2.50 in ∼45 years at the present stage, while the particle flow contributes approximately 25% of the total rotational energy loss rate; (3) strikingly, the characteristic age has the maximum limit of ∼10 kyr, meaning that it is not always a good indicator of a real age. Furthermore, we discussed the evolutionary path of the Crab pulsar from the MDR to the wind domination by comparing with the possible wind braking candidate pulsar PSR J1734-3333.

On a Theory of the Origin of Quasi-Harmonic Bursts on the Crab Pulsar

On a Theory of the Origin of Quasi-Harmonic Bursts on the Crab Pulsar

Experimental verification of off-axis polarimetry with cadmium zinc telluride detectors of AstroSat-CZT Imager

The cadmium zinc telluride imager (CZTI) on board AstroSat consists of an array of a large number of pixelated cadmium zinc telluride (CZT) detectors capable of measuring the polarization of incident hard x-rays. The polarization measurement capability of CZTI for on-axis sources was experimentally confirmed before the launch. CZTI has yielded tantalizing results on the x-ray polarization of the Crab nebula and pulsar in the energy range of 100 to 380 keV. CZTI has also contributed to the measurement of prompt emission polarization for several gamma-ray bursts (GRBs). However, polarization measurements of off-axis sources such as GRBs are challenging. It is vital to experimentally calibrate the CZTI sensitivity to off-axis sources to enhance the credence of the measurements. In this context, we report the verification of the off-axis polarimetric capability of pixelated CZT detectors through controlled experiments carried out with a CZT detector similar to that used in CZTI and extensive Geant4 simulations of the experimental setup. Our current results show that the CZT detectors can be used to measure the polarization of bright GRBs with off-axis angles of up to ∼60 deg. However, at incidence angles between 45 deg and 60 deg, there might be some systematic effects that need to be taken into account when interpreting the measured polarization fraction.

Extending the energy range of AstroSat-CZTI up to 380 keV with compton spectroscopy

ABSTRACT The CZTI (Cadmium Zinc Telluride Imager) onboard AstroSat is a high energy coded mask imager and spectrometer in the energy range of 20–100 keV. Above 100 keV, the dominance of Compton scattering cross-section in CZTI results in a significant number of 2-pixel Compton events and these have been successfully utilized for polarization analysis of Crab pulsar and nebula (and transients like Gamma-ray bursts) in 100–380 keV. These 2-pixel Compton events can also be used to extend the spectroscopic energy range of CZTI up to 380 keV for bright sources. However, unlike the spectroscopy in primary energy range, where simultaneous background measurement is available from masked pixels, Compton spectroscopy requires blank sky observation for background measurement. Background subtraction, in this case, is non-trivial because of the presence of both short-term and long-term temporal variations in the data, which depend on multiple factors like earth rotation and the effect of South Atlantic Anomaly (SAA) regions etc. We have developed a methodology of background selection and subtraction that takes into account for these effects. Here, we describe these background selection and subtraction techniques and validate them using spectroscopy of Crab in the extended energy range of 30–380 keV region, and compare the obtained spectral parameters with the INTEGRAL results. This new capability allows for the extension of the energy range of AstroSat spectroscopy and will also enable the simultaneous spectropolarimetric study of other bright sources like Cygnus X-1.

A novel pulsar-based template-independent navigation method

AbstractBecause of the high photon flux, the Crab nebula pulsar is widely used as the observation target for X-ray pulsar-based navigation. The built profile of the Crab pulsar will change over time, however, which means that the pre-calibrated template cannot be used for the long term. In this paper, a novel pulsar-based template-independent navigation method is proposed. The detected phase propagation model is given as a term of position of the vehicle, taking the orbital motion into account. A different method of time-of-arrival process between the recovered profiles is introduced. With the aid of orbital transition matrix, a measurement model is derived to be a term of velocity error of the vehicle varying with time. The state errors of the vehicle are transformed into velocity errors by performing multi-segment observations to achieve the navigation system observability. The navigation equations of the system are then established and can be solved directly. Some simulations are performed to verify the method and suggest that the proposed method is feasible, effective and easy to implement. The precise orbit information of the vehicle can be determined. The state estimation accuracy is basically consistent with the traditional filtering algorithms, and the computational cost is still very low.

Single Pulse Dispersion Measure of the Crab Pulsar

We investigate the use of bright single pulses from the Crab pulsar to determine separately the dispersion measure (DM) for the Main Pulse and Interpulse components. We develop two approaches using cross-correlation functions (CCFs). The first method computes the CCF of the total intensity of each of the 64 frequency channels with a reference channel and converts the time lag of maximum correlation into a DM. The second method separately computes the CCF between every pair of channels for each individual bright pulse and extracts an average DM from the distribution of all channel-pair DMs. Both methods allow the determination of the DM with a relative uncertainty of better than 10−5 and provide robust estimates for the uncertainty of the best-fit value. We find differences in DM between the Main Pulse, the Low Frequency Interpulse, and the High Frequency Interpulse using both methods in a frequency range from 4 to 6 GHz. Earlier observations of the High Frequency Interpulse carried out by Hankins et al. (2016) resulted in DMHFIP–DMMP of 0.010 ± 0.016 pc cm−3. Our results indicate a DMHFIP–DMMP of 0.0127 ± 0.0011 pc cm−3 (with DMcomp being the DM value of the respective emission component), confirming earlier results with an independent method. During our studies we also find a relation between the brightness of single pulses in the High Frequency Interpulse and their DM. We also discuss the application of the developed methods on the identification of substructures in the case of Fast Radio Bursts.

