PSR B0329 Research Articles

A glitch in the millisecond pulsar J0613−0200

We present evidence for a small glitch in the spin evolution of the millisecond pulsar J0613$-$0200, using the EPTA Data Release 1.0, combined with Jodrell Bank analogue filterbank TOAs recorded with the Lovell telescope and Effelsberg Pulsar Observing System TOAs. A spin frequency step of 0.82(3) nHz and frequency derivative step of ${-1.6(39) \times 10^{-19}\,\text{Hz} \ \text{s}^{-1}}$ are measured at the epoch of MJD 50888(30). After PSR B1821$-$24A, this is only the second glitch ever observed in a millisecond pulsar, with a fractional size in frequency of ${\Delta \nu/\nu=2.5(1) \times 10^{-12}}$, which is several times smaller than the previous smallest glitch. PSR J0613$-$0200 is used in gravitational wave searches with pulsar timing arrays, and is to date only the second such pulsar to have experienced a glitch in a combined 886 pulsar-years of observations. We find that accurately modelling the glitch does not impact the timing precision for pulsar timing array applications. We estimate that for the current set of millisecond pulsars included in the International Pulsar Timing Array, there is a probability of $\sim 50$% that another glitch will be observed in a timing array pulsar within 10 years.

PSR B0329+54: STATISTICS OF SUBSTRUCTURE DISCOVERED WITHIN THE SCATTERING DISK ON RADIOASTRON BASELINES OF UP TO 235,000 km

ABSTRACT We discovered fine-scale structure within the scattering disk of PSR B0329+54 in observations with the RadioAstron ground–space radio interferometer. Here we describe this phenomenon, characterize it with averages and correlation functions, and interpret it as the result of decorrelation of the impulse-response function of interstellar scattering between the widely separated antennas. This instrument included the 10 m Space Radio Telescope, the 110 m Green Bank Telescope, the 14 × 25 m Westerbork Synthesis Radio Telescope, and the 64 m Kalyazin Radio Telescope. The observations were performed at 324 MHz on baselines of up to 235,000 km in 2012 November and 2014 January. In the delay domain, on long baselines the interferometric visibility consists of many discrete spikes within a limited range of delays. On short baselines it consists of a sharp spike surrounded by lower spikes. The average envelope of correlations of the visibility function shows two exponential scales, with characteristic delays of τ 1 = 4.1 ± 0.3 μ s and τ 2 = 23 ± 3 μ s , indicating the presence of two scales of scattering in the interstellar medium. These two scales are present in the pulse-broadening function. The longer scale contains 0.38 times the scattered power of the shorter one. We suggest that the longer tail arises from highly scattered paths, possibly from anisotropic scattering or from substructure at large angles.

STRUCTURES OF THE VELA PULSAR AND THE GLITCH CRISIS FROM THE BRUECKNER THEORY

ABSTRACT Detailed structures of the Vela pulsar (PSR B0833-45, with a period of 89.33 ms) are predicted by adopting a recently constructed unified treatment of all parts of neutron stars: the outer crust, the inner crust, and the core based on modern microscopic Brueckner–Hartree–Fock calculations. Taking a pulsar mass in the range from 1.0 to 2.0 M ⊙, we calculate the central density, the core/crust radii, the core/crustal mass, the core/crustal thickness, the moment of inertia, and the crustal moment of inertia. Among them, the crustal moment of inertia could be effectively constrained from the accumulated glitch observations, which has been a great debate recently, known as the “glitch crisis.” Namely, superfluid neutrons contained in the inner crust, which are regarded as the origin of the glitch in the standard two-component model, could be largely entrained in the nuclei lattices, and then there may not be enough superfluid neutrons (∼4/5 less than the previous value) to trigger the large glitches (Δν/ν 0 ∼ 10−6) in the Vela pulsar. By confronting the glitch observations with the theoretical calculations for the crustal moment of inertia, we find that despite some recent opposition to the crisis argument, the glitch crisis is still present, which means that besides the crustal superfluid neutrons, core neutrons might be necessary for explaining the large glitches of the Vela pulsar.

