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Abstract We present 15 yr of Nançay and Green Bank radio telescope timing observations for PSR J1231−1411. This millisecond pulsar is a primary science target for the Neutron Star Interior Composition Explorer telescope (NICER, which discovered its X-ray pulsations), has accumulated near-continuousγ-ray data since the Fermi-Large Area Telescope’s launch, and has been studied extensively with the Green Bank and Nançay radio telescopes. We have undertaken a campaign with the Green Bank Telescope targeting specific orbital phases designed to improve our constraint on the pulsar’s mass through the detection of a relativistic Shapiro delay. Both frequentist and Bayesian techniques—the latter incorporating priors from white dwarf binary evolution models—are applied to 15 yr of radio observations, yielding relatively weak constraints on the companion and pulsar masses of $0.23_{-0.06}^{+0.09}$ M_⊙and $1.87_{-0.67}^{+1.11}$ M_⊙, respectively (68.3% CI from Bayesian fits); however, the orbital inclination is measured to better relative precision ( $79.80_{-4.70}^{+3.47}$ °). Restricting the maximum allowed pulsar mass to 3M_⊙improves the constraint and lowers the measured mass to $1.71_{-0.56}^{+0.70}$ M_⊙. A fully generalized Bayesian fit that simultaneously samples the noise and timing models yields a pulsar mass in close agreement with this value. While our radio-derived inclination result has informed recent NICER X-ray studies of J1231−1411, the lessons learned from this troublesome pulsar will also bolster future high-precision mass measurement campaigns and resulting constraints on the neutron star interior equation of state. 

Pulsar timing arrays (PTAs) are ensembles of millisecond pulsars observed for years to decades. The primary goal of PTAs is to study gravitational-wave astronomy at nanohertz frequencies, with secondary goals of undertaking other fundamental tests of physics and astronomy. Recently, compelling evidence has emerged in established PTA experiments for the presence of a gravitational-wave background. To accelerate a confident detection of such a signal and then study gravitational-wave emitting sources, it is necessary to observe a larger number of millisecond pulsars to greater timing precision. The SKA telescopes, which will be a factor of three to four greater in sensitivity compared to any other southern hemisphere facility, is poised to make such an impact. In this chapter, we motivate an SKAO pulsar timing array (SKAO PTA) experiment. We discuss the classes of gravitational waves present in PTA observations and how an SKAO PTA can detect and study them. We then describe the sources that can produce these signals. We discuss the astrophysical noise sources that must be mitigated to undertake the most sensitive searches. We then describe a realistic PTA experiment implemented with the SKA and place it in context alongside other PTA experiments likely ongoing in the 2030s. We describe the techniques necessary to search for gravitational waves in the SKAO PTA and motivate how very long baseline interferometry can improve the sensitivity of an SKAO PTA. The SKAO PTA will provide a view of the Universe complementary to those of the other large facilities of the 2030s. 

Abstract Evidence for a low-frequency gravitational-wave background using pulsar timing arrays has generated recent interest in its underlying contributing sources. However, multiple investigations have seen that the significance of the evidence does not change with the choice of pulsar modeling techniques, but the resulting parameters from the gravitational wave searches do. PSR J1455−3330 is one of the longest-observed pulsars in the array monitored by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), but showed no evidence for long-timescale red noise, either intrinsic or the common signal found among many pulsars in the array. In this work, we argue that NANOGrav’s piecewise-constant function used to model variations in radio-frequency-dependent dispersive delay should not be used for this pulsar, and a much simpler physical model of a fixed solar wind density plus a linear or quadratic trend in dispersion measure is preferred. When the original model is replaced, (i) the pulsar’s timing parallax signal changes from an upper limit to a significant detection, (ii) red noise becomes significant, and (iii) the red noise is consistent with the common signal found for the other pulsars. Neither of these signals is radio-frequency dependent. While the same physical motivation will not apply to many of the pulsars currently used in pulsar timing arrays, we argue for careful, physically motivated timing and noise modeling of pulsars used in precision timing experiments. 