Searches for Gravitational Waves from Known Pulsars at Two Harmonics in the Second and Third LIGO-Virgo Observing Runs

We present a targeted search for continuous gravitational waves (GWs) from 236 pulsars using data from the third observing run of LIGO and Virgo (O3) combined with data from the second observing run (O2). Searches were for emission from the l = m = 2 mass quadrupole mode with a frequency at only twice the pulsar rotation frequency (single harmonic) and the l = 2, m = 1, 2 modes with a frequency of both once and twice the rotation frequency (dual harmonic). No evidence of GWs was found, so we present 95% credible upper limits on the strain amplitudes h 0 for the single-harmonic search along with limits on the pulsars’ mass quadrupole moments Q 22 and ellipticities ε. Of the pulsars studied, 23 have strain amplitudes that are lower than the limits calculated from their electromagnetically measured spin-down rates. These pulsars include the millisecond pulsars J0437−4715 and J0711−6830, which have spin-down ratios of 0.87 and 0.57, respectively. For nine pulsars, their spin-down limits have been surpassed for the first time. For the Crab and Vela pulsars, our limits are factors of ∼100 and ∼20 more constraining than their spin-down limits, respectively. For the dual-harmonic searches, new limits are placed on the strain amplitudes C 21 and C 22. For 23 pulsars, we also present limits on the emission amplitude assuming dipole radiation as predicted by Brans-Dicke theory.

Implementation of the Polarimetry Focusing Telescope Array Observation Simulator on board the X-Ray Timing and Polarimetry Observatory

An observation simulator is established, on an event-by-event basis, for the Polarimetry Focusing telescope Array (PFA) on board the planned enhanced X-ray Timing and Polarimetry observatory (eXTP). An event generator, based on XIMPOL, is used to sample the parameters of the X-rays reaching the aperture of the telescope. The trajectories and interactions of X-rays through the telescope and the corresponding secondaries are calculated using the optics and detector simulation model built in GEANT4, before being translated into signals in the pixelated readout electronics. It is shown that mirror deformation is required for the optics simulation model, and transportation of ionization electrons is required for the detector simulation model to reproduce the overall performance of the telescope. The developed tool is useful in different mission phases, such as payload optimization in the design phase, discrimination of new phenomena against known physics models in the calibration phases, and sensitivity studies of potential polarized X-ray sources in observation planning. The sensitivity of PFA to the Crab Nebula and Crab pulsar is investigated to demonstrate the application of the tool. Even with the dilution effect, space-resolved and phase-resolved polarimetry can reveal important aspects of the Crab Nebula and Crab pulsar and help break the degeneracy between different models.

Probing the New Generation Geodetic Radio Telescopes for FRB Observations

We investigate the possibility of fast radio burst (FRB) observation on new special geodetic 13[Formula: see text]m wideband radio telescopes in Very Large Base Interferometry (VLBI) and single-dish modes. The Crab Pulsar Giant Pulses (GPs) were used as a reference source of FRB. In order to verify our results we use joint simultaneous observations with 32[Formula: see text]m legacy and 13[Formula: see text]m new VLBI Global Observing System (VGOS) radio telescopes of the Quasar VLBI network in the L and S/X frequency bands. The special observation session contains two 10-min scans of Crab Pulsar. We successfully detect a total of 712 pulses with flux density [Formula: see text][Formula: see text]Jy at 1653.5[Formula: see text]MHz on 32-m antenna and 262 pulses with flux density [Formula: see text][Formula: see text]Jy at 2406.3[Formula: see text]MHz on 13-m antenna in Badary observatory. The VLBI fringes were obtained for approximately every third pulse. The energy distribution of detected pulses has a break in the power law fit at [Formula: see text] and [Formula: see text]-values are [Formula: see text]0.2 and [Formula: see text]1.8 for lower and higher energies. A GP with a fluence of the order of 190[Formula: see text][Formula: see text] in L-band was detected and 48[Formula: see text][Formula: see text] in S-band. We found that the peak coincidence of right and left circular polarizations of dedispersed data on a single antenna can provide a maximum detection rate with fixed false probability. It was shown that the best GP detection rate on 13[Formula: see text]m VGOS radio telescope was achieved at Badary observatory with 13 pulses per minute in the S-band.

