Pulsar Data Sets Research Articles

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.

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.

The data center construction of the Xinjiang Astronomical Observatory based on virtual observatory standards

As part of the Chinese National Astronomical Data Center, the Xinjiang Astronomical Observatory Data Center is built based on the virtual observatory standards. The data resources mainly include the pulsar dataset, the molecular spectral lines dataset, the intra-day variability source dataset generated by the Nanshan 25 m radio telescope, and the Nanshan 1 m wide-field telescope dataset, published through about a dozen data services, including a Table Access Protocol (TAP) endpoint. Some of these data services are registered with the International Virtual Observatory Alliance. Users can use standard virtual observatory tools, browsers, and scripts to retrieve all the metadata information in the data center and to realize simple data analysis, processing, and visualization operations.

AdaBoost-MICNN: a new network framework for pulsar candidate selection

ABSTRACT Pulsar observation and research are of great significance. With the gradual increase in the performance and quantity of observing equipment, the received pulsar observation data also increase geometrically. Machine learning can mine large-scale pulsar data sets to realize automatic pulsar candidate identification. However, the pulsar candidate and non-pulsar candidate data sets are highly imbalanced. The traditional classifier trained on the data set with imbalanced class distribution usually shows poor generalization performance, which will cause the classifier to be biased towards negative instances. To address the problem of poor identification algorithm performance caused by sample imbalance, we describe a new framework, namely AdaBoost-multi-input-CNN (AdaBoost-MICNN). In AdaBoost, multiple baseline models are trained sequentially, and the weight of each training sample changes as the training progresses. Especially the minority samples, which are more easily ignored, will get more attention in subsequent baseline models. This will solve the problem of imbalanced classification. Meanwhile, there are usually four pulsar diagnostic plots. To automatically extract and integrate these four diagnostic plots features, we use multi-input-CNN (MICNN) as the baseline model of AdaBoost. The attention mechanism is introduced to enhance the performance of MICNN’s extraction of features, and design an objective function that adds the maximum mean discrepancy to enhance the anti-interference ability of the model. Finally, the proposed method is tested in the High Time Resolution Universe Medlat Data, and the experimental results verify the effectiveness and efficiency of the method.

Classification of pulsars using Extreme Deconvolution

We carry out a classification of the observed pulsar dataset into distinct clusters, based on the P−Ṗ diagram, using Extreme Deconvolution based Gaussian Mixture Model. We then use the Bayesian Information Criterion to select the optimum number of clusters. We find in accord with previous works, that the pulsar dataset can be optimally classified into six clusters, with two for the millisecond pulsar population, and four for the ordinary pulsar population. Beyond that, however we do not glean any additional insight into the pulsar population based on this classification. Using numerical experiments, we confirm that Extreme Deconvolution-based classification is less sensitive to variations in the dataset compared to ordinary Gaussian Mixture Models. All our analysis codes used for this work have been made publicly available.

Research on Pulsar Candidate Identification Method Based on Deep Residual Neural Network

As the next-generation radio astronomical telescopes continuously improve and develop, the pulsar survey will produce millions of pulsar candidates, which pose considerable challenges for pulsar identification and classification. The rapidly evolving artificial intelligence (AI) techniques are being used for pulsar identification and discovery of new pulsars. Using the pulsar data set observed with the Parkes telescope, namely the High Time Resolution Universe Survey (HTRUS), a 14-layer deep residual network has been designed (called the Residual Network, ResNet) for pulsar candidate classifications. In the HTRUS sample data, the number of non-pulsar candidates (i.e., negative samples) is much larger than that of pulsar candidates (i.e., positive samples). The imbalance between the positive and negative samples is prone to result in model misjudgement. By using the over-sampling technique to enhance the data of positive samples in the training set and adjusting the ratio of positive and negative samples, we have solved this imbalance problem. In the training process, the hyperparameters are adjusted by means of 5-fold cross validation to build the model. The test results indicate that the model can achieve a high precision (98%) and recall (100%), the F1-score can reach 99%, and that the implementation of each sample test needs only 7 ms, it has provided a feasible approach for the future big-data analysis of pulsars.