SIMULTANEOUS OBSERVATIONS OF GIANT PULSES FROM PULSAR PSR B0031-07 AT 38 AND 74 MHz

ABSTRACT The first station of the Long Wavelength Array was used to study PSR B0031-07 with simultaneous observations at 38 and 74 MHz. We found that 158 (0.35%) of the observed pulses at 38 MHz and 221 (0.49%) of the observed pulses at 74 MHz qualified as giant pulses (GPs) in a total of 12 hr of observations. GPs are defined as having flux densities of a factor of ≥90 times that of an average pulse (AP) at 38 MHz and ≥80 times that of an AP at 74 MHz. The cumulative distribution of pulse strength follows a power law, with an index of −4.2 at 38 MHz and −4.9 at 74 MHz. This distribution has a much more gradual slope than would be expected if observing the tail of a Gaussian distribution of normal pulses. The dispersion measure (DM) value which resulted in the largest signal to noise for dedispersed pulses was DM = 10.9 pc cm−3. No other transient pulses were detected in the data in the wide DM range from 1 to 5000 pc cm−3. There were 12 GPs detected within the same period from both 38 and 74 MHz, meaning that the majority of them are not generated in a wide band.

Pulsar lensing geometry

Our analysis of archival VLBI data of PSR 0834+06 revealed that its scintillation properties can be precisely modelled using the inclined sheet model (Pen & Levin 2014), resulting in two distinct lens planes. These data strongly favour the grazing sheet model over turbulence as the primary source of pulsar scattering. This model can reproduce the parameters of the observed diffractive scintillation with an accuracy at the percent level. Comparison with new VLBI proper motion results in a direct measure of the ionized ISM screen transverse velocity. The results are consistent with ISM velocities local to the PSR 0834+06 sight-line (through the Galaxy). The simple 1D structure of the lenses opens up the possibility of using interstellar lenses as precision probes for pulsar lens mapping, precision transverse motions in the ISM, and new opportunities for removing scattering to improve pulsar timing. We describe the parameters and observables of this double screen system. While relative screen distances can in principle be accurately determined, a global conformal distance degeneracy exists that allows a rescaling of the absolute distance scale. For PSR B0834+06, we present VLBI astrometry results that provide (for the fist time) a direct measurement of the distance of the pulsar. For targets where independent distance measurements are not available, which are the cases for most of the recycled millisecond pulsars that are the targets of precision timing observations, the degeneracy presented in the lens modelling could be broken if the pulsar resides in a binary system.

SIMULTANEOUS OBSERVATIONS OF GIANT PULSES FROM PULSAR PSR B0950+08 AT 42 AND 74 MHz

ABSTRACT We report the detection of giant pulse (GP) emission from PSR B0950+08 in 12 hr of observations made simultaneously at 42 and 74 MHz, using the first station of the Long Wavelength Array. We detected 275 GPs (in 0.16% of the pulse periods) and 465 GPs (0.27%) at 42 and 74 MHz, respectively. The pulsar is weaker and produces less frequent GPs than at 100 MHz. Here, GPs are taken as having ≥ ?> 10 times the flux density of an average pulse (AP); their cumulative distribution of pulse strength follows a power law, with an index of −4.1 at 42 MHz and −5.1 at 74 MHz, which is much less steep than would be expected if we were observing the tail of a Gaussian distribution of normal pulses. We detected no other transient pulses in a wide dispersion measure range from 1 to 5000 pc cm−3. There were 128 GPs detected within the same periods from both 42 and 74 MHz, which means more than half of them are not generated in a wide band. The CLEAN-based algorithm was used to deconvolve the the effect of scattering broadening and we have concluded that the scattering effect from the interstellar medium at 42 and 74 MHz is weak and cannot be distinguished from the pulse profiles. We calculated the altitude r of the emission region using the dipolar magnetic field model. We found r(42 MHz) = 29.27 km (0.242% of R LC) and r(74 MHz) = 29.01 km (0.240% of R LC) for the AP, while for GPs, r(42 MHz) = 29.10 km (0.241% of R LC) and r(74 MHz) = 28.95 km (0.240% of R LC). GPs, which have a double-peak structure, have a smaller mean peak-to-peak separation compared to the AP.

