Individual Pulsars Research Articles

The Galactic population of canonical pulsar. II. Taking into account several evolutionary paths: Interstellar medium interaction, Galactic potential, and a death valley

Pulsars are highly magnetised rotating neutron stars, emitting in a broad electromagnetic energy range. These objects were discovered more than 55 years ago and are astrophysical laboratories for studying physics at extreme conditions. Reproducing the observed pulsar population helps refine our understanding of their formation and evolution scenarios, as well as their radiation processes and geometry. In this paper, we improve our previous population synthesis by focusing on both the radio and gamma -ray pulsar populations, investigating the impact of the Galactic gravitational potential and of the radio emission death line. To elucidate the necessity of a death line, we implemented our refined initial distributions of the spin period and spacial position at birth. This approach allowed us to elevate the sophistication of our simulations to the most recent state-of-the-art approaches. The motion of each individual pulsar was tracked in the Galactic potential by a fourth-order symplectic integration scheme. Our pulsar population synthesis took into account the secular evolution of the force-free magnetosphere and magnetic field decay simultaneously and self-consistently. Each pulsar was evolved from birth to the present time. The radio and gamma -ray emission locations were modelled by the polar cap geometry and striped wind model, respectively. By simulating ten million pulsars, we found that including a death line allows us to better reproduce the observational trend. However, when simulating one million pulsars, we obtained an even more realistic $P- P $ diagram, whether or not a death line was included. This suggests that the ages of the detected pulsars might be overestimated and so, it sets the need for a death line in pulsar population studies into question. Kolmogorov-Smirnov tests confirm the statistical similarity between the observed and simulated $P- P $ diagram. Additionally, simulations with increased gamma -ray telescope sensitivities hint at a significant contribution coming from the gamma -ray pulsars to the GeV excess in the Galactic centre.

Topology of Pulsar Profiles (ToPP)

Some of the most important information on a radio pulsar is derived from its average pulse profile. Many early pulsar studies were necessarily based on only a few such profiles. In these studies, discrete profile components were linked to emission mechanism models for individual stars through human interpretation. For the population as a whole, profile morphology must reflect the geometry and overall evolution of the radio emitting regions. The problem, however, is that this population is becoming too large for individual intensive studies of each source. Moreover, connecting profiles from a large collection of pulsars rapidly becomes cumbersome. In this article, we present ToPP, the first-ever unsupervised method to sort pulsars by profile-shape similarity using graph topology. We applied ToPP to the publicly available European Pulsar Network profile database, providing the first organised visual overview of multi-frequency profiles representing 90 individual pulsars. We found discrete evolutionary tracks varying from simple single-component profiles at all frequencies towards diverse mixtures of more complex profiles with frequency evolution. The profile evolution is continuous, extending out to millisecond pulsars, and does not fall into sharp classes. We interpret the profiles as being a mixture of pulsar core-cone emission type, spin-down energetics, and the line-of-sight impact angle towards the magnetic axis. We show how ToPP can systematically classify sources into the Rankin empirical profile scheme. ToPP comprises one of the key unsupervised methods that will be essential to exploring upcoming pulsar census data, such as the data expected from the Square Kilometer Array.

Multi-wavelength pulse profiles from the force-free neutron star magnetosphere

Context. The last two decades have witnessed dramatic progress in our understanding of neutron star magnetospheres thanks to force-free and particle-in-cell simulations. However, the associated particle dynamics and its emission mechanisms and locations have not been fully constrained, notably in X-rays. Aims. In this paper, we compute a full atlas of radio, X-ray, and γ-ray pulse profiles, relying on the force-free magnetosphere model. Our goal is to use such a data bank of multi-wavelength profiles to fit a substantial number of radio-loud γ-ray pulsars that have also been detected in non-thermal X-rays to decipher the X-ray radiation mechanism and sites. Using results from the third γ-ray pulsar catalogue (3PC), we investigate the statistical properties of this population. Methods. We assume that radio emission emanates from field lines rooted to the polar caps, at varying height above the surface, close to the surface, at an altitude about 5–10% of the light cylinder radius, r L. The X-ray photons are produced in the separatrix region within the magnetosphere; that is, the current sheet formed by the jump from closed to open magnetic field lines. We allow for substantial variations in emission height. The γ-rays are produced within the current sheet of the striped wind, outside the light cylinder. Results. A comprehensive set of radio, X-ray, and γ-ray light curves was computed. Based on only geometric considerations about magnetic obliquity, line-of-sight inclination, and the radio beam cone opening angle, pulsars can be classified as radio-loud or quiet and as γ-ray-loud or quiet. We found that the 3PC sample is compatible with an isotropic distribution of obliquity and line of sight. Conclusions. The atlases constructed in this work are the fundamental tools with which to explore individual pulsars and fit their multi-wavelength pulse profiles in order to constrain their magnetic topology, the emission sites, and the observer’s line of sight.

