Pulsar Timing Experiments Research Articles

Pulsar scintillation studies with LOFAR: II. Dual-frequency scattering study of PSR J0826+2637 with LOFAR and NenuFAR

ABSTRACT Interstellar scattering (ISS) of radio pulsar emission can be used as a probe of the ionized interstellar medium (IISM) and causes corruptions in pulsar timing experiments. Two types of ISS phenomena (intensity scintillation and pulse broadening) are caused by electron density fluctuations on small scales (< 0.01 au). Theory predicts that these are related, and both have been widely employed to study the properties of the IISM. Larger scales (∼1 – 100 au) cause measurable changes in dispersion and these can be correlated with ISS observations to estimate the fluctuation spectrum over a very wide scale range. IISM measurements can often be modelled by a homogeneous power-law spatial spectrum of electron density with the Kolmogorov (−11/3) spectral exponent. Here, we aim to test the validity of using the Kolmogorov exponent with PSR J0826+2637. We do so using observations of intensity scintillation, pulse broadening and dispersion variations across a wide fractional bandwidth (20–180 MHz). We present that the frequency dependence of the intensity scintillation in the high-frequency band matches the expectations of a Kolmogorov spectral exponent, but the pulse broadening in the low-frequency band does not change as rapidly as predicted with this assumption. We show that this behaviour is due to an inhomogeneity in the scattering region, specifically that the scattering is dominated by a region of transverse size ∼40 au. The power spectrum of the electron density, however, maintains the Kolmogorov spectral exponent from spatial scales of 5 × 10−6 au to ∼100 au.

Stochastic processes for pulsar timing noise: fluctuations in the internal and external torques

AbstractYoung pulsars deviate from a perfectly regular spin-down by two non-deterministic phenomena: impulsive glitches and timing noise. Both phenomena are interesting per se and may provide insights into the superfluid properties of neutron stars, but they also act as a barrier to high-precision pulsar timing and gravitational wave experiments. We study a minimal stochastic model to describe the spin-down of a multicomponent neutron star, with fluctuations in both the internal and external torques. The power spectral density and timing noise strength of this kind of model can be obtained analytically and compared with known results from pulsar timing observational campaigns. In particular, the presence of flat regions of the power spectral density can be interpreted as a signature of the presence of internal superfluid components. We also derive the expected scaling of the timing noise strength with the pulsar’s rotational parameters (or characteristic age). Therefore, the present framework offers a theoretical guideline to interpret the observed features of timing noise in both single pulsars and across the pulsar population.

Pulsar scintillation studies with LOFAR

Context. Interstellar scintillation (ISS) of pulsar emission can be used both as a probe of the ionized interstellar medium (IISM) and cause corruptions in pulsar timing experiments. Of particular interest are so-called scintillation arcs which can be used to measure time-variable interstellar scattering delays directly, potentially allowing high-precision improvements to timing precision. Aims. The primary aim of this study is to carry out the first sizeable and self-consistent census of diffractive pulsar scintillation and scintillation-arc detectability at low frequencies, as a primer for larger-scale IISM studies and pulsar-timing related propagation studies with the LOw-Frequency ARray (LOFAR) High Band Antennae (HBA). Methods. We use observations from five international LOFAR stations and the LOFAR core in the Netherlands. We analyze the 2D auto-covariance function of the dynamic spectra of these observations to determine the characteristic bandwidth and timescale of the ISS toward the pulsars in our sample and investigate the 2D power spectra of the dynamic spectra to determine the presence of scintillation arcs. Results. In this initial set of 31 sources, 15 allow for the full determination of the scintillation properties; nine of these show detectable scintillation arcs at 120–180 MHz. Eight of the observed sources show unresolved scintillation; and the final eight do not display diffractive scintillation. Some correlation between scintillation detectability and pulsar brightness and a dispersion measure is apparent, although no clear cut-off values can be determined. Our measurements across a large fractional bandwidth allow a meaningful test of the frequency scaling of scintillation parameters, uncorrupted by influences from refractive scintillation variations. Conclusions. Our results indicate the powerful advantage and great potential of ISS studies at low frequencies and the complex dependence of scintillation detectability on parameters such as pulsar brightness and interstellar dispersion. This work provides the first installment of a larger-scale census and longer-term monitoring of ISS effects at low frequencies.