MULTI-FREQUENCY RADIO PROFILES OF PSR B1133+16: RADIATION LOCATION AND PARTICLE ENERGY

ABSTRACT The pulse profile of PSR B1133+16 is usually regarded as a conal double structure. However, its multi-frequency profiles cannot simply be fitted with two Gaussian functions, and a third component is always needed to fit the bridge region (between two peaks). This would introduce additional, redundant parameters. In this paper, through a comparison of five fitting functions (Gaussian, von Mises, hyperbolic secant, square hyperbolic secant, and Lorentz), it is found that the square hyperbolic secant function can best reproduce the profile, yielding an improved fit. Moreover, a symmetric 2D radiation beam function, instead of a simple 1D Gaussian function, is used to fit the profile. Each profile with either well-resolved or not-so-well-resolved peaks could be fitted adequately using this beam function, and the bridge emission between the two peaks does not need to be a new component. Adopting inclination and impact angles based on polarization measurements, the opening angle ( θ &mgr; 0 ?> ) of the radiation beam in a certain frequency band is derived from beam-function fitting. The corresponding radiation altitudes are then calculated. Based on multi-frequency profiles, we also computed the Lorentz factors of the particles and their dispersion at those locations in both the curvature-radiation and inverse-Compton-scattering models. We found that the Lorentz factors of the particles decrease rapidly as the radiation altitude increases. Besides, the radiation prefers to be generated in an annular region rather than the core region, and this needs further validation.

X-Ray Pulsar Profile Recovery Based on Tracking-Differentiator

The profile recovery is an important work in X-ray pulsar-based navigation. It is a key step for the analysis on the pulsar signal’s characteristic and the computing of time of arrival (TOA). This paper makes an argument for an algorithm based on the tracking-differentiator (TD) to recover the profile from the low Signal-to-Noise Ratio (SNR) signals. In the method, a TD filter with cascade structure is designed which has very low phase delay and amplitude distortion. In the simulation experiment, two typical pulsars (PSR B0531+21 and PSR B1937+21) are used to verify the algorithm’s performance. The simulation results show that the method satisfies the application requirements in the aspects of SNR and profile fidelity. By processing the data collected by the Rossi X-Ray Timing Explorer (RXTE) satellite in space, similar results can also be achieved.

Time delay estimation method of X-ray pulsar observed profile based on the optimal frequency band

In order to improve the time delay estimation accuracy of the observed profile in the X-ray pulsar based navigation, the spectral characteristics of the observed profile of X-ray pulsar and the drawback of the classical Taylor fast Fourier transform (FFT) time delay estimation method are analyzed. It is found that when estimating the time delay, we can abandon the higher frequency components that are always affected by noise seriously, but only utilize the information about the low frequency part. Based on this idea, by modifying the weigh function of the classical Taylor FFT time delay estimation method, a new time delay estimation algorithm based on the optimal frequency band is proposed, in which the optimal frequency band is determined by establishing the relationship between the selected frequency band and the time delay estimation accuracy under different signal-to-noise ratios (SNRs). Then by using the real data obtained with the proportional counter array, the low-energy (2-60 keV) detection instrument boarded on the Rossi X-ray Timing Explorer satellite, the optimal frequency as a function the SNR of observed profile is given for the PSR B0531+21 (namely the Crab pulsar) through the Monte-Carlo technique. Since the parameters of different pulsars are known, in practical navigation, the optimal frequency in an observation time for a certain pulsar can be estimated in advance by using the simulation data or the obtained real data of the pulsar, which can remarkably alleviate the onboard computational burden. Finally, a series of numerical simulations and experiments using real data of Crab pulsar are designed to evaluate the performance of the proposed time delay estimation algorithm. The main results can be summarized as follows: the proposed estimator outperforms the normally used fast approximate maximum-likelihood (FAML), cross correlation (CC), nonlinear least square (NLS) and weighted nonlinear least-square (WNLS) estimators when the observation time is short or the source flux is small; when the observation time is long or the source flux is large, its estimation accuracy is almost the same as those of CC and NLS estimators and lower than those of the FAML and WNLS estimators, but its computational complexity is smaller than those of NLS, FAML and WNLS estimators. The above results indicate the high estimation accuracy and high computational efficiency of the proposed time delay estimation method, which can be used in the case that the observation time is restricted to be short or the source flux of the usable pulsar is small in X-ray pulsar based navigation.