Abstract PINTis a pure-Python framework for high-precision pulsar timing developed on top of widely used and well-tested Python libraries, supporting both interactive and programmatic data analysis workflows. We present a new frequentist framework withinPINTto characterize the single-pulsar noise processes present in pulsar timing data sets. This framework enables parameter estimation for both uncorrelated and correlated noise processes, as well as model comparison between different timing and noise models in a computationally inexpensive way. We demonstrate the efficacy of the new framework by applying it to simulated data sets as well as a real data set of PSR B1855+09. We also describe the new features implemented inPINTsince it was first described in the literature. 

Abstract Pulsar timing array experiments have recently uncovered evidence for a nanohertz gravitational wave background by precisely timing an ensemble of millisecond pulsars. The next significant milestones for these experiments include characterizing the detected background with greater precision, identifying its source(s), and detecting continuous gravitational waves from individual supermassive black hole binaries. To achieve these objectives, generating accurate and precise times of arrival of pulses from pulsar observations is crucial. Incorrect polarization calibration of the observed pulsar profiles may introduce errors in the measured times of arrival. Further, previous studies have demonstrated that robust polarization calibration of pulsar profiles can reduce noise in the pulsar timing data and improve timing solutions. In this paper, we investigate and compare the impact of different polarization calibration methods on pulsar timing precision using three distinct calibration techniques: the Ideal Feed Assumption (IFA), Measurement Equation Modeling (MEM), and Measurement Equation Template Matching (METM). Three NANOGrav pulsars—PSRs J1643−1224, J1744−1134, and J1909−3744—observed with the 800 MHz and 1.5 GHz receivers at the Green Bank Telescope (GBT) are utilized for our analysis. Our findings reveal that all three calibration methods enhance timing precision compared to scenarios where no polarization calibration is performed. Additionally, among the three calibration methods, the IFA approach generally provides the best results for timing analysis of pulsars observed with the GBT receiver system. We attribute the comparatively poorer performance of the MEM and METM methods to potential instabilities in the reference noise diode coupled to the receiver and temporal variations in the profile of the reference pulsar, respectively. 

Abstract Pulsar timing arrays (PTAs) have recently entered the detection era, quickly moving beyond the goal of simply improving sensitivity at the lowest frequencies for the sake of observing the stochastic gravitational wave background (GWB), and focusing on its accurate spectral characterization. While all PTA collaborations around the world use Fourier-domain Gaussian processes to model the GWB and intrinsic long time-correlated (red) noise, techniques to model the time-correlated radio-frequency-dependent (chromatic) processes have varied from collaboration to collaboration. Here we test a new class of models for PTA data, Gaussian processes based on time-domain kernels that model the statistics of the chromatic processes starting from the covariance matrix. As we will show, these models can be effectively equivalent to Fourier-domain models in mitigating chromatic noise. This work presents a method for Bayesian model selection across the various choices of kernel as well as deterministic chromatic models for nonstationary chromatic events and the solar wind. As PTAs turn toward high frequency (>1 yr⁻¹) sensitivity, the size of the basis used to model these processes will need to increase, and these time-domain models present some computational efficiencies compared to Fourier-domain models. 

Abstract Accurate pulsar astrometric estimates are essential to almost all high-precision pulsar timing experiments. Traditional pulsar timing techniques refine these estimates by including them as free parameters when fitting a model to observed pulse time-of-arrival measurements. However, reliable submilliarcsecond astrometric estimations require years of observations. Even then, power from red noise can be inadvertently absorbed into astrometric parameter fits. This effect biases the resulting estimates and reduces the sensitivity to red noise processes, including gravitational waves (GWs). In this work, we seek to mitigate these shortcomings by using pulsar astrometric estimates derived from very long baseline interferometry (VLBI) as priors for the timing fit. First, we used VLBI and timing astrometric estimates of 18 millisecond pulsars to calibrate a rotation between the reference frames used in timing and VLBI, with a precision of ∼0.7 mas. Through this frame tie, we combined timing- and VLBI-based probabilities to obtain a maximum-posterior astrometric solution. We found offsets between our results and the timing-based astrometric solutions, which, if real, would lead to the absorption of spectral power at the frequencies of interest for single-source GW searches. However, we do not find significant power absorption due to astrometric fitting at the low-frequency domain of the GW background. 

