Integrated Pulse Profile Research Articles

X-ray pulsars time delay estimation using GSO-based bispectral feature points

In order to reduce the calculation time and improve the performance of X-ray pulsar-based navigation (XNAV), we choose the bispectral feature points by the glowworm swarm optimization (GSO) algorithm, and to estimate the time delay for the pulsar integrated pulse profile. The proposed method is used to extract the bispectral feature points of the standard pulsar integrated pulse profile by the GSO algorithm on the ground control center, and store these feature points into the spacecraft's database. Then to estimate the time delay, it is only necessary to calculate the self-bispectrum and the cross-bispectrum of the standard pulsar integrated pulse profile and the observed one at the extracted bispectral feature points during flying. The results showed that the proposed method not only has the advantages of the traditional bispectrum algorithm that it can suppress the Gauss noise completely, but also reduced the calculation time greatly.

A robust compressed sensing based method for X-ray Pulsar Profile construction

X-ray pulse profile is an important physical quantity for X-ray pulsar based navigation (XPNAV). In order to improve the Signal-to-Noise-Ratio (SNR) of pulse profile and reduce computation complexity, this paper proposed an efficient pulse profile construction method based on Compressed Sensing (CS). This method first builds models for standard and integrated pulse profiles. Then, a sensing matrix based on Hadamard matrix is proposed for enhancing the percentage of successful construction. Finally, based on the sparse coefficient vector calculated by the proposed CS method, a pulse profile with high SNR will be obtained. The proposed method is validated using the real data of Crab pulsar observed by Rossi X-ray Timing Explorer (RXTE). Compared with the random 0–1 matrix and random Gaussian matrix, the pulse profile can be completely constructed by using the proposed matrix when the sampling ratio is 0.6, and compared with Epoch Folding method, the proposed CS method can improve the SNR of the pulse profile at least 15.859dB when the observation time is 1s and at least 20.33dB when the observation time is 700s. The results demonstrate the high performance of the proposed method in constructing pulse profile of high SNR with short-time observation data, which can significantly facilitate the real-time and high precision time-of-arrival (TOA) estimation and the position and velocity measurement in XPNAV.

A sparse representation-based optimization algorithm for measuring the time delay of pulsar integrated pulse profile

The time delay of the pulsar integrated pulse profile relative to standard pulse profile is one of the important observations in X-ray pulsar-based navigation system, which accuracy directly affects the accuracy of the pulsar-based navigation system. In order to improve the measuring accuracy of the time delay of the pulsar integrated pulse profile and reduce computation complexity, a novel optimization algorithm based on sparse representation is proposed in this paper. This method firstly constructs a waveform-matched dictionary in accordance with standard pulse profile. On the basis of the dictionary, first order sparse coefficient vector that contains the phase information of time delay is used to represent measurement pulse profile. Then, the time delay for integrated pulse profile is calculated with the sparse coefficient by the matching pursuit algorithm. The proposed algorithm is validated with the real data observed by Rossi X-ray Timing Explorer. Comparing with the state-of-the-art fast Fourier transform algorithm, experiments show that the proposed algorithm can significantly reduce the impact of signal-to-noise ratio of the observed pulse profile on the measuring accuracy of the time delay. Even in a short observation time, the proposed algorithm can still maintain the high measuring accuracy. In addition, the measuring accuracy of the proposed algorithm can be further improved when the redundant dictionary is constructed with more sampling phase bins of the standard pulse profile.