On the fraction of particles involved in magneto-centrifugally generated ultra-high energy electrons in the Crab pulsar

The earthward journey of ultra high energy electrons (∼600TeV) produced in the Pulsar atmosphere by Landau damping of magneto-centrifugally excited Langmuir waves (drawing energy form the rotational slowdown) on primary electrons, is charted. It is shown, that just as they escape the light cylinder zone, the ultra-high energy particles, interacting with the medium of the Crab nebula, rapidly loose their energy via the quantum synchrotron process, producing highly energetic gamma rays ∼0.6 PeV. Interacting with the cosmic background radiation in the interstellar medium, only a tiny fraction of these ultra high energy photons (via the γγ channel) are, then transformed into electron–positron pairs. Detected flux of these photons imposes an upper limit on the fraction (4×10−7) of the magnetospheric particles involved in the process of generation of ultra-high energy photons (up to 600TeV).

Characteristics of stripes-pattern radio-emission sources

ABSTRACT An investigation of the generation mechanism for stripes-pattern radio spectra is important for an understanding of the dynamics of non-thermal electrons in several astronomical objects, including the Sun, Jupiter, and the Crab Pulsar. A new analytical study is carried out to identify the plasma characteristics of fiber- and zebra-pattern emission sources without an underlying density or magnetic model. The analysis demonstrates that the source region of the stripes emission is located underneath the reconnection point, where the ratio s of the instability growth rate to the electron gyrofrequency ωc does not equal unity; that is, s = k⊥v⊥/ωc ≠ 1. When |s| < 1, the plasma condition of the source region becomes k⊥v⊥ < ωp < ωc, where ωp is the plasma frequency, and the emission source is likely to produce a fiber radio burst. For |s| > 1, the plasma condition of the source region is ωc < ωp < k⊥v⊥, and the emission source is likely to produce zebra-pattern emission. This indicates that the magnetic field in the source region of zebra-pattern radio emission is weak and it is relatively high in the source region of fiber-pattern emission. An approach is applied to estimate the plasma parameters of a zebra-pattern emission source observed on 2011 June 21. The behaviour of the blasted medium, which is produced by magnetic reconnection, is investigated. The results show that the blasted medium propagates isothermally as a sausage-like wave for a short time during the emission. The study discusses the conditions for producing different types of striped radio emission and provides a simple computational approach that could be useful in a number of astronomical contexts.

Neutrino Rocket Jet Model: An Explanation of High-velocity Pulsars and Their Spin-down Evolution

The fact that the spatial velocity of pulsars is generally higher than that of their progenitor stars has bothered astronomers for nearly 50 years. It has been extensively argued that the high pulsar velocity should be acquired during a natal kick process on a timescale of 100 ms–10 s in the supernova explosion, in which some asymmetrical dynamical mechanism plays a key role. However, a satisfactory picture generally is still lacking. In this study, it is argued that the neutrino rocket model can well account for the high speed as well as the long-term evolution behaviors of pulsars. The neutrinos are emitted from superfluid vortex neutrons through the neutrino cyclotron radiation mechanism. The unique characters of left-handed neutrinos and right-handed antineutrinos resulting from the nonconservation of parity in weak interactions play a major role in the spatial asymmetry. The continuous acceleration of pulsars can be naturally explained by this model, which yields a maximum velocity surpassing 1000 km s−1. The alignment between the spinning axis and the direction of motion observed for the Crab pulsar (PSR 0531) and the Vela pulsar (PSR 0833) can be well accounted for. The observed correlation between the spin-down rate and the period of long-period pulsars with P ≳ 0.5 s can also be satisfactorily explained.

Invariable X-Ray Profile and Flux of the Crab Pulsar during Its Two Glitches

We compare the X-ray profiles and fluxes of the Crab pulsar before and after the glitches in 2017 and 2019, using the data collected by the Insight-HXMT, NICER, and Fermi/GBM, to test whether there is any evidence for magnetosphere rearrangement after glitch. For the 2017 glitch, the profiles from Insight-HXMT (27–200 keV) and NICER (0.5–10 keV) remain unchanged within rms 0.47% and 0.28%, respectively, while the pulsed fluxes measured by these two detectors remain stable with 1σ uncertainty of 0.07% and 0.011%. Considering that the persistent offset of the spin-down rate post-glitch is 0.13% and the X-ray luminosity of the Crab pulsar is proportional to , we find that the X-ray flux does not increase proportionally to the spin-down power at a significance of about 2.8σ by fitting the flux measurements with a Heaviside function, and thus the additional torque constantly braking the pulsar spin post-glitch is unlikely due to a global magnetosphere variation. For the 2019 glitch, after which a possible soft X-ray polarization variation was detected, the profiles remain unchanged within rms 2.02%, 0.35%, 0.90%, and 0.47% in 10–200, 0.5–10, 3–4.5, and 27–200 keV, respectively, suggesting that the geometry of the X-ray emitting region after the glitch is similar to the pre-glitch one. Therefore the possible polarization variation during the 2019 glitch is unlikely a consequence of the overall magnetosphere changes. The invariance of the pulse profiles is also verified by Kolmogorov–Smirnov tests and that of pulsed fluxes by Z-tests.