Pulsar observations at low frequencies: applications to pulsar timing and solar wind models

ABSTRACT Efforts are underway to use high-precision timing of pulsars in order to detect low-frequency gravitational waves. A limit to this technique is the timing noise generated by dispersion in the plasma along the line of sight to the pulsar, including the solar wind. The effects due to the solar wind vary with time, influenced by the change in solar activity on different time-scales, ranging up to ∼11 yr for a solar cycle. The solar wind contribution depends strongly on the angle between the pulsar line of sight and the solar disc, and is a dominant effect at small separations. Although solar wind models to mitigate these effects do exist, they do not account for all the effects of the solar wind and its temporal changes. Since low-frequency pulsar observations are most sensitive to these dispersive delays, they are most suited to test the efficacy of these models and identify alternative approaches. Here, we investigate the efficacy of some solar wind models commonly used in pulsar timing using long-term, high-cadence data on six pulsars taken with the Long Wavelength Array, and compare them with an operational solar wind model. Our results show that stationary models of the solar wind correction are insufficient to achieve the timing noise desired by pulsar timing experiments, and we need to use non-stationary models, which are informed by other solar wind observations, to obtain accurate timing residuals.

A comparative analysis of pulse time-of-arrival creation methods

Context.Extracting precise pulse times of arrival (TOAs) and their uncertainties is the first and most fundamental step in high-precision pulsar timing. In the classical method, TOAs are derived from total intensity pulse profiles of pulsars via cross-correlation with an idealised 1D template of that profile. While a number of results have been presented in the literature that rely on the ever increasing sensitivity of these pulsar timing experiments, there is no consensus on the most reliable methods for creating TOAs, and, more importantly, on the associated TOA uncertainties for each scheme.Aims.We present a comprehensive comparison of TOA determination practices. We focus on creating timing templates, TOA determination methods, and the most useful TOA bandwidth. The aim is to present a possible approach towards TOA optimisation, the (partial) identification of an optimal TOA-creation scheme, and the demonstration of optimisation differences between pulsars and data sets.Methods.We compared the values of data-derived template profiles with analytic profiles and evaluated the three most commonly used template-matching methods. Finally, we studied the relation between timing precision and TOA bandwidth to identify any potential breaks in this relation. As a practical demonstration, we applied our selected methods to European Pulsar Timing Array data on three test pulsars, PSRs J0218+4232, J1713+0747, and J2145−0750.Results.Our demonstration shows that data-derived and smoothed templates are typically preferred to some more commonly applied alternatives. The template-matching method called Fourier domain with Markov chain Monte Carlo is generally superior to or competitive with other methods. While the optimal TOA bandwidth is strongly dependent on pulsar brightness, telescope sensitivity, and scintillation properties, some significant frequency averaging seems required for the data we investigated.

Constraining Scalar-tensor Theories Using Neutron Star–Black Hole Gravitational Wave Events

Abstract With the continuous upgrade of detectors, greater numbers of gravitational wave (GW) events have been captured by the LIGO Scientific Collaboration and Virgo Collaboration (LVC), which offer a new avenue to test general relativity and explore the nature of gravity. Although various model-independent tests have been performed by LVC in previous works, it is still interesting to ask what constraints can be placed on specific models by current GW observations. In this work, we focus on three models of scalar-tensor theories, the Brans–Dicke theory (BD), the theory with scalarization phenomena proposed by Damour and Esposito-Farèse (DEF), and screened modified gravity (SMG). Of the four possible neutron star–black hole events that have occurred so far, we use two of them to place constraints. The other two are excluded in this work because of possible unphysical deviations. We consider the inspiral range with the cutoff frequency at the innermost stable circular orbit and add a modification of dipole radiation into the waveform template. The scalar charges of neutron stars in the dipole term are derived by solving the Tolman–Oppenheimer–Volkoff equations for different equations of state. The constraints are obtained by performing the full Bayesian inference with the help of the open source software Bilby. The results show that the constraints given by GWs are comparable to those given by pulsar timing experiments for DEF theory, but are not competitive with the current solar system constraints for BD and SMG theories.