RXTE/HEXTE ANALYSIS OF THE CRAB PULSAR GLITCH OF 2000 JULY

Hard X-ray data from the RXTE observatory (HEXTE energy range 15–240 keV) have been analyzed to obtain a phase-coherent timing solution for the Crab pulsar glitch of 2000 July 15. The results are: (1) the step change in the rotation frequency of the Crab pulsar at the epoch of the glitch is ; (2) the step change in its time derivative is ; and (3) the timescale of decay of the step change is days. The first two results are consistent with those obtained at radio frequencies by the Jodrell Bank observatory. The last result has not been quoted in the literature, but could be an underestimate due to a lack of observations very close to the glitch epoch. Through comparison with the monthly timing ephemeris published by the Jodrell group for the Crab pulsar, the time delay between the main peaks of the hard X-ray and radio pulse profiles is estimated to be +411 ± 167 μs. Although this number is not very significant, it is consistent with the number derived for the 2–16 keV energy range, using the Proportional Counter Array instrument of RXTE. The separation between the two peaks of the integrated pulse profile of the Crab pulsar and the ratio of their intensities are both statistically similar before and after the glitch. The dead time corrected integrated photon flux within the integrated pulse profile appears to decrease after the glitch, although this is not a statistically strong result. This work achieves what can be considered to be an almost absolute timing analysis of the Crab pulsar hard X-ray data.

Single-pulse and profile-variability study of PSR J1022+1001

Millisecond pulsars (MSPs) are known as highly stable celestial clocks. Nevertheless, recent studies have revealed the unstable nature of their integrated pulse profiles, which may limit the achievable pulsar timing precision. In this paper, we present a case study on the pulse profile variability of PSR J1022+1001. We have detected approximately 14,000 sub-pulses (components of single pulses) in 35-hr long observations, mostly located at the trailing component of the integrated profile. Their flux densities and fractional polarisation suggest that they represent the bright end of the energy distribution in ordinary emission mode and are not giant pulses. The occurrence of sub-pulses from the leading and trailing components of the integrated profile is shown to be correlated. For sub-pulses from the latter, a preferred pulse width of approximately 0.25 ms has been found. Using simultaneous observations from the Effelsberg 100-m telescope and the Westerbork Synthesis Radio Telescope, we have found that the integrated profile varies on a timescale of a few tens of minutes. We show that improper polarisation calibration and diffractive scintillation cannot be the sole reason for the observed instability. In addition, we demonstrate that timing residuals generated from averages of the detected sub-pulses are dominated by phase jitter, and place an upper limit of ~700 ns for jitter noise based on continuous 1-min integrations.

A Research on the Relation between the Widths of Core and Cone Components of Pulsars

The central and outer components from the radiation beam of a pulsar are called the core and cone components, respectively. It was found in some early researches that a proportion of 0.7 exists between the widths of core and cone components of pulsars. 33 pulsars with significant core and cone components are selected to verify it. The component separations are made by fitting the integrated pulse profiles of these pulsars with Gaussian functions, so as to obtain the widths and errors of all the core and cone components. The relation between the widths of core and cone components is investigated for the triple-peaked and quintuple-peaked pulsars, respectively. We find that there are no significant differences between the widths of core and cone components, the proportion of between the widths of core and cone components that reported by previous studies does not exist.

PULSE BROADENING MEASUREMENTS FROM THE GALACTIC CENTER PULSAR J1745-2900

We present temporal scattering measurements of single pulses and average profiles of PSR J1745--2900, a magnetar recently discovered only 3 arcsec away from Sagittarius A* (Sgr A*), from 1.2 - 18.95 GHz using the Effelsberg 100-m Radio Telescope, the Nan\c{c}ay Decimetric Radio Telescope, and the Jodrell Bank Lovell Telescope. Single pulse analysis shows that the integrated pulse profile above 2 GHz is dominated by pulse jitter, while below 2 GHz the pulse profile shape is dominated by scattering. The high dispersion measure and rotation measure of the magnetar suggest that it is close to Sgr A* (within ~0.1 pc). This is the first object in the GC with both pulse broadening and angular broadening measurements. We measure a pulse broadening spectral index of alpha = -3.8 +/- 0.2 and a pulse broadening time scale at 1 GHz of tau_GHz = 1.3 +/- 0.2 s, which is several orders of magnitude lower than the scattering predicted by the NE2001 model (Cordes and Lazio 2002). If this scattering timescale is representative of the GC as a whole, then previous surveys should have detected many pulsars. The lack of detections implies either our understanding of scattering in the GC is incomplete or there are fewer pulsars in the GC than previously predicted. Given that magnetars are a rare class of radio pulsar, we believe that there are many canonical and millisecond pulsars in the GC, and not surprisingly, scattering regions in the GC have complex spatial structures.