Abstract Free-floating objects (FFOs) in interstellar space—rogue planets, brown dwarfs, and large asteroids that are not gravitationally bound to any star—are expected to be ubiquitous throughout the Milky Way. Recent microlensing surveys have discovered several free-floating planets that are not bound to any known stellar systems. Additionally, three interstellar objects, namely 1I/’Oumuamua, 2I/Borisov, and 3I/ATLAS, have been detected passing through our solar system on hyperbolic trajectories. In this work, we search for FFOs on hyperbolic orbits that pass near millisecond pulsars (MSPs), where their gravitational influence can induce detectable perturbations in pulse arrival times. Using the NANOGrav 15 yr narrow band dataset, which contains high-precision timing data for 68 MSPs, we conduct a search for such hyperbolic scattering events between FFOs and pulsars. Although no statistically significant events were detected, this nondetection enables us to place upper limits (ULs) on the number density of FFOs as a function of their mass within our local region of the Galaxy. For example, the UL on the number density for Jupiter-mass FFOs (∼10^−2.5–10^−3.5M_⊙) obtained from different pulsars ranges from 5.25 × 10⁶pc⁻³to 5.37 × 10⁹pc⁻³, while the UL calculated by combining results from all the pulsars is 6.03 × 10⁵pc⁻³. These results represent the first constraints on FFO population derived from pulsar timing data. 

Abstract Noise characterization for pulsar-timing applications accounts for interstellar dispersion by assuming a known frequency dependence of the delay it introduces in the times of arrival (TOAs). However, calculations of this delay suffer from misestimations due to other chromatic effects in the observations. The precision in modeling dispersion is dependent on the observed bandwidth. In this work, we calculate the offsets in infinite-frequency TOAs due to misestimations in the modeling of dispersion when using varying bandwidths at the Green Bank Telescope. We use a set of broadband observations of PSR J1643−1224, a pulsar with unusual chromatic timing behavior. We artificially restricted these observations to a narrowband frequency range, then used both the broad- and narrowband data sets to calculate residuals with a timing model that does not account for time variations in the dispersion. By fitting the resulting residuals to a dispersion model and comparing the fits, we quantify the error introduced in the timing parameters due to using a reduced frequency range. Moreover, by calculating the autocovariance function of the parameters, we obtained a characteristic timescale over which the dispersion misestimates are correlated. For PSR J1643−1224, which has one of the highest dispersion measures (DM) in the NANOGrav pulsar timing array, we find that the infinite-frequency TOAs suffer from a systematic offset of ∼22μs due to incomplete frequency sampling, with correlations over about one month. For lower-DM pulsars, the offset is ∼7μs. This error quantification can be used to provide more robust noise modeling in the NANOGrav data, thereby increasing the sensitivity and improving the parameter estimation in gravitational wave searches. 

Abstract Based on the rate of change of its orbital period, PSR J2043+1711 has a substantial peculiar acceleration of 3.5 ± 0.8 mm s^–1yr^–1, which deviates from the acceleration predicted by equilibrium Milky Way (MW) models at a 4σlevel. The magnitude of the peculiar acceleration is too large to be explained by disequilibrium effects of the MW interacting with orbiting dwarf galaxies (∼1 mm s^–1yr^–1), and too small to be caused by period variations due to the pulsar being a redback. We identify and examine two plausible causes for the anomalous acceleration: a stellar flyby, and a long-period orbital companion. We identify a main-sequence star in Gaia DR3 and Pan-STARRS DR2 with the correct mass, distance, and on-sky position to potentially explain the observed peculiar acceleration. However, the star and the pulsar system have substantially different proper motions, indicating that they are not gravitationally bound. However, it is possible that this is an unrelated star that just happens to be located near J2043+1711 along our line of sight (chance probability of 1.6%). Therefore, we also constrain possible orbital parameters for a circumbinary companion in a hierarchical triple system with J2043+1711; the changes in the spindown rate of the pulsar are consistent with an outer object that has an orbital period of 60 kyr, a companion mass of 0.3M_⊙(indicative of a white dwarf or low-mass star), and a semimajor axis of 1900 au. Continued timing and/or future faint optical observations of J2043+1711 may eventually allow us to differentiate between these scenarios.