Magnetic field growth in young glitching pulsars with a braking index

In the standard scenario for spin evolution of isolated neutron stars, a young pulsar slows down with a surface magnetic field B that does not change. Thus the pulsar follows a constant B trajectory in the phase space of spin period and spin period time derivative. Such an evolution predicts a braking index n = 3 while the field is constant and n > 3 when the field decays. This contrasts with all nine observed values being n < 3. Here we consider a magnetic field that is buried soon after birth and diffuses to the surface. We use a model of a growing surface magnetic field to fit observations of the three pulsars with lowest n: PSR J0537-6910 with n = -1.5, PSR B0833-45 (Vela) with n = 1.4, and PSR J1734-3333 with n = 0.9. By matching the age of each pulsar, we determine their magnetic field and spin period at birth and confirm the magnetar-strength field of PSR J1734-3333. Our results indicate that all three pulsars formed in a similar way to central compact objects (CCOs), with differences due to the amount of accreted mass. We suggest that magnetic field emergence may play a role in the distinctive glitch behaviour of low braking index pulsars, and we propose glitch behaviour and characteristic age as possible criteria in searches for CCO descendants.

Modeling the evolution and distribution of the frequency's second derivative and the braking index of pulsar spin**Supported by the National Natural Science Foundation of China.

We model the evolution of the spin frequency's second derivative v̈ and the braking index n of radio pulsars with simulations within the phenomenological model of their surface magnetic field evolution, which contains a long-term power-law decay modulated by short-term oscillations. For the pulsar PSR B0329+54, a model with three oscillation components can reproduce its v̈ variation. We show that the “averaged” n is different from the instantaneous n, and its oscillation magnitude decreases abruptly as the time span increases, due to the “averaging” effect. The simulated timing residuals agree with the main features of the reported data. Our model predicts that the averaged v̈ of PSR B0329+54 will start to decrease rapidly with newer data beyond those used in Hobbs et al. We further perform Monte Carlo simulations for the distribution of the reported data in |v̈| and |n| versus characteristic age τC diagrams. It is found that the magnetic field oscillation model with decay index α = 0 can reproduce the distributions quite well. Compared with magnetic field decay due to the ambipolar diffusion (α = 0.5) and the Hall cascade (α = 1.0), the model with no long term decay (α = 0) is clearly preferred for old pulsars by the p-values of the two-dimensional Kolmogorov-Smirnov test.

A Bayesian method for pulsar template generation

Extracting Times of Arrival from pulsar radio signals depends on the knowledge of the pulsars pulse profile and how this template is generated. We examine pulsar template generation with Bayesian methods. We will contrast the classical generation mechanism of averaging intensity profiles with a new approach based on Bayesian inference. We introduce the Bayesian measurement model imposed and derive the algorithm to reconstruct a "statistical template" out of noisy data. The properties of these "statistical templates" are analysed with simulated and real measurement data from PSR B1133+16. We explain how to put this new form of template to use in analysing secondary parameters of interest and give various examples: We implement a nonlinear filter for determining ToAs of pulsars. Applying this method to data from PSR J1713+0747 we derive ToAs self consistently, meaning all epochs were timed and we used the same epochs for template generation. While the average template contains fluctuations and noise as unavoidable artifacts, we find that the "statistical template" derived by Bayesian inference quantifies fluctuations and remaining uncertainty. This is why the algorithm suggested turns out to reconstruct templates of statistical significance from ten to fifty single pulses. A moving data window of fifty pulses, taking out one single pulse at the beginning and adding one at the end of the window unravels the characteristics of the methods to be compared. It shows that the change induced in the classical reconstruction is dominated by random fluctuations for the average template, while statistically significant changes drive the dynamics of the proposed method's reconstruction. The analysis of phase shifts with simulated data reveals that the proposed nonlinear algorithm is able to reconstruct correct phase information along with an acceptable estimation of the remaining uncertainty.

