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Context.High-precision pulsar timing is highly dependent on the precise and accurate modelling of any effects that can potentially impact the data. In particular, effects that contain stochastic elements contribute to some level of corruption and complexity in the analysis of pulsar-timing data. It has been shown that commonly used solar wind models do not accurately account for variability in the amplitude of the solar wind on both short and long timescales. Aims.In this study, we test and validate a new, cutting-edge solar wind modelling method included in theenterprisesoftware suite (widely used for pulsar noise analysis) through extended simulations. We use it to investigate temporal variability in LOFAR data. Our model testing scheme in itself provides an invaluable asset for pulsar timing array (PTA) experiments. Since, improperly accounting for the solar wind signature in pulsar data can induce false-positive signals, it is of fundamental importance to include in any such investigations. Methods.We employed a Bayesian approach utilising a continuously varying Gaussian process to model the solar wind. It uses a spherical approximation that modulates the electron density. This method, which we refer to as a solar wind Gaussian process (SWGP), has been integrated into existing noise analysis software, specificallyenterprise. Our Validation of this model was performed through simulations. We then conduct noise analysis on eight pulsars from the LOFAR dataset, with most pulsars having a time span of ∼11 years encompassing one full solar activity cycle. Furthermore, we derived the electron densities from the dispersion measure values obtained by the SWGP model. Results.Our analysis reveals a strong correlation between the electron density at 1 AU and the ecliptic latitude (ELAT) of the pulsar. Pulsars with |ELAT|< 3° exhibit significantly higher average electron densities. Furthermore, we observed distinct temporal patterns in the electron densities in different pulsars. In particular, pulsars within |ELAT|< 3° exhibit similar temporal variations, while the electron densities of those outside this range correlate with the solar activity cycle. Notably, some pulsars exhibit sensitivity to the solar wind up to 45° away from the Sun in LOFAR data. Conclusions.The continuous variability in electron density offered in this model represents a substantial improvement over previous models, that assume a single value for piece-wise bins of time. This advancement holds promise for solar wind modelling in future International Pulsar Timing Array (IPTA) data combinations. 

Abstract Single-pulse studies are important to understand the pulsar emission mechanism and the noise floor in precision timing. We study total intensity and polarimetry properties of three bright millisecond pulsars – PSRs J1022+1001, J1713+0747, and B1855+09 – that have detectable single pulses at multiple frequencies. We report for the first time the detection of single pulses from PSRs J1022+1001 and J1713+0747 at 4.5 GHz. In addition, for those two pulsars, the fraction of linear polarization in the average profile is significantly reduced at 4.5 GHz, compared to 1.38 GHz, which could support the expected deviation from a dipolar field closer to the pulsar surface. There is a hint of orthogonal modes in the single pulses of PSR J1713+0747. More sensitive multifrequency observations may be useful to confirm these findings. The jitter noise contributions at 1.38 GHz, scaled to one hour, for PSRs J1022+1001, J1713+0747, and B1855+09 are ≈135, ≈45, and ≈60 ns, respectively and are consistent with previous studies. We also show that selective bright-pulse timing of PSR J1022+1001 yields improved root-mean-square residuals of ≈22 $$\mu$$s, which is a factor of ≈3 better than timing using single pulses alone. 

ABSTRACT The International Pulsar Timing Array 2nd data release is the combination of data sets from worldwide collaborations. In this study, we search for continuous waves: gravitational wave signals produced by individual supermassive black hole binaries in the local universe. We consider binaries on circular orbits and neglect the evolution of orbital frequency over the observational span. We find no evidence for such signals and set sky averaged 95 per cent upper limits on their amplitude h95. The most sensitive frequency is 10 nHz with h95 = 9.1 × 10−15. We achieved the best upper limit to date at low and high frequencies of the PTA band thanks to improved effective cadence of observations. In our analysis, we have taken into account the recently discovered common red noise process, which has an impact at low frequencies. We also find that the peculiar noise features present in some pulsars data must be taken into account to reduce the false alarm. We show that using custom noise models is essential in searching for continuous gravitational wave signals and setting the upper limit. 

Abstract The Australian, Chinese, European, Indian, and North American pulsar timing array (PTA) collaborations recently reported, at varying levels, evidence for the presence of a nanohertz gravitational-wave background (GWB). Given that each PTA made different choices in modeling their data, we perform a comparison of the GWB and individual pulsar noise parameters across the results reported from the PTAs that constitute the International Pulsar Timing Array (IPTA). We show that despite making different modeling choices, there is no significant difference in the GWB parameters that are measured by the different PTAs, agreeing within 1σ. The pulsar noise parameters are also consistent between different PTAs for the majority of the pulsars included in these analyses. We bridge the differences in modeling choices by adopting a standardized noise model for all pulsars and PTAs, finding that under this model there is a reduction in the tension in the pulsar noise parameters. As part of this reanalysis, we “extended” each PTA’s data set by adding extra pulsars that were not timed by that PTA. Under these extensions, we find better constraints on the GWB amplitude and a higher signal-to-noise ratio for the Hellings–Downs correlations. These extensions serve as a prelude to the benefits offered by a full combination of data across all pulsars in the IPTA, i.e., the IPTA’s Data Release 3, which will involve not just adding in additional pulsars but also including data from all three PTAs where any given pulsar is timed by more than a single PTA. 

ABSTRACT We searched for an isotropic stochastic gravitational wave background in the second data release of the International Pulsar Timing Array, a global collaboration synthesizing decadal-length pulsar-timing campaigns in North America, Europe, and Australia. In our reference search for a power-law strain spectrum of the form $$h_c = A(f/1\, \mathrm{yr}^{-1})^{\alpha }$$, we found strong evidence for a spectrally similar low-frequency stochastic process of amplitude $$A = 3.8^{+6.3}_{-2.5}\times 10^{-15}$$ and spectral index α = −0.5 ± 0.5, where the uncertainties represent 95 per cent credible regions, using information from the auto- and cross-correlation terms between the pulsars in the array. For a spectral index of α = −2/3, as expected from a population of inspiralling supermassive black hole binaries, the recovered amplitude is $$A = 2.8^{+1.2}_{-0.8}\times 10^{-15}$$. None the less, no significant evidence of the Hellings–Downs correlations that would indicate a gravitational-wave origin was found. We also analysed the constituent data from the individual pulsar timing arrays in a consistent way, and clearly demonstrate that the combined international data set is more sensitive. Furthermore, we demonstrate that this combined data set produces comparable constraints to recent single-array data sets which have more data than the constituent parts of the combination. Future international data releases will deliver increased sensitivity to gravitational wave radiation, and significantly increase the detection probability.