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.
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Aims.
The nanohertz gravitational wave background (GWB) is expected to be an aggregate signal of an ensemble of gravitational waves emitted predominantly by a large population of coalescing ...supermassive black hole binaries in the centres of merging galaxies. Pulsar timing arrays (PTAs), which are ensembles of extremely stable pulsars at approximately kiloparsec distances precisely monitored for decades, are the most precise experiments capable of detecting this background. However, the subtle imprints that the GWB induces on pulsar timing data are obscured by many sources of noise that occur on various timescales. These must be carefully modelled and mitigated to increase the sensitivity to the background signal.
Methods.
In this paper, we present a novel technique to estimate the optimal number of frequency coefficients for modelling achromatic and chromatic noise, while selecting the preferred set of noise models to use for each pulsar. We also incorporated a new model to fit for scattering variations in the Bayesian pulsar timing package temponest. These customised noise models enable a more robust characterisation of single-pulsar noise. We developed a software package based on tempo2 to create realistic simulations of European Pulsar Timing Array (EPTA) datasets that allowed us to test the efficacy of our noise modelling algorithms.
Results.
Using these techniques, we present an in-depth analysis of the noise properties of 25 millisecond pulsars (MSPs) that form the second data release (DR2) of the EPTA and investigate the effect of incorporating low-frequency data from the Indian Pulsar Timing Array collaboration for a common sample of ten MSPs. We used two packages, enterprise and temponest, to estimate our noise models and compare them with those reported using EPTA DR1. We find that, while in some pulsars we can successfully disentangle chromatic from achromatic noise owing to the wider frequency coverage in DR2, in others the noise models evolve in a much more complicated way. We also find evidence of long-term scattering variations in PSR J1600-3053. Through our simulations, we identify intrinsic biases in our current noise analysis techniques and discuss their effect on GWB searches. The analysis and results discussed in this article directly help to improve the sensitivity to the GWB signal and they are already being used as part of global PTA efforts.
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ABSTRACT
Recently, global pulsar timing arrays have released results from searching for a nano-Hertz gravitational wave background signal. Although there has not been any definite evidence of the ...presence of such a signal in residuals of pulsar timing data yet, with more and improved data in future, a statistically significant detection is expected to be made. Stochastic algorithms are used to sample a very large parameter space to infer results from data. In this paper, we attempt to rule out effects arising from the stochasticity of the sampler in the inference process. We compare different configurations of nested samplers and the more commonly used markov chain monte carlo method to sample the pulsar timing array parameter space and account for times taken by the different samplers on same data. Although we obtain consistent results on parameters from different sampling algorithms, we propose two different samplers for robustness checks on data in the future to account for cross-checks between sampling methods as well as realistic run-times.
The European Pulsar Timing Array (EPTA) and Indian Pulsar Timing Array (InPTA) collaborations have measured a low-frequency common signal in the combination of their second and first data releases, ...respectively, with the correlation properties of a gravitational wave background (GWB). Such a signal may have its origin in a number of physical processes including a cosmic population of inspiralling supermassive black hole binaries (SMBHBs); inflation, phase transitions, cosmic strings, and tensor mode generation by the non-linear evolution of scalar perturbations in the early Universe; and oscillations of the Galactic potential in the presence of ultra-light dark matter (ULDM). At the current stage of emerging evidence, it is impossible to discriminate among the different origins. Therefore, for this paper, we consider each process separately, and investigated the implications of the signal under the hypothesis that it is generated by that specific process. We find that the signal is consistent with a cosmic population of inspiralling SMBHBs, and its relatively high amplitude can be used to place constraints on binary merger timescales and the SMBH-host galaxy scaling relations. If this origin is confirmed, this would be the first direct evidence that SMBHBs merge in nature, adding an important observational piece to the puzzle of structure formation and galaxy evolution. As for early Universe processes, the measurement would place tight constraints on the cosmic string tension and on the level of turbulence developed by first-order phase transitions. Other processes would require non-standard scenarios, such as a blue-tilted inflationary spectrum or an excess in the primordial spectrum of scalar perturbations at large wavenumbers. Finally, a ULDM origin of the detected signal is disfavoured, which leads to direct constraints on the abundance of ULDM in our Galaxy.
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ABSTRACT
We present results from the search for a stochastic gravitational-wave background (GWB) as predicted by the theory of General Relativity using six radio millisecond pulsars from the Data ...Release 2 (DR2) of the European Pulsar Timing Array (EPTA) covering a timespan up to 24 yr. A GWB manifests itself as a long-term low-frequency stochastic signal common to all pulsars, a common red signal (CRS), with the characteristic Hellings-Downs (HD) spatial correlation. Our analysis is performed with two independent pipelines, ENTERPRISE, and TEMPONEST+FORTYTWO, which produce consistent results. A search for a CRS with simultaneous estimation of its spatial correlations yields spectral properties compatible with theoretical GWB predictions, but does not result in the required measurement of the HD correlation, as required for GWB detection. Further Bayesian model comparison between different types of CRSs, including a GWB, finds the most favoured model to be the common uncorrelated red noise described by a power law with $A = 5.13_{-2.73}^{+4.20} \times 10^{-15}$ and $\gamma = 3.78_{-0.59}^{+0.69}$ (95 per cent credible regions). Fixing the spectral index to γ = 13/3 as expected from the GWB by circular, inspiralling supermassive black hole binaries results in an amplitude of $A =2.95_{-0.72}^{+0.89} \times 10^{-15}$. We implement three different models, BAYESEPHEM, LINIMOSS, and EPHEMGP, to address possible Solar system ephemeris (SSE) systematics and conclude that our results may only marginally depend on these effects. This work builds on the methods and models from the studies on the EPTA DR1. We show that under the same analysis framework the results remain consistent after the data set extension.