The impact of solar wind variability on pulsar timing

Context. High-precision pulsar timing requires accurate corrections for dispersive delays of radio waves, parametrized by the dispersion measure (DM), particularly if these delays are variable in time. In a previous paper, we studied the solar wind (SW) models used in pulsar timing to mitigate the excess of DM that is annually induced by the SW and found these to be insufficient for high-precision pulsar timing. Here we analyze additional pulsar datasets to further investigate which aspects of the SW models currently used in pulsar timing can be readily improved, and at what levels of timing precision SW mitigation is possible. Aims. Our goals are to verify: (a) whether the data are better described by a spherical model of the SW with a time-variable amplitude, rather than a time-invariant one as suggested in literature, and (b) whether a temporal trend of such a model’s amplitudes can be detected. Methods. We use the pulsar timing technique on low-frequency pulsar observations to estimate the DM and quantify how this value changes as the Earth moves around the Sun. Specifically, we monitor the DM in weekly to monthly observations of 14 pulsars taken with parts of the LOw-Frequency ARray (LOFAR) across time spans of up to 6 years. We develop an informed algorithm to separate the interstellar variations in the DM from those caused by the SW and demonstrate the functionality of this algorithm with extensive simulations. Assuming a spherically symmetric model for the SW density, we derive the amplitude of this model for each year of observations. Results. We show that a spherical model with a time-variable amplitude models the observations better than a spherical model with a constant amplitude, but that both approaches leave significant SW-induced delays uncorrected in a number of pulsars in the sample. The amplitude of the spherical model is found to be variable in time, as opposed to what has been previously suggested.

Minimum interpretation by autoencoder-based serial and enhanced mutual information production

The present paper aims to propose an information-theoretic method for interpreting the inference mechanism of neural networks. The new method aims to interpret the inference mechanism minimally by disentangling complex information into simpler and easily interpretable information. This disentanglement of complex information can be realized by maximizing mutual information between input patterns and the corresponding neurons. However, because the use of mutual information has faced difficulty in computation, we use the well-known autoencoder to increase mutual information by re-interpreting the sparsity constraint, which is considered a device to increase mutual information. The computational procedures to increase mutual information are decomposed into the serial operation of equal use of neurons and specific responses to input patterns. The specific responses are realized by enhancing the results by the equal use of neurons. The method was applied to three data sets: the glass, office equipment, and pulsar data sets. With all three data sets, we could observe that, when the number of neurons was forced to increase, mutual information could be increased. Then, collective weights, or average collectively treated weights, showed that the method could extract the simple and linear relations between inputs and targets, making it possible to interpret the inference mechanism minimally.

Pulsar candidate classification using generative adversary networks

ABSTRACT Discovering pulsars is a significant and meaningful research topic in the field of radio astronomy. With the advent of astronomical instruments, the volume and rate of data acquisition have grown exponentially. This development necessitates a focus on artificial intelligence (AI) technologies that can mine large astronomical data sets. Automatic pulsar candidate identification (APCI) can be considered as a task determining potential candidates for further investigation and eliminating the noise of radio-frequency interference and other non-pulsar signals. As reported in the existing literature, AI techniques, especially convolutional neural network (CNN)-based techniques, have been adopted for APCI. However, it is challenging to enhance the performance of CNN-based pulsar identification because only an extremely limited number of real pulsar samples exist, which results in a crucial class imbalance problem. To address these problems, we propose a framework that combines a deep convolution generative adversarial network (DCGAN) with a support vector machine (SVM). The DCGAN is used as a sample generation and feature learning model, and the SVM is adopted as the classifier for predicting the label of a candidate at the inference stage. The proposed framework is a novel technique, which not only can solve the class imbalance problem but also can learn the discriminative feature representations of pulsar candidates instead of computing hand-crafted features in the pre-processing steps. The proposed method can enhance the accuracy of the APCI, and the computer experiments performed on two pulsar data sets verified the effectiveness and efficiency of the proposed method.