Fresnel models for gravitational wave effects on pulsar timing

ABSTRACT Merging supermassive black hole binaries produce low-frequency gravitational waves, which pulsar timing experiments are searching for. Much of the current theory is developed within the plane-wave formalism, and here we develop the more general Fresnel formalism. We show that Fresnel corrections to gravitational wave timing residual models allow novel measurements to be made, such as direct measurements of the source distance from the timing residual phase and frequency, as well as direct measurements of chirp mass from a monochromatic source. Probing the Fresnel corrections in these models will require future pulsar timing arrays with more distant pulsars across our Galaxy (ideally at the distance of the Magellanic Clouds), timed with precisions less than 100 ns, with distance uncertainties reduced to the order of the gravitational wavelength. We find that sources with chirp mass of order 109 M⊙ and orbital frequency ω0 > 10 nHz are good candidates for probing Fresnel corrections. With these conditions met, the measured source distance uncertainty can be made less than 10 per cent of the distance to the source for sources out to ∼100 Mpc, source sky localization can be reduced to sub-arcminute precision, and source volume localization can be made to less than 1 Mpc3 for sources out to 1-Gpc distances.

Effects of periodicity in observation scheduling on parameter estimation of pulsar glitches

ABSTRACT In certain pulsar timing experiments, where observations are scheduled approximately periodically (e.g. daily), timing models with significantly different frequencies (including but not limited to glitch models with different frequency increments) return near-equivalent timing residuals. The average scheduling aperiodicity divided by the phase error due to time-of-arrival uncertainties is a useful indicator when the degeneracy is important. Synthetic data are used to explore the effect of this degeneracy systematically. It is found that phase-coherent tempo2 or temponest-based approaches are biased sometimes towards reporting small glitch sizes regardless of the true glitch size. Local estimates of the spin frequency alleviate this bias. A hidden Markov model is free from bias towards small glitches and announces explicitly the existence of multiple glitch solutions but sometimes fails to recover the correct glitch size. Two glitches in the UTMOST public data release are reassessed, one in PSR J1709−4429 at MJD 58178 and the other in PSR J1452−6036 at MJD 58600. The estimated fractional frequency jump in PSR J1709−4429 is revised upward from Δf/f = (54.6 ± 1.0) × 10−9 to (2432.2 ± 0.1) × 10−9 with the aid of additional data from the Parkes radio telescope. We find that the available UTMOST data for PSR J1452−6036 are consistent with Δf/f = 270 × 10−9 + N/(fT) with N = 0, 1, and 2, where $T \approx 1\, \text{sidereal day}$ is the observation scheduling period. Data from the Parkes radio telescope can be included, and the N = 0 case is selected unambiguously with a combined data set.

PINT: A Modern Software Package for Pulsar Timing

Abstract Over the past few decades, the measurement precision of some pulsar timing experiments has advanced from ∼10 μs to ∼10 ns, revealing many subtle phenomena. Such high precision demands both careful data handling and sophisticated timing models to avoid systematic error. To achieve these goals, we present PINT (PINT Is Not T empo3), a high-precision Python pulsar timing data analysis package, which is hosted on GitHub and available on the Python Package Index (PyPI) as pint-pulsar. PINT is well tested, validated, object oriented, and modular, enabling interactive data analysis and providing an extensible and flexible development platform for timing applications. It utilizes well-debugged public Python packages (e.g., the NumPy and Astropy libraries) and modern software development schemes (e.g., version control and efficient development with git and GitHub) and a continually expanding test suite for improved reliability, accuracy, and reproducibility. PINT is developed and implemented without referring to, copying, or transcribing the code from other traditional pulsar timing software packages (e.g., Tempo/Tempo2) and therefore provides a robust tool for cross-checking timing analyses and simulating pulse arrival times. In this paper, we describe the design, use, and validation of PINT, and we compare timing results between it and Tempo and Tempo2.