The thousand-pulsar-array programme on MeerKAT XIII: Timing, flux density, rotation measure and dispersion measure timeseries of 597 pulsars

Abstract We report here on the timing of 597 pulsars over the last four years with the MeerKAT telescope. We provide Times-of-Arrival, pulsar ephemeris files and per-epoch measurements of the flux density, dispersion measure (DM) and rotation measure (RM) for each pulsar. In addition we use a Gaussian process to model the timing residuals to measure the spin frequency derivative at each epoch. We also report the detection of 11 glitches in 9 individual pulsars. We find significant DM and RM variations in 87 and 76 pulsars respectively. We find that the DM variations scale approximately linearly with DM, which is broadly in agreement with models of the ionised interstellar medium. The observed RM variations seem largely independent of DM, which may suggest that the RM variations are dominated by variations in the interstellar magnetic field on the line of sight, rather than varying electron density. We also find that normal pulsars have around 5 times greater amplitude of DM variability compared to millisecond pulsars, and surmise that this is due to the known difference in their velocity distributions.

A stacked search for spatial coincidences between IceCube neutrinos and radio pulsars

We carry out a stacked search for spatial coincidences between all the known radio pulsars and TeV neutrinos from the IceCube 10 year (2008–2018) muon track data, as a followup to our previous work on searching for spatial coincidences with individual pulsars. We consider three different weighting schemes to stack the contributions from each pulsar. We do not find a statistically significant excess using this method. We report the 95% c.l. neutrino flux upper limit as a function of the neutrino energy. We have also made our analysis codes publicly available.

Characterizing the Gamma-Ray Emission Properties of the Globular Cluster M5 with the Fermi-LAT

We analyzed the globular cluster M5 (NGC 5904) using 15 yr of gamma-ray data from the Fermi Large Area Telescope (LAT). Using rotation ephemerides generated from Arecibo and FAST radio telescope observations, we searched for gamma-ray pulsations from the seven millisecond pulsars (MSPs) identified in M5. We detected no significant pulsations from any of the individual pulsars. In addition, we searched for possible variations of the gamma-ray emission as a function of orbital phase for all six MSPs in binary systems, but we did not detect any significant modulations. The gamma-ray emission from the direction of M5 is well described by an exponentially cutoff power-law spectral model, although other models cannot be excluded. The phase-averaged emission is consistent with being steady on a timescale of a few months. We estimate the number of MSPs in M5 to be between 1 and 10, using the gamma-ray conversion efficiencies for well-characterized gamma-ray MSPs in the Third Fermi-LAT Catalog of Gamma-ray Pulsars, suggesting that the sample of known MSPs in M5 is (nearly) complete, even if it is not currently possible to rule out a diffuse component of the observed gamma rays from the cluster.

A Gaussian-processes approach to fitting for time-variable spherical solar wind in pulsar timing data

ABSTRACT Propagation effects are one of the main sources of noise in high-precision pulsar timing. For pulsars below an ecliptic latitude of 5°, the ionized plasma in the solar wind can introduce dispersive delays of order $100\, \mu \mathrm{s}$ around solar conjunction at an observing frequency of 300 MHz. A common approach to mitigate this assumes a spherical solar wind with a time-constant amplitude. However, this has been shown to be insufficient to describe the solar wind. We present a linear, Gaussian-process piecewise Bayesian approach to fit a spherical solar wind of time-variable amplitude, which has been implemented in the pulsar software run_enterprise. Through simulations, we find that the current EPTA+InPTA data combination is not sensitive to such variations; however, solar wind variations will become important in the near future with the addition of new InPTA data and data collected with the low-frequency LOFAR telescope. We also compare our results for different high-precision timing data sets (EPTA+InPTA, PPTA, and LOFAR) of 3 ms pulsars (J0030+0451, J1022+1001, J2145−0450), and find that the solar-wind amplitudes are generally consistent for any individual pulsar, but they can vary from pulsar to pulsar. Finally, we compare our results with those of an independent method on the same LOFAR data of the three millisecond pulsars. We find that differences between the results of the two methods can be mainly attributed to the modelling of dispersion variations in the interstellar medium, rather than the solar wind modelling.