Correcting for the solar wind in pulsar timing observations: the role of simultaneous and low-frequency observations

The primary goal of pulsar timing array projects is to detect ultra-low-frequency gravitational waves. Pulsar data sets are affected by numerous noise processes including varying dispersive delays in the interstellar medium and from the solar wind. The solar wind can lead to rapidly changing variations that, with existing telescopes, can be hard to measure and then remove. In this paper we study the possibility of using a low frequency telescope to aid in such correction for the Parkes Pulsar Timing Array (PPTA) and also discuss whether the ultra-wide-bandwidth receiver for the FAST telescope is sufficient to model solar wind variations. Our key result is that a single wide-bandwidth receiver can be used to model and remove the effect of the solar wind. However, for pulsars that pass close to the Sun such as PSR J1022 + 1022, the solar wind is so variable that observations at two telescopes separated by a day are insufficient to correct the solar wind effect.

Finding Pulsar Variability in 50 Years of Data

AbstractFifty years of pulsar data has led to the discovery of emission and rotation variability on timescales of months and years; we have developed techniques to identify this long timescale variability. Individual observations may be too noisy to identify subtle changes in a pulse profile; we use Gaussian process regression to model noisy observations and produce a continuous map of pulse profile variability. Generally, multiple observing epochs are required to obtain the pulsar spin frequency derivative. Gaussian process regression is, therefore, also used to monitor this rate of spindown. We have applied variability detection techniques to both millisecond and long period pulsar datasets. I will discuss the techniques used and present the most interesting results from the pulsars analysed.

Proper motions of 15 pulsars: a comparison between Bayesian and frequentist algorithms

We present proper motions for 15 pulsars which are observed regularly by the Nanshan 25-m radio telescope. Two methods, the frequentist method (Coles et al.2011) and the Bayesian (Lentati et al. 2014) method, are used and the results are compared. We demonstrate that the two methods can be applied to young pulsar data sets that exhibit large amounts of timing noise with steep spectral exponents and give consistent results. The measured positions also agree with very-long-baseline interferometric positions. Proper motions for four pulsars are obtained for the first time, and improved values are obtained for five pulsars.

Do pulsar radio fluxes violate the inverse-square law?

Singleton et al (2009) have argued that the flux of pulsars measured at 1400 MHz shows an apparent violation of the inverse-square law with distance ($r$), and it is consistent with $1/r$ scaling. They deduced this from the fact that the convergence error obtained in reconstructing the luminosity function of pulsars using an iterative maximum likelihood procedure is about $10^5$ times larger for a distance exponent of two (corresponding to the inverse-square law) compared to an exponent of one. When we applied the same technique to this pulsar dataset with two different values for the trial luminosity function in the zeroth iteration, we find that neither of them can reproduce a value of $10^5$ for the ratio of the convergence error between these distance exponents. We then reconstruct the differential pulsar luminosity function using Lynden-Bell's $C^{-}$ method after positing both an inverse-linear and an inverse-square scalings with distance. We show this method cannot help in discerning between the two exponents. Finally, when we tried to estimate the power law exponent with a Bayesian regression procedure, we do not get a best-fit value of one for the distance exponent. The model residuals obtained from our fitting procedure are larger for the inverse-linear law compared to the inverse-square law. Moreover, the observed pulsar flux cannot be parameterized only by power-law functions of distance, period, and period derivative. Therefore, we conclude from our analysis using multiple methods that there is no evidence that the pulsar radio flux at 1400 MHz violates the inverse-square law.

European Pulsar Timing Array limits on an isotropic stochastic gravitational-wave background