Pulsar signal detection based on S-transform

In order to increase the detection speed and to improve the detection rate in low signal-to-noise ratio, a novel detection algorithm for pulsar integrated pulse profile is proposed based on S-transform. We prove that the local S-transform spectrum of Gaussian white noise follows chi-square distribution with two degrees of freedom in this paper, and based on this, threshold processing is operated on the S-transform power spectra of cumulative signal; then, the total energy of the time-frequency power spectral after threshold processing is accumulated to construct the detecting statistics to obtain the statistic decision. Moreover, the time-frequency power spectra after threshold processing can also be used to measure the time delay of pulsar signal. The simulation result verifies the effectiveness of the proposed method which is superior to a similar method based on the Gaussian distribution; in addition, it can give the time delay with a certain accuracy.

Radio emission evolution, polarimetry and multifrequency single pulse analysis of the radio magnetar PSR J1622−4950

Here we report on observations of the radio magnetar PSR J1622-4950 at frequencies from 1.4 to 17 GHz. We show that although its flux density is varying up to a factor of ~10 within a few days, it has on average decreased by a factor of 2 over the last 700 days. At the same time, timing analysis indicates a trend of decreasing spin-down rate over our entire data set, again of about a factor of 2 over 700 days, but also an erratic variability in the spin-down rate within this time span. Integrated pulse profiles are often close to 100 per cent linearly polarized, but large variations in both the profile shape and fractional polarization are regularly observed. Furthermore, the behaviour of the position angle of the linear polarization is very complex - offsets in both the absolute position angle and the phase of the position angle sweep are often seen and the occasional presence of orthogonal mode jumps further complicates the picture. However, model fitting indicates that the magnetic and rotation axes are close to aligned. Finally, a single pulse analysis has been carried out at four observing frequencies, demonstrating that the wide pulse profile is built up of narrow spikes of emission, with widths that scale inversely with observing frequency. All three of the known radio magnetars seem to have similar characteristics, with highly polarized emission, time-variable flux density and pulse profiles, and with spectral indices close to zero.

Profile-shape stability and phase-jitter analyses of millisecond pulsars

Millisecond pulsars (MSPs) have been studied in detail since their discovery in 1982. The integrated pulse profiles of MSPs appear to be stable, which enables precision monitoring of the pulse times of arrival (TOAs). However, for individual pulses the shape and arrival phase can vary dramatically, which is known as pulse jitter. In this paper, we investigate the stability of integrated pulse profiles for 5 MSPs, and estimate the amount of jitter for PSR J0437-4715. We do not detect intrinsic profile shape variation based on integration times from ~10 to ~100 s with the provided instrumental sensitivity. For PSR J0437-4715 we calculate the jitter parameter to be f_J=0.067+-0.002, and demonstrate that the result is not significantly affected by instrumental TOA uncertainties. Jitter noise is also found to be independent of observing frequency and bandwidth around 1.4 GHz on frequency scales of <100 MHz, which supports the idea that pulses within narrow frequency scale are equally jittered. In addition, we point out that pulse jitter would limit TOA calculation for the timing observations with future telescopes like the Square Kilometre Array and the Five hundred metre Aperture Spherical Telescope. A quantitative understanding of pulse profile stability and the contribution of jitter would enable improved TOA calculations, which are essential for the ongoing endeavours in pulsar timing, such as the detection of the stochastic gravitational wave background.