The second data release from the European Pulsar Timing Array

Pulsar timing arrays offer a probe of the low-frequency gravitational wave spectrum (1–100 nHz), which is intimately connected to a number of markers that can uniquely trace the formation and evolution of the Universe. We present the dataset and the results of the timing analysis from the second data release of the European Pulsar Timing Array (EPTA). The dataset contains high-precision pulsar timing data from 25 millisecond pulsars collected with the five largest radio telescopes in Europe, as well as the Large European Array for Pulsars. The dataset forms the foundation for the search for gravitational waves by the EPTA, presented in associated papers. We describe the dataset and present the results of the frequentist and Bayesian pulsar timing analysis for individual millisecond pulsars that have been observed over the last ~25 yr. We discuss the improvements to the individual pulsar parameter estimates, as well as new measurements of the physical properties of these pulsars and their companions. This data release extends the dataset from EPTA Data Release 1 up to the beginning of 2021, with individual pulsar datasets with timespans ranging from 14 to 25 yr. These lead to improved constraints on annual parallaxes, secular variation of the orbital period, and Shapiro delay for a number of sources. Based on these results, we derived astrophysical parameters that include distances, transverse velocities, binary pulsar masses, and annual orbital parallaxes.

Pulsar polarization: a partial-coherence model

ABSTRACT The population of radio pulsars is observed to demonstrate certain polarization properties not explained by the conventional picture of pulsar polarization, namely frequency evolution of polarization, deviations of the linear polarization angle from a curve of geometric origins, and the presence of features in the circular polarization. We present the partial-coherence model as a way to explain the co-occurrence of these features and to provide an origin for circular polarization in radio pulsar profiles. We describe the mathematics of the model and demonstrate how it can explain these observed features, both on a population level and for the idiosyncrasies of individual pulsars. The partial coherence model can account for complex polarization behaviour, enabling improved access to information about pulsar geometries. We discuss the scientific implications of this for our understanding of pulsar radio emission and propagation.

The NANOGrav 15 yr Data Set: Detector Characterization and Noise Budget

Pulsar timing arrays (PTAs) are galactic-scale gravitational wave (GW) detectors. Each individual arm, composed of a millisecond pulsar, a radio telescope, and a kiloparsecs-long path, differs in its properties but, in aggregate, can be used to extract low-frequency GW signals. We present a noise and sensitivity analysis to accompany the NANOGrav 15 yr data release and associated papers, along with an in-depth introduction to PTA noise models. As a first step in our analysis, we characterize each individual pulsar data set with three types of white-noise parameters and two red-noise parameters. These parameters, along with the timing model and, particularly, a piecewise-constant model for the time-variable dispersion measure, determine the sensitivity curve over the low-frequency GW band we are searching. We tabulate information for all of the pulsars in this data release and present some representative sensitivity curves. We then combine the individual pulsar sensitivities using a signal-to-noise ratio statistic to calculate the global sensitivity of the PTA to a stochastic background of GWs, obtaining a minimum noise characteristic strain of 7 × 10−15 at 5 nHz. A power-law-integrated analysis shows rough agreement with the amplitudes recovered in NANOGrav’s 15 yr GW background analysis. While our phenomenological noise model does not model all known physical effects explicitly, it provides an accurate characterization of the noise in the data while preserving sensitivity to multiple classes of GW signals.

Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array

Pulsar timing arrays aim to detect nanohertz-frequency gravitational waves (GWs). A background of GWs modulates pulsar arrival times and manifests as a stochastic process, common to all pulsars, with a signature spatial correlation. Here we describe a search for an isotropic stochastic gravitational-wave background (GWB) using observations of 30 millisecond pulsars from the third data release of the Parkes Pulsar Timing Array (PPTA), which spans 18 yr. Using current Bayesian inference techniques we recover and characterize a common-spectrum noise process. Represented as a strain spectrum , we measure and α = −0.45 ± 0.20, respectively (median and 68% credible interval). For a spectral index of α = −2/3, corresponding to an isotropic background of GWs radiated by inspiraling supermassive black hole binaries, we recover an amplitude of . However, we demonstrate that the apparent signal strength is time-dependent, as the first half of our data set can be used to place an upper limit on A that is in tension with the inferred common-spectrum amplitude using the complete data set. We search for spatial correlations in the observations by hierarchically analyzing individual pulsar pairs, which also allows for significance validation through randomizing pulsar positions on the sky. For a process with α = −2/3, we measure spatial correlations consistent with a GWB, with an estimated false-alarm probability of p ≲ 0.02 (approx. 2σ). The long timing baselines of the PPTA and the access to southern pulsars will continue to play an important role in the International Pulsar Timing Array.

Targeted search for the stochastic gravitational-wave background from the galactic millisecond pulsar population

The millisecond pulsars, old-recycled objects spinning with high frequency $\mathcal{O}$ (kHz) sustaining the deformation from their spherical shape, may emit gravitational waves (GW). These are one of the potential candidates contributing to the anisotropic stochastic gravitational-wave background (SGWB) observable in the ground-based GW detectors. Here, we present the results from a likelihood-based targeted search for the SGWB due to millisecond pulsars in the Milky Way, by analyzing the data from the first three observing runs of Advanced LIGO and Advanced Virgo detector. We assume that the shape of SGWB power spectra and the sky distribution is known a priori from the population synthesis model. The information of the ensemble source properties, i.e., the in-band number of pulsars, ${N}_{\mathrm{obs}}$ and the averaged ellipticity, ${\ensuremath{\mu}}_{\ensuremath{\epsilon}}$ is encoded in the maximum likelihood statistic. We do not find significant evidence for the SGWB signal from the considered source population. The best Bayesian upper limit with 95% confidence for the parameters are ${N}_{\mathrm{obs}}\ensuremath{\le}8.8\ifmmode\times\else\texttimes\fi{}{10}^{4}$ and ${\ensuremath{\mu}}_{ϵ}\ensuremath{\le}1.4\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}6}$, which is comparable to the bounds on mean ellipticity with the GW observations of the individual pulsars. Finally, we show that for the plausible case of ${N}_{\mathrm{obs}}=40000$, with the one year of observations, the one-sigma sensitivity on ${\ensuremath{\mu}}_{\ensuremath{\epsilon}}$ might reach $1.5\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}7}$ and $4.1\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}8}$ for the second-generation detector network having $\mathrm{A}+$ sensitivity and third-generation detector network, respectively.

A parallelized Bayesian approach to accelerated gravitational-wave background characterization

The characterization of nanohertz-frequency gravitational waves (GWs) with pulsar-timing arrays requires a continual expansion of datasets and monitored pulsars. Whereas detection of the stochastic GW background is predicated on measuring a distinctive pattern of inter-pulsar correlations, characterizing the background's spectrum is driven by information encoded in the power spectra of the individual pulsars' time series. We propose a new technique for rapid Bayesian characterization of the stochastic GW background that is fully parallelized over pulsar datasets. This Factorized Likelihood (FL) technique empowers a modular approach to parameter estimation of the GW background, multi-stage model selection of a spectrally-common stochastic process and quadrupolar inter-pulsar correlations, and statistical cross-validation of measured signals between independent pulsar sub-arrays. We demonstrate the equivalence of this technique's efficacy with the full pulsar-timing array likelihood, yet at a fraction of the required time. Our technique is fast, easily implemented, and trivially allows for new data and pulsars to be combined with legacy datasets without re-analysis of the latter.