We present new limits on an isotropic stochastic gravitational-wave background (GWB) using a six pulsar dataset spanning 18 yr of observations from the 2015 European Pulsar Timing Array data release. Performing a Bayesian analysis, we fit simultaneously for the intrinsic noise parameters for each pulsar, along with common correlated signals including clock, and Solar System ephemeris errors, obtaining a robust 95$\%$ upper limit on the dimensionless strain amplitude $A$ of the background of $A<3.0\times 10^{-15}$ at a reference frequency of $1\mathrm{yr^{-1}}$ and a spectral index of $13/3$, corresponding to a background from inspiralling super-massive black hole binaries, constraining the GW energy density to $\Omega_\mathrm{gw}(f)h^2 < 1.1\times10^{-9}$ at 2.8 nHz. We also present limits on the correlated power spectrum at a series of discrete frequencies, and show that our sensitivity to a fiducial isotropic GWB is highest at a frequency of $\sim 5\times10^{-9}$~Hz. Finally we discuss the implications of our analysis for the astrophysics of supermassive black hole binaries, and present 95$\%$ upper limits on the string tension, $G\mu/c^2$, characterising a background produced by a cosmic string network for a set of possible scenarios, and for a stochastic relic GWB. For a Nambu-Goto field theory cosmic string network, we set a limit $G\mu/c^2<1.3\times10^{-7}$, identical to that set by the {\it Planck} Collaboration, when combining {\it Planck} and high-$\ell$ Cosmic Microwave Background data from other experiments. For a stochastic relic background we set a limit of $\Omega^\mathrm{relic}_\mathrm{gw}(f)h^2<1.2 \times10^{-9}$, a factor of 9 improvement over the most stringent limits previously set by a pulsar timing array.

GRAVITATIONAL WAVES FROM INDIVIDUAL SUPERMASSIVE BLACK HOLE BINARIES IN CIRCULAR ORBITS: LIMITS FROM THE NORTH AMERICAN NANOHERTZ OBSERVATORY FOR GRAVITATIONAL WAVES

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) project currently observes 43 pulsars using the Green Bank and Arecibo radio telescopes. In this work we use a subset of 17 pulsars timed for a span of roughly five years (2005--2010). We analyze these data using standard pulsar timing models, with the addition of time-variable dispersion measure and frequency-variable pulse shape terms. Within the timing data, we perform a search for continuous gravitational waves from individual supermassive black hole binaries in circular orbits using robust frequentist and Bayesian techniques. We find that there is no evidence for the presence of a detectable continuous gravitational wave; however, we can use these data to place the most constraining upper limits to date on the strength of such gravitational waves. Using the full 17 pulsar dataset we place a 95% upper limit on the sky-averaged strain amplitude of $h_0\lesssim 3.8\times 10^{-14}$ at a frequency of 10 nHz. Furthermore, we place 95% \emph{all sky} lower limits on the luminosity distance to such gravitational wave sources finding that the $d_L \gtrsim 425$ Mpc for sources at a frequency of 10 nHz and chirp mass $10^{10}{\rm M}_{\odot}$. We find that for gravitational wave sources near our best timed pulsars in the sky, the sensitivity of the pulsar timing array is increased by a factor of $\sim$4 over the sky-averaged sensitivity. Finally we place limits on the coalescence rate of the most massive supermassive black hole binaries.

THE BENEFITS OF VLBI ASTROMETRY TO PULSAR TIMING ARRAY SEARCHES FOR GRAVITATIONAL RADIATION

Precision astrometry is an integral component of successful pulsar timing campaigns. Astrometric parameters are commonly derived by fitting them as parameters of a timing model to a series of pulse times of arrival (TOAs). TOAs measured to microsecond precision over several-year spans can yield position measurements with sub-milliarcsecond precision. However, timing-based astrometry can become biased if a pulsar displays any red spin noise, which can be compared to the red noise signal produced by the stochastic gravitational wave background. We investigate how noise of different spectral types is absorbed by timing models, leading to significant estimation errors in the astrometric parameters. We find that commonly used techniques for fitting timing models in the presence of red noise (Cholesky whitening) prevent the absorption of noise into the timing model remarkably well if the time baseline of observations exceeds several years, but are inadequate for dealing with shorter pulsar data sets. Independent of timing, pulsar-optimized very long baseline interferometry (VLBI) is capable of providing position estimates precise to the sub-milliarcsecond levels needed for high-precision timing. We compute a necessary transformation between the International Celestial Reference Frame and pulsar timing frames and quantitatively discuss how the transformation will improve in coming years. We find that incorporating VLBI astrometry into the timing models of pulsars for which only a couple of years of timing data exist will lead to more realistic assessments of red spin noise and could enhance the amplitude of gravitational wave signatures in post-fit timing residuals by factors of 20 or more.