MODELING MULTI-WAVELENGTH PULSE PROFILES OF THE MILLISECOND PULSAR PSR B1821–24

PSR B1821$-$24 is a solitary millisecond pulsar (MSP) which radiates multi-wavelength pulsed photons. It has complex radio, X-ray and $\gamma$-ray pulse profiles with distinct peak phase-separations that challenge the traditional caustic emission models. Using the single-pole annular gap model with suitable magnetic inclination angle ($\alpha=40^\circ$) and viewing angle ($\zeta=75^\circ$), we managed to reproduce its pulse profiles of three wavebands. It is found that the middle radio peak is originated from the core gap region at high altitudes, and the other two radio peaks are originated from the annular gap region at relatively low altitudes. Two peaks of both X-ray and $\gamma$-ray wavebands are fundamentally originated from annular gap region, while the $\gamma$-ray emission generated from the core gap region contributes somewhat to the first $\gamma$-ray peak. Precisely reproducing the multi-wavelength pulse profiles of PSR B1821$-$24 enables us to understand emission regions of distinct wavebands and justify pulsar emission models.

OBSERVATIONS OF GIANT PULSES FROM PULSAR B0950+08 USING LWA1

We report the detection of giant pulse emission from PSR B0950+08 in 24 hours of observations made at 39.4 MHz, with a bandwidth of 16 MHz, using the first station of the Long Wavelength Array, LWA1. We detected 119 giant pulses from PSR B0950+08 (at its dispersion measure), which we define as having SNRs at least 10 times larger than for the mean pulse in our data set. These 119 pulses are 0.035% of the total number of pulse periods in the 24 hours of observations. The rate of giant pulses is about 5.0 per hour. The cumulative distribution of pulse strength $S$ is a steep power law, $N(>S)\propto S^{-4.7}$, but much less steep than would be expected if we were observing the tail of a Gaussian distribution of normal pulses. We detected no other transient pulses in a dispersion measure range from 1 to 90 pc cm$^{-3}$, in the beam tracking PSR B0950+08. The giant pulses have a narrower temporal width than the mean pulse (17.8 ms, on average, vs. 30.5 ms). The pulse widths are consistent with a previously observed weak dependence on observing frequency, which may be indicative of a deviation from a Kolmogorov spectrum of electron density irregularities along the line of sight. The rate and strength of these giant pulses is less than has been observed at $\sim$100 MHz. Additionally, the mean (normal) pulse flux density we observed is less than at $\sim$100 MHz. These results suggest this pulsar is weaker and produces less frequent giant pulses at 39 MHz than at 100 MHz.

Explaining the subpulse drift velocity of pulsar magnetosphere within the space-charge limited flow model

We try to explain the subpulse drift phenomena adopting the space-charge limited flow (SCLF) model and comparing the plasma drift velocity in the inner region of pulsar magnetospheres with the observed velocity of drifting subpulses. We apply the approach described in a recent paper of van Leeuwen & Timokhin (2012), where it was shown that the standard estimation of the subpulse drift velocity through the total value of the scalar potential drop in the inner gap gives inaccurate results, while the exact expression relating the drift velocity to the gradient of the scalar potential should be used instead. After considering a selected sample of sources taken from the catalog of Weltevrede, Edwards & Stappers (2006) with coherently drifting subpulses and reasonably known observing geometry, we show that their subpulse drift velocities would correspond to the drift of the plasma located very close or above the pair formation front. Moreover, a detailed analysis of PSR B0826-34 and PSR B0818-41 reveals that the variation of the subpulse separation with the pulse longitude can be successfully explained by the dependence of the plasma drift velocity on the angular coordinates.

Analysis of single pulse radio flux measurements of PSR B1133+16 at 4.85 and 8.35 GHz

We show the results of microsecond resolution radio data analysis focused on flux measurements of single pulses of PSR B1133+16. The data were recorded at 4.85 GHz and 8.35 GHz with 0.5 GHz and 1.1 GHz bandwidth, respectively, using Radio Telescope Effelsberg (MPIfR). The most important conclusion of the analysis is, that the strongest single pulse emission at 4.85 GHz and 8.35 GHz contributes almost exclusively to the trailing part of the leading component of the pulsar mean profile, whereas studies at lower frequencies report that the contribution is spread almost uniformly covering all phases of the pulsar mean profile. We also estimate the radio emission heights to be around 1%--2% of the light cylinder radius which is in agreement with previous studies. Additionally these observations allowed us to add two more measurements of the flux density to the PSR B1133+16 broadband radio spectrum covering frequencies from 16.7 MHz up to 32 GHz. We fit two different models to the spectrum: the broken power law and the spectrum based on flicker noise model, which represents the spectrum in a simpler but similarly accurate way.