An updated glitch rate law inferred from radio pulsars

ABSTRACT Radio pulsar glitches probe far-from-equilibrium processes involving stress accumulation and relaxation in neutron star interiors. Previous studies of glitch rates have focused on individual pulsars with as many recorded glitches as possible. In this work, we analyse glitch rates using all available data including objects that have glitched never or once. We assume the glitch rate follows a homogeneous Poisson process, and therefore exclude pulsars that exhibit quasiperiodic glitching behaviour. Calculating relevant Bayes factors shows that a model in which the glitch rate λ scales as a power of the characteristic age τ is preferred over models that depend arbitrarily on powers of the spin frequency ν and/or its time derivative $\dot{\nu }$. For λ = A(τ/τref)−γ, where τref = 1 yr is a reference time, the posterior distributions are unimodal with $A=0.0066_{-0.002}^{+0.003}\ \rm {yr}^{-1}$ and $\gamma =0.27_{-0.03}^{+0.03}$. Importantly, the data exclude with 99 per cent confidence the possibility γ = 1 canvassed in the literature. When objects with zero-recorded glitches are included, the age-based rate law is still preferred and the posteriors change to give $A=0.0099_{-0.003}^{+0.004}\ \rm {yr}^{-1}$ and $\gamma =0.31_{-0.03}^{+0.03}$. The updated estimates still support increased glitch activity for younger pulsars, while demonstrating that the large number of objects with zero glitches contain important statistical information about the rate, provided that they are part of the same population as opposed to a disjoint population which never glitches for some unknown physical reason.

A method for detecting continuous gravitational wave signals from an ensemble of known pulsars

This work describes a method to improve the detection efficiency for continuous gravitational waves by combining information from known pulsars, which emission is too low to be individually detectable. We propose a new ensemble statistic t, which combines statistics from individual pulsars, defined through the five-vector method. Using a collection of band sample data files from the LIGO science run O2, we test the method with software injections in order to study the statistical properties of t. We also study the performance of our method by varying the number of injected signals and their amplitude. We propose and test a possible strategy for the application of the ensemble method to a set of real pulsars.

Pulsars in supernova remnants

ABSTRACT A comparative analysis of the properties of 60 pulsars located in supernova remnants (SNRs) was carried out. We found that (1) anomalous X-ray pulsars (AXPs) and soft gamma repeaters (SGRs) are characterized by longer periods and higher values of period derivatives, (2) the remainder of the pulsars in this sample have shorter periods compared to the bulk of radio pulsars, (3) rotation of their neutron stars is braking faster, (4) this braking seems unlikely to be solely a result of the loss of angular momentum through magnetic dipole radiation. Using the measured and the estimated braking indices of individual pulsars, we calculated their birth periods. We found that (1) AXPs/SGRs are formed with periods of order of several seconds at the time of birth, (2) the remainder of the pulsars show the wide distribution of initial periods from 13 to 1300 ms with no predominance of millisecond values. Estimates of angles β between the rotation axis and the magnetic moment of the neutron stars are obtained. We found that the distribution of these angles is very close to the uniform distribution. This suggests that pulsars are born with arbitrary values of β. We found that the radio luminosities of pulsars observed inside their SNRs are, on average, one order of magnitude less than the average for neutron stars outside their SNRs. While we note that our data set of pulsars within SNRs of 60 is rather small our findings suggest that these pulsars do not show a decrease in their radio luminosity during their evolution.

The influence of the observational strategies of pulsar timing on the properties of pulsar clocks

Pulsars are very stable spinning stars, which have the potential to application in the work of time-keeping and autonomous navigation in deep space. For time application, an individual pulsar can be regarded as a clock. The accuracy and stability of a pulsar clock are mainly determined by various timing noises and the measurement errors; however, they would be affected by the concrete observational strategy. Taking four millisecond pulsars from the first data released by International Pulsar Timing Array (IPTA) as an example, we investigated the influences of different observational strategies on the properties of pulsar clocks by removing some data in various ways. We find that the long-term stabilities of pulsar clocks are nearly not affected by increasing the observational cadence with a fixed time span. It is also found that the capabilities of prediction by pulsar clocks are also hardly affected by different observational strategies, which is reflected by both the stable weighted root-mean-square (wrms) and the stability of the resulting pre-fit timing residuals, unless the data span is too short or the data period is too far from the start of prediction.