Dispersion measure variability for 36 millisecond pulsars at 150 MHz with LOFAR

Context. Radio pulses from pulsars are affected by plasma dispersion, which results in a frequency-dependent propagation delay. Variations in the magnitude of this effect lead to an additional source of red noise in pulsar timing experiments, including pulsar timing arrays (PTAs) that aim to detect nanohertz gravitational waves. Aims. We aim to quantify the time-variable dispersion with much improved precision and characterise the spectrum of these variations. Methods. We use the pulsar timing technique to obtain highly precise dispersion measure (DM) time series. Our dataset consists of observations of 36 millisecond pulsars, which were observed for up to 7.1 yr with the LOw Frequency ARray (LOFAR) telescope at a centre frequency of ~150 MHz. Seventeen of these sources were observed with a weekly cadence, while the rest were observed at monthly cadence. Results. We achieve a median DM precision of the order of 10−5 cm−3 pc for a significant fraction of our sources. We detect significant variations of the DM in all pulsars with a median DM uncertainty of less than 2 × 10−4 cm−3 pc. The noise contribution to pulsar timing experiments at higher frequencies is calculated to be at a level of 0.1–10 μs at 1.4 GHz over a timespan of a few years, which is in many cases larger than the typical timing precision of 1 μs or better that PTAs aim for. We found no evidence for a dependence of DM on radio frequency for any of the sources in our sample. Conclusions. The DM time series we obtained using LOFAR could in principle be used to correct higher-frequency data for the variations of the dispersive delay. However, there is currently the practical restriction that pulsars tend to provide either highly precise times of arrival (ToAs) at 1.4 GHz or a high DM precision at low frequencies, but not both, due to spectral properties. Combining the higher-frequency ToAs with those from LOFAR to measure the infinite-frequency ToA and DM would improve the result.

Timing of young radio pulsars – I. Timing noise, periodic modulation, and proper motion

ABSTRACT The smooth spin-down of young pulsars is perturbed by two non-deterministic phenomenon, glitches, and timing noise. Although the timing noise provides insights into nuclear and plasma physics at extreme densities, it acts as a barrier to high-precision pulsar timing experiments. An improved methodology based on the Bayesian inference is developed to simultaneously model the stochastic and deterministic parameters for a sample of 85 high-$\dot{E}$ radio pulsars observed for ∼10 yr with the 64-m Parkes radio telescope. Timing noise is known to be a red process and we develop a parametrization based on the red-noise amplitude (Ared) and spectral index (β). We measure the median Ared to be $-10.4^{+1.8}_{-1.7}$ yr3/2 and β to be $-5.2^{+3.0}_{-3.8}$ and show that the strength of timing noise scales proportionally to $\nu ^{1}|\dot{\nu }|^{-0.6\pm 0.1}$, where ν is the spin frequency of the pulsar and $\dot{\nu }$ is its spin-down rate. Finally, we measure significant braking indices for 19 pulsars and proper motions for 2 pulsars, and discuss the presence of periodic modulation in the arrival times of 5 pulsars.

On the usefulness of existing solar wind models for pulsar timing corrections

Dispersive delays due to the Solar wind introduce excess noise in high-precision pulsar timing experiments, and must be removed in order to achieve the accuracy needed to detect, e.g., low-frequency gravitational waves. In current pulsar timing experiments, this delay is usually removed by approximating the electron density distribution in the Solar wind either as spherically symmetric, or with a two-phase model that describes the contributions from both high- and low-speed phases of the Solar wind. However, no dataset has previously been available to test the performance and limitations of these models over extended timescales and with sufficient sensitivity. Here we present the results of such a test with an optimal dataset of observations of pulsar J0034-0534, taken with the German stations of LOFAR. We conclude that the spherical approximation performs systematically better than the two-phase model at almost all angular distances, with a residual root-mean-square (rms) given by the two-phase model being up to 28% larger than the result obtained with the spherical approximation. Nevertheless, the spherical approximation remains insufficiently accurate in modelling the Solar-wind delay (especially within 20 degrees of angular distance from the Sun), as it leaves timing residuals with rms values that reach the equivalent of 0.3 microseconds at 1400 MHz. This is because a spherical model ignores the large daily variations in electron density observed in the Solar wind. In the short term, broadband observations or simultaneous observations at low frequencies are the most promising way forward to correct for Solar-wind induced delay variations.