We present the results of the search for an isotropic stochastic gravitational wave background (GWB) at nanohertz frequencies using the second data release of the European Pulsar Timing Array (EPTA) ...for 25 millisecond pulsars and a combination with the first data release of the Indian Pulsar Timing Array (InPTA). A robust GWB detection is conditioned upon resolving the Hellings-Downs angular pattern in the pairwise cross-correlation of the pulsar timing residuals. Additionally, the GWB is expected to yield the same (common) spectrum of temporal correlations across pulsars, which is used as a null hypothesis in the GWB search. Such a common-spectrum process has already been observed in pulsar timing data. We analysed (i) the full 24.7-year EPTA data set, (ii) its 10.3-year subset based on modern observing systems, (iii) the combination of the full data set with the first data release of the InPTA for ten commonly timed millisecond pulsars, and (iv) the combination of the 10.3-year subset with the InPTA data. These combinations allowed us to probe the contributions of instrumental noise and interstellar propagation effects. With the full data set, we find marginal evidence for a GWB, with a Bayes factor of four and a false alarm probability of 4%. With the 10.3-year subset, we report evidence for a GWB, with a Bayes factor of 60 and a false alarm probability of about 0.1% (≳3
σ
significance). The addition of the InPTA data yields results that are broadly consistent with the EPTA-only data sets, with the benefit of better noise modelling. Analyses were performed with different data processing pipelines to test the consistency of the results from independent software packages. The latest EPTA data from new generation observing systems show non-negligible evidence for the GWB. At the same time, the inferred spectrum is rather uncertain and in mild tension with the common signal measured in the full data set. However, if the spectral index is fixed at 13/3, the two data sets give a similar amplitude of (2.5 ± 0.7) × 10
−15
at a reference frequency of 1 yr
−1
. Further investigation of these issues is required for reliable astrophysical interpretations of this signal. By continuing our detection efforts as part of the International Pulsar Timing Array (IPTA), we expect to be able to improve the measurement of spatial correlations and better characterise this signal in the coming years.
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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.
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We report on radio timing observations of PSR J0210+5845 that reveal large deviations from typical pulsar spin-down behaviour. We interpret these deviations as being due to the binary motion around ...the V = 13.5 star 2MASS J02105640+5845176, which is coincident in terms of its celestial position and distance with the pulsar. Archival observations and new optical spectroscopy have identified this object as a B6 V star, with a temperature of T eff ≈ 14 000 K and a mass of M c = 3.5 to 3.8 M ⊙ , making it the lowest mass for a main sequence star known to be orbiting a non-recycled pulsar. We find that the timing observations constrain the binary orbit to be wide and moderately eccentric, with an orbital period of P b = 47 −14 +40 yr and eccentricity of e = 0.46 −0.07 +0.10 . We predict that the next periastron passage will occur between 2030 and 2034. Due to the low companion mass, we find that the probability for a system with the properties of PSR J0210+5845 and its binary companion to survive the supernova is low. We show that a low velocity and fortuitously directed natal kick is required for the binary to remain bound during the supernova explosion and we argue that an electron-capture supernova is a plausible formation scenario for the pulsar.
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We report on radio timing observations of the black widow binary pulsar J0610−2100 and optical observations of its binary companion. The radio timing observations extend the timing baseline to 16 yr ...and reveal a marginal detection of the orbital period derivative, but they show no significant evidence of orbital variations such as those seen in other black widow pulsars. Furthermore, no eclipses are seen in the observations at observing frequencies ranging from 310 to 2700 MHz. The optical
VRI
light curves were modulated with the orbital period, reaching maximum brightness of
V
= 26.8,
R
= 25.4, and
I
= 23.8 at superior conjunction of the companion, confirming irradiation of the companion by the pulsar. Modelling the light curves indicates that the companion is likely not filling its Roche lobe, while having a moderate inclination (
i
> 54°). We find an unusually low temperature and a low irradiation for the irradiated hemisphere of the companion. We investigate the absence of radio eclipses in PSR J0610−2100 and in other black widow systems in relation to their binary, pulsar, and companion properties. We also discuss the suitability of PSR J0610−2100 for pulsar timing array observations aimed at detecting nano-Hertz gravitational waves.
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ABSTRACT
The European Pulsar Timing Array (EPTA) collaboration has recently released an extended data set for six pulsars (DR2) and reported evidence for a common red noise signal. Here we present a ...noise analysis for each of the six pulsars. We consider several types of noise: (i) radio frequency independent, ‘achromatic’, and time-correlated red noise; (ii) variations of dispersion measure and scattering; (iii) system and band noise; and (iv) deterministic signals (other than gravitational waves) that could be present in the PTA data. We perform Bayesian model selection to find the optimal combination of noise components for each pulsar. Using these custom models we revisit the presence of the common uncorrelated red noise signal previously reported in the EPTA DR2 and show that the data still supports it with a high statistical significance. Next, we confirm that there is no preference for or against the Hellings–Downs spatial correlations expected for the stochastic gravitational-wave background. The main conclusion of the EPTA DR2 paper remains unchanged despite a very significant change in the noise model of each pulsar. However, modelling the noise is essential for the robust detection of gravitational waves and its impact could be significant when analysing the next EPTA data release, which will include a larger number of pulsars and more precise measurements.
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