An improved phase measurement method of integrated pulse profile for pulsar

Integrated profile is one of the basic characteristic of X-ray pulsar. Gaussian function fit is used to model the components of X-ray pulsar profile, and it is combined with Poisson distribution model of X-ray pulsar to analyze Cramer-Rao low bound (CRLB) of phase, phase rate estimation and relation between CRLB and profile components. Then, a time domain method using minimum entropy is proposed for profile phase and phase rate estimation, and its effectiveness is explained using simulation examples.

A method for improving the SNR of X-ray pulsar pulse profile based on Poisson distribution

The radiation model of pulsar and the construction of pulsar integrated pulse profile are discussed, and a smoothing algorithm for improving the SNR of pulsar integrated pulse profile which obeys Poisson distribution is proposed based on Kullback-leibler distance function. The formula for calculating smoothing parameter and smoothing integrated pulse profile are deduced. A simulation experiment system for X-ray pulsar based navigation is setup in order to study the key technologies of X-ray pulsar navigation. The time of arrival of individual X-ray photon from the simulation X-ray pulsar source is recorded, the integrated pulse profile is constructed and the time of arrival of pulse is calculated in the simulation system. The smoothing algorithm is verified in the simulation system, and the results show that SNR can be improved by 10 dB.

A transient component in the pulse profile of PSR J0738−4042

One of the tenets of the radio pulsar observational picture is that the integrated pulse profiles are constant with time. This assumption underpins much of the fantastic science made possible via pulsar timing. Over the past few years, however, this assumption has come under question with a number of pulsars showing pulse shape changes on a range of timescales. Here, we show the dramatic appearance of a bright component in the pulse profile of PSR J0738-4042 (B0736-40). The component arises on the leading edge of the profile. It was not present in 2004 but strongly present in 2006 and all observations thereafter. A subsequent search through the literature shows the additional component varies in flux density over timescales of decades. We show that the polarization properties of the transient component are consistent with the picture of competing orthogonal polarization modes. Faced with the general problem of identifying and characterising average profile changes, we outline and apply a statistical technique based on a Hidden Markov Model. The value of this technique is established through simulations, and is shown to work successfully in the case of low signal-to-noise profiles.

A RADIO-LOUD MAGNETAR IN X-RAY QUIESCENCE

As part of a survey for radio pulsars with the Parkes 64-m telescope we have discovered PSR J1622-4950, a pulsar with a 4.3-s rotation period. Follow-up observations show that the pulsar has the highest inferred surface magnetic field of the known radio pulsars (B ~ 3e14 G), exhibits significant timing noise and appears to have an inverted spectrum. Unlike the vast majority of the known pulsar population, PSR J1622-4950 appears to switch off for many hundreds of days and even in its on-state exhibits extreme variability in its flux density. Furthermore, the integrated pulse profile changes shape with epoch. All of these properties are remarkably similar to the only two magnetars previously known to emit radio pulsations. The position of PSR J1622-4950 is coincident with an X-ray source that, unlike the other radio pulsating magnetars, was found to be in quiescence. We conclude that our newly discovered pulsar is a magnetar - the first to be discovered via its radio emission.

Time offset measurement algorithm based on bispectrum for pulsar integrated pulse profiles

In order to improve time offset measurement precision of pulsar integrated pulse profile and enhance the capability of noise suppression, a time offset measurement algorithm based on bispectrum for pulsar integrated pulse profile was proposed. Theoretically, bispectrum can completely suppress the additive Gaussian white noise, and the time offset in the third-order cumulants will result in phase rotation in the bispectrum. Time offset measurement algorithm based on bispectrum can be deduced by contrasting self-bispectrum and cross-bispectrum and solving the extremum formula. The results of experiments show that time offset measurement algorithm based on bispectrum can suppress the additive Gaussian white noise, and its precision is higher than that based on power spectrum proposed by Taylor.

A Summary of Pulsar Circular Polarization

We update the systematic studies of circular polarization in integrated pulse profiles of Han et al. Sense reversal can occur in either core or cone components, or near the intersection between the components. The correlation between the sense of circular polarization and the sense of position angle variation for conal double pulsars is confirmed with a much larger database. Some pulsars show clear changes of circular polarization with frequency. Circular polarization is marginally different between millisecond and normal pulsars.