Measuring interstellar delays of PSR J0613−0200 over 7 yr, using the Large European Array for Pulsars

ABSTRACT Using data from the Large European Array for Pulsars, and the Effelsberg telescope, we study the scintillation parameters of the millisecond pulsar PSR J0613−0200 over a 7 yr timespan. The ‘secondary spectrum’ – the 2D power spectrum of scintillation – presents the scattered power as a function of time delay, and contains the relative velocities of the pulsar, observer, and scattering material. We detect a persistent parabolic scintillation arc, suggesting scattering is dominated by a thin, anisotropic region. The scattering is poorly described by a simple exponential tail, with excess power at high delays; we measure significant, detectable scattered power at times out to ${\sim}5 \, \mu {\rm s}$, and measure the bulk scattering delay to be between 50 to 200 ns with particularly strong scattering throughout 2013. These delays are too small to detect a change of the pulse profile shape, yet they would change the times of arrival as measured through pulsar timing. The arc curvature varies annually, and is well fitted by a one-dimensional scattering screen ${\sim}40{{\ \rm per\ cent}}$ of the way towards the pulsar, with a changing orientation during the increased scattering in 2013. Effects of uncorrected scattering will introduce time delays correlated over time in individual pulsars, and may need to be considered in gravitational wave analyses. Pulsar timing programmes would benefit from simultaneously recording in a way that scintillation can be resolved, in order to monitor the variable time delays caused by multipath propagation.

The effect of non-linear mutual friction on pulsar glitch sizes and rise times

ABSTRACT Observations of pulsar glitches have the potential to provide constraints on the dynamics of the high density interior of neutron stars. However, to do so, realistic glitch models must be constructed and compared to the data. We take a step towards this goal by testing non-linear models for the mutual friction force, which is responsible for the exchange of angular momentum between the neutron superfluid and the observable normal component in a glitch. In particular, we consider a non-linear dependence of the drag force on the relative velocity between superfluid vortices and the normal component, in which the contributions of both kelvin and phonon excitations are included. This non-linear model produces qualitatively new features, and is able to reproduce the observed bimodal distribution of glitch sizes in the pulsar population. The model also suggests that the differences in size distributions in individual pulsars may be due to the glitches being triggered in regions with different pinning strengths, as stronger pinning leads to higher vortex velocities and a qualitatively different mutual friction coupling with respect to the weak pinning case. Glitches in pulsars that appear to glitch quasi-periodically with similar sizes may thus be due to the same mechanisms as smaller events in pulsars that have no preferred glitch size, but simply originate in stronger pinning regions, possibly in the core of the star.

Classification of Young Pulsars and Empirical Evolution of Regular Braking Index

Abstract—The distribution of young pulsars in the log(dP/dt)–log(tc) diagram that have a characteristic age tc ~10–16 is analyzed. Six clusters-stripes are revealed for the first time, along which the long-term evolution tracks of individual pulsars pass. The mean track in a stripe corresponds to the long-term regular evolution for a typical pulsar of this stripe. The clusters-stripes population composition is analyzed by object types. Rotating radio transients (RRATs) are present in all clusters-stripes at tc > 105 yr. It turns out that three stripes contain objects of only one of the three numerous (≥10) known types: magnetars, pulsars with a high magnetic field, and Vela-like pulsars. In three other clusters-stripes, objects of the indicated three types are not found. The following object classification in the composition of six clusters-stripes is proposed: magnetars (M), pulsars with a high magnetic field (HB), pulsars with a sub-high magnetic field (S-HB), Vela-type pulsars (V), sub-Vela pulsars (SV), and low magnetic field pulsars (LB). Four pulsars that are outside the stripes are referred to peculiar. Analytical formulas are presented for calculating evolution parameters in the log(dP/dt)–log(tc) diagram. As a result of the optimal fitting of the mean clusters-stripes track by the appropriate empirical function, long-term regular values of the braking index and the second derivative of the period are estimated for 327 pulsars for the first time. As a consequence of the clusters-stripes presence, the “striped” distribution of the dipole magnetic field at pulsar birth indicates the intervality in the mass distribution of pulsar progenitor stars. The recent supernovae explosion models (Pejcha & Thomson, 2015) also produce an interval mass distribution of progenitors generating neutron stars, which confirm that pulsar clusters-stripes do exist and their origin can be naturally explained.