First detection of frequency-dependent, time-variable dispersion measures

Context. High-precision pulsar-timing experiments are affected by temporal variations of the dispersion measure (DM), which are related to spatial variations in the interstellar electron content and the varying line of sight to the source. Correcting for DM variations relies on the cold-plasma dispersion law which states that the dispersive delay varies with the squared inverse of the observing frequency. This may, however, give incorrect measurements if the probed electron content (and therefore the DM) varies with observing frequency, as is predicted theoretically due to the different refraction angles at different frequencies. Aims. We study small-scale density variations in the ionised interstellar medium. These structures may lead to frequency-dependent DMs in pulsar signals. Such an effect could inhibit the use of lower-frequency pulsar observations as tools to correct time-variable interstellar dispersion in higher-frequency pulsar-timing data. Methods. We used high-cadence, low-frequency observations with three stations from the German LOng-Wavelength (GLOW) consortium, which are part of the LOw-Frequency ARray (LOFAR). Specifically, 3.5 yr of weekly observations of PSR J2219+4754 are presented. Results. We present the first detection of frequency-dependent DMs towards any interstellar object and a precise multi-year time-series of the time- and frequency-dependence of the measured DMs. The observed DM variability is significant and may be caused by extreme scattering events. Potential causes for frequency-dependent DMs are quantified and evaluated. Conclusions. We conclude that frequency dependence of DMs has been reliably detected and is indeed caused by small-scale (up to tens of AUs) but steep density variations in the interstellar electron content. We find that long-term trends in DM variability equally affect DMs measured at both ends of our frequency band and hence the negative impact on long-term high-precision timing projects is expected to be limited.

Mode Changing and Giant Pulses in the Millisecond Pulsar PSR B1957+20

Abstract Many radio pulsars have stable pulse profiles, but some exhibit mode changing where the profile switches between two or more quasi-stable modes of emission. So far, these effects had only been seen in relatively slow pulsars, but we show here that the pulse profile of PSR B1957+20, a millisecond pulsar, switches between two modes, with a typical time between mode changes of only 1.7 s (or ∼1000 rotations), the shortest observed to date. The two modes differ in both intensity and polarization, with relatively large differences in the interpulse and much more modest ones in the main pulse. We find that the changes in the interpulse precede those in the main pulse by ∼25 ms, placing an empirical constraint on the timescale over which mode changes occurs. We also find that the properties of the giant pulses emitted by PSR B1957+20 are correlated with the mode of the regular emission: their rate and the rotational phase at which they are emitted both depend on mode. Furthermore, the energy distribution of the giant pulses emitted near the main pulse depends on mode as well. We discuss the ramifications for our understanding of the radio emission mechanisms as well as for pulsar timing experiments.

Gravitational wave searches with pulsar timing arrays: Cancellation of clock and ephemeris noises

We propose a data processing technique to cancel monopole and dipole noise sources (such as clock and ephemeris noises respectively) in pulsar timing array searches for gravitational radiation. These noises are the dominant sources of correlated timing fluctuations in the lower-part ($ \approx 10^{-9} - 10^{-8}$ Hz) of the gravitational wave band accessible by pulsar timing experiments. After deriving the expressions that reconstruct these noises from the timing data, we estimate the gravitational wave sensitivity of our proposed processing technique to single-source signals to be at least one order of magnitude higher than that achievable by directly processing the timing data from an equal-size array. Since arrays can generate pairs of clock and ephemeris-free timing combinations that are no longer affected by correlated noises, we implement with them the cross-correlation statistic to search for an isotropic stochastic gravitational wave background. We find the resulting optimal signal-to-noise ratio to be more than one order of magnitude larger than that obtainable by correlating pairs of timing data from arrays of equal size.