Circular Polarization in Pulsar Integrated Profiles: Updates

We update the systematic studies of circular polarization in integrated pulse profiles by Han et al. Data of circular polarization profiles are compiled. Sense reversals can occur in core or cone components, or near the intersection between components. The correlation between the sense of circular polarization and the sense of position angle variation for conal-double pulsars is confirmed with a much large database. Circular polarization of some pulsars has clear changes with frequency. Circular polarization of millisecond pulsars is marginally different from that of normal pulsars.

Green Bank Telescope Studies of Giant Pulses from Millisecond Pulsars

We have conducted a search for giant pulses from four millisecond pulsars using the 100m Green Bank Telescope. Coherently dedispersed time-series from PSR J0218+4232 were found to contain giant pulses of very short intrinsic duration whose energies follow power-law statistics. The giant pulses are in phase with the two minima of the radio integrated pulse profile but are phase aligned with the peaks of the X-ray profile. Historically, individual pulses more than 10-20 times the mean pulse energy have been deemed to be ``giant pulses''. As only 4 of the 155 pulses had energies greater than 10 times the mean pulse-energy, we argue the emission mechanism responsible for giant pulses should instead be defined through: (a) intrinsic timescales of microsecond or nanosecond duration; (b) power-law energy statistics; and (c) emission occurring in narrow phase-windows coincident with the phase windows of non-thermal X-ray emission. Four short-duration pulses with giant-pulse characteristics were also observed from PSR B1957+20. As the inferred magnetic fields at the light cylinders of the millisecond pulsars that emit giant pulses are all very high, this parameter has previously been considered to be an indicator of giant pulse emissivity. However, the frequency of giant pulse emission from PSR~B1957+20 is significantly lower than for other millisecond pulsars that have similar magnetic fields at their light cylinders. This suggests that the inferred magnetic field at the light cylinder is a poor indicator of the rate of emission of giant pulses.

A Search for Giant Pulses from Millisecond Pulsars

We have searched for microsecond-timescale broadband emission from a sample of 18 millisecond pulsars. Our study places strong limits on such emission from several millisecond pulsars and shows that it is only present in a small subset of millisecond pulsars. Giant pulses of up to 64 times the mean pulse energy were detected from PSR J1823-3021A in the globular cluster NGC 6624. In contrast to the giant pulses of PSR B1937+21, nearly all of the giant pulses from PSR J1823-3021A were distributed within the trailing half of the main-pulse component of the integrated pulse profile. The fact that no giant pulses were observed on the leading side of the main-pulse component suggests that giant pulses are preferentially emitted closer to the last open field line than ordinary emission. The correlation between giant pulse emissivity and spin-down luminosity in millisecond pulsars suggests that the high period derivative of PSR J1823-3021A is intrinsic and is not just an artifact of its acceleration in the gravitational potential of NGC 6624.

A Model for the Challenging "Bi-drifting" Phenomenon in PSR J0815+09

A new drifting pulsar, PSR J0815+09, was discovered in the Arecibo drift-scan searches. An intriguing feature of this source is that within the four pulse components in the integrated pulse profile, the subpulse drifting direction in the two leading components is opposite from that in the two trailing components. In the view that the leading theoretical model for pulsar subpulse drifting can only interpret one-direction subpulse drifting, the observed bi-drifting phenomenon from PSR J0815+09 poses a great challenge to the pulsar theory. The inner annular gap (IAG), a new type of inner particle accelerator, was recently proposed to explain both γ-ray and radio emission from pulsars. Here we show that the coexistence of the IAG and the conventional inner core gap offers a natural interpretation to the bi-drifting phenomenon. In particular, the peculiar drifting behavior in PSR J0815+09 can be reproduced within the inverse Compton scattering model for pulsar radio emission.