X-ray pulsar signal detection using photon interarrival time

The distribution probability of the photon interarrival time (PIT) without signal initial phases is derived based on the Poisson model of X-ray pulsar signals, and a pulsar signal detection algorithm employing the PIT sequence is put forward. The joint probability of the PIT sequence is regarded as a function of the distribution probability and used to compare a constant radiation intensity model with the nonhomogeneous Poisson model for the signal detection. The relationship between the number of detected photons and the probabilities of false negative and positive is studied, and the success rate and mean detection time are estimated based on the number of the given photons. For the spacecraft velocity data detection, the changes of time of photon arrival (TOPA) and PIT caused by spacecraft motion are presented first, then the influences on detection are analyzed respectively. By using the analytical pulse profile of PSR B0531+21, the simulation of the X-ray pulsar signal detection is implemented. The simulation results verify the effectiveness of the proposed method, and the contrast tests show that the proposed method is suitable for the spacecraft velocity data detection.

On the PSR B1133+16 optical counterpart★

The aim of this work is confirming the optical identification of PSR B1133+16, whose candidate optical counterpart was detected in Very Large Telescope (VLT) images obtained back in 2003. We used new deep optical images of the PSR B1133+16 field obtained with both the 10.4 m Gran Telescopio Canarias (GTC) and the VLT in the g' and B bands, respectively, to confirm the detection of its candidate optical counterpart and its coincidence with the most recent pulsar's radio coordinates. We did not detect any object at the position of the pulsar candidate counterpart (B~28), measured in our 2003 VLT images. However, we tentatively detected an object of comparable brightness in both the 2012 GTC and VLT images, whose position is offset by ~3.03" from that of the pulsar's candidate counterpart in the 2003 VLT images and lies along the pulsar's proper motion direction. Accounting for the time span of ~9 years between the 2012 quasi-contemporary GTC and VLT images and the 2003 VLT one, this offset is consistent with the yearly displacement of the pulsar due to its proper motion. Therefore, both the flux of the object detected in the 2012 GTC and VLT images and its position, consistent with the proper motion-corrected pulsar radio coordinates, suggest that we have detected the candidate pulsar counterpart that has moved away from its 2003 discovery position.

THE VELA-X PULSAR WIND NEBULA REVISITED WITH FOUR YEARS OFFERMILARGE AREA TELESCOPE OBSERVATIONS

The Vela supernova remnant is the closest supernova remnant to Earth containing an active pulsar, the Vela pulsar (PSR B0833-45). This pulsar is the archetype of the middle-aged pulsar class and powers a bright pulsar wind nebula (PWN), Vela-X, spanning a region of 2{\deg} x 3{\deg} south of the pulsar and observed in the radio, X-ray and very high energy gamma-ray domains. The detection of the Vela-X PWN by the Fermi Large Area Telescope (LAT) was reported in the first year of the mission. Subsequently, we have re-investigated this complex region and performed a detailed morphological and spectral analysis of this source using 4 years of Fermi-LAT observations. This study lowers the threshold for morphological analysis of the nebula from 0.8 GeV to 0.3 GeV, allowing inspection of distinct energy bands by the LAT for the first time. We describe the recent results obtained on this PWN and discuss the origin of the newly detected spatial features.

PSR B1133+16: radio emission height and plasma composition

Abstract Recent operation of LOFAR by Hassall et al. has produced severe constraints on the size and altitude of the 40 MHz emission region in this pulsar. It is shown that these limits, given a limited number of unexceptionable assumptions, demonstrate that an electron–positron plasma cannot be the source of the emission. A physically acceptable plasma source composed of protons and ions arises naturally in pulsars having positive corotational polar-cap charge density. Acceptance of this would greatly clarify the classification of pulsar types within the whole.