Phenomenological constraints on accretion of non-annihilating dark matter on the PSR B1257+12 pulsar from orbital dynamics of its planets

We analytically compute the effects that a pulsar's mass variation, whatever its physical origin may be, has on the standard Keplerian changes ΔτKep in the times of arrival of its pulses due to potential test particle companions, and on their orbital dynamics over long time scales. We apply our results to the planetary system of the PSR B1257+12 pulsar, located in the Galaxy at ∼ 600 pc from us, to phenomenologically constrain a putative accretion of non-annihilating dark matter on the hosting neutron star. By comparing our prediction for ΔτṀ/M to the root-mean-square accuracy of the timing residuals δ(Δτ) = 3.0μs we find for the mass variation rate Ṁ/M ⩽ 1.3 × 10−6 yr−1. Actually, considerations related to the pulsar's lifetime, of the order of Δt ∼ 0.8 Gyr, and to the currently accepted picture of the formation of its planets point toward a tighter constrain on the mass accretion rate, i.e. Ṁ/M ⩽ 10−9 yr−1. Otherwise, the planets would have formed at about 300–700 au from PSR B1257+12, i.e. too far with respect to the expected extension of 1–2 au of the part of the protoplanetary disk containing the solid constituents from which they likely originated. In fact, an even smaller upper limit, Ṁ/M ⩽ 10−11 yr−1, would likely be more realistic to avoid certain technical inconsistencies with the quality of the fit of the timing data, performed by keeping the standard value M = 1.4M⊙ fixed for the neutron star's mass. Anyway, the entire pulsar data set should be re-processed by explicitly modeling the mass variation rate and solving for it. Model-dependent theoretical predictions for the pulsar's mass accretion, in the framework of the mirror matter scenario, yield a mass increment rate of about 10−16 yr−1 for a value of the density of mirror matter ρdm as large as 10−17 g cm−3 = 5.6 × 106 GeV cm−3. Such a rate corresponds to a fractional mass variation of ΔM/M ∼ 10−7 over the pulsar's lifetime. It would imply a formation of a black hole from the accreted dark matter inner core for values of the dark matter particle's mass mdm larger than 3 × 103 Gev, which are, thus, excluded since PSR B1257+12 is actually not such a kind of compact object. Instead, by assuming ρdm ∼ 10−24 g cm−3 = 0.56 GeV cm−3, the mass accretion rate would be Ṁ/M ∼ 10−23 yr−1, with a fractional mass variation of the order of ΔM/M ∼ 10−14. It rules out mdm ⩾ 8 × 106 Gev. Extreme values ρdm = 1.8 × 10−13 g cm−3 = 1011 GeV cm−3 for non-annihilating dark matter in central spike may yield the constraint Ṁ/M ⩽ 10−11 yr−1; over Δt = 0.8 Gyr, it rules out mdm ⩾ 12 Gev.

TEMPO2: a New Pulsar Timing Package

TEMPO2 is a new pulsar timing package that provides the precision necessary for modern millisecond timing projects and should supersede all existing pulsar timing packages such as TEMPO and PSRTIME. As TEMPO2 is the only program available that can analyse multiple pulsar datasets simultaneously it will become an integral part of pulsar timing array projects which aim to detect the signatures of gravitational radiation in pulsar timing residuals. In this paper we describe the basic functionality of TEMPO2.

The S2 Baseband Processing System for Phase-coherent Pulsar Observations

AbstractThe phase-coherent recording of pulsar data and subsequent software dispersion removal provide a flexible way to reach the limits of high time resolution, useful for more precise pulse timing and the study of fast signal fluctuations within a pulse. Because of the huge data rate and lack of adequate recording and computing capabilities, this technique has been used mostly only for small pulsar data sets. In recent years, however, the development of very capable, reasonably inexpensive high-speed recording systems and computers has made feasible the notion of pulsar baseband recording and subsequent processing with a workstation/computer. In this paper we discuss the development of a phase-coherent baseband processing system for radio pulsar observations. This system is based on the S2 VLBI recorder developed at ISTS/York University in Toronto, Canada. We present preliminary first results for data from the Vela pulsar, obtained at Parkes, Australia, and processed at ISTS/York University, and discuss plans for future developments.