Causal properties of nonlinear gravitational waves in modified gravity

Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial $f(R)$ gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial $f(R)$ gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient $a_{2}$ of the Taylor expansion of $f(R)$ is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of $a_{2}$. Anisotropic solutions are found, whose wave-fronts trace out time- or space-like hypersurfaces with complicated geometric properties. We show that the solutions exist in $f(R)$ theories that are consistent with Solar System and pulsar timing experiments.

Experimental Studies on the Lorentz Symmetry in Post-Newtonian Gravity with Pulsars

Local Lorentz invariance (LLI) is one of the most important fundamental symmetries in modern physics. While the possibility of LLI violation (LLIv) was studied extensively in flat spacetime, its counterpart in gravitational interaction also deserves significant examination from experiments. In this contribution, I review several recent studies of LLI in post-Newtonian gravity, using powerful tools of pulsar timing. It shows that precision pulsar timing experiments hold a unique position to probe LLIv in post-Newtonian gravity.

SYSTEMATIC AND STOCHASTIC VARIATIONS IN PULSAR DISPERSION MEASURES

ABSTRACT We analyze deterministic and random temporal variations in the dispersion measure (DM) from the full three-dimensional velocities of pulsars with respect to the solar system, combined with electron-density variations over a wide range of length scales. Previous treatments have largely ignored pulsars’ changing distances while favoring interpretations involving changes in sky position from transverse motion. Linear trends in pulsar DMs observed over 5–10 year timescales may signify sizable DM gradients in the interstellar medium (ISM) sampled by the changing direction of the line of sight to the pulsar. We show that motions parallel to the line of sight can also account for linear trends, for the apparent excess of DM variance over that extrapolated from scintillation measurements, and for the apparent non-Kolmogorov scalings of DM structure functions inferred in some cases. Pulsar motions through atomic gas may produce bow-shock ionized gas that also contributes to DM variations. We discuss the possible causes of periodic or quasi-periodic changes in DM, including seasonal changes in the ionosphere, annual variations of the solar elongation angle, structure in the heliosphere and ISM boundary, and substructure in the ISM. We assess the solar cycle’s role on the amplitude of ionospheric and solar wind variations. Interstellar refraction can produce cyclic timing variations from the error in transforming arrival times to the solar system barycenter. We apply our methods to DM time series and DM gradient measurements in the literature and assess their consistency with a Kolmogorov medium. Finally, we discuss the implications of DM modeling in precision pulsar timing experiments.

Intrinsic instrumental polarization and high-precision pulsar timing

Radio telescopes are used to accurately measure the time of arrival (ToA) of radio pulses in pulsar timing experiments that target mostly millisecond pulsars (MSPs) due to their high rotational stability. This allows for detailed study of MSPs and forms the basis of experiments to detect gravitational waves. Apart from intrinsic and propagation effects, such as pulse-to-pulse jitter and dispersion variations in the interstellar medium, timing precision is limited in part by the following: polarization purity of the telescope's orthogonally polarized receptors, the signal-to-noise ratio (S/N) of the pulsar profile, and the polarization fidelity of the system. Using simulations, we present how fundamental limitations in recovering the true polarization reduce the precision of ToA measurements. Any real system will respond differently to each source observed depending on the unique pulsar polarization profile. Using the profiles of known MSPs we quantify the limits of observing system specifications that yield satisfactory ToA measurements, and we place a practical design limit beyond which improvement of the system results in diminishing returns. Our aim is to justify limits for the front-end polarization characteristics of next generation radio telescopes, leading to the Square Kilometre Array (SKA).

Possibility of setting a new constraint to scalar-tensor theories

Scalar-tensor theories (STTs) are a widely studied alternative to general relativity (GR) in which gravity is endowed with an additional scalar degree of freedom. Although severely constrained by solar system and pulsar timing experiments, there remains a large set of STTs which are consistent with all present day observations. In this paper, we investigate the possibility of probing a yet unconstrained region of the parameter space of STTs based on the fact that stability properties of highly compact neutron stars in these theories may radically differ from those in GR.