Radio timing constraints on the mass of the binary pulsar PSR J1528-3146

PSR J1528-3146 is a 60.8 ms pulsar orbiting a heavy white dwarf (WD) companion, with an orbital period of 3.18 d. This work aimed at characterizing the pulsar's astrometric, spin and orbital parameters by analyzing timing measurements conducted at the Parkes, MeerKAT and Nan\c{c}ay radio telescopes over almost two decades. The measurement of post-Keplerian perturbations to the pulsar's orbit can be used to constrain the masses of the two component stars of the binary, and in turn inform us on the history of the system. We analyzed timing data from the Parkes, MeerKAT and Nan\c{c}ay radio telescopes collected over $\sim$16 yrs, obtaining a precise rotation ephemeris for PSR J1528-3146. A Bayesian analysis of the timing data was carried out to constrain the masses of the two components and the orientation of the orbit. We further analyzed the polarization properties of the pulsar, in order to constrain the orientations of the magnetic axis and of the line-of-sight with respect to the spin axis. We measured a significant rate of advance of periastron for the first time, and put constraints on the Shapiro delay in the system and on the rate of change of the projected semi-major axis of the pulsar's orbit. The Bayesian analysis yielded measurements for the pulsar and companion masses of respectively $M_p = 1.61_{-0.13}^{+0.14}$ M$_\odot$ and $M_c = 1.33_{-0.07}^{+0.08}$ M$_\odot$ (68\% C.L.), confirming that the companion is indeed massive. This companion mass as well as other characteristics of PSR J1528$-$3146 make this pulsar very similar to PSR J2222-0137, a 32.8 ms pulsar orbiting a WD whose heavy mass ($\sim 1.32$ M$_\odot$) was unique among pulsar-WD systems until now. Our measurements therefore suggest common evolutionary scenarios for PSRs J1528-3146 and J2222-0137.Comment: 13 pages, 8 figures, abstract shortened to match astro-ph limi

Practical approaches to analyzing PTA data: Cosmic strings with six pulsars

We search for a stochastic gravitational wave background (SGWB) generated by a network of cosmic strings using six millisecond pulsars from Data Release 2 (DR2) of the European Pulsar Timing Array (EPTA). We perform a Bayesian analysis considering two models for the network of cosmic string loops, and compare it to a simple power-law model which is expected from the population of supermassive black hole binaries. Our main strong assumption is that the previously reported common red noise process is a SGWB. We find that the one-parameter cosmic string model is slightly favored over a power-law model thanks to its simplicity. If we assume a two-component stochastic signal in the data (supermassive black hole binary population and the signal from cosmic strings), we get a $95\%$ upper limit on the string tension of $\log_{10}(G\mu) < -9.9$ ($-10.5$) for the two cosmic string models we consider. In extended two-parameter string models, we were unable to constrain the number of kinks. We test two approximate and fast Bayesian data analysis methods against the most rigorous analysis and find consistent results. These two fast and efficient methods are applicable to all SGWBs, independent of their source, and will be crucial for analysis of extended data sets.Comment: 13 pages, 5 figure

The second data release from the European Pulsar Timing Array I. The dataset and timing analysis

Pulsar timing arrays offer a probe of the low-frequency gravitational wave spectrum (1 - 100 nanohertz), 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 years. 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 years. 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.Comment: 29 pages, 9 figures, 13 tables, Astronomy & Astrophysics in pres

Practical approaches to analyzing PTA data: Cosmic strings with six pulsars

We search for a stochastic gravitational wave background (SGWB) generated by a network of cosmic strings using six millisecond pulsars from Data Release 2 (DR2) of the European Pulsar Timing Array (EPTA). We perform a Bayesian analysis considering two models for the network of cosmic string loops, and compare it to a simple power-law model which is expected from the population of supermassive black hole binaries. Our main strong assumption is that the previously reported common red noise process is a SGWB. We find that the one-parameter cosmic string model is slightly favored over a power-law model thanks to its simplicity. If we assume a two-component stochastic signal in the data (supermassive black hole binary population and the signal from cosmic strings), we get a 95% upper limit on the string tension of log10(Gμ)<-9.9 (-10.5) for the two cosmic string models we consider. In extended two-parameter string models, we were unable to constrain the number of kinks. We test two approximate and fast Bayesian data analysis methods against the most rigorous analysis and find consistent results. These two fast and efficient methods are applicable to all SGWBs, independent of their source, and will be crucial for analysis of extended datasets

The second data release from the European Pulsar Timing Array IV. Search for continuous gravitational wave signals

We present the results of a search for continuous gravitational wave signals (CGWs) in the second data release (DR2) of the European Pulsar Timing Array (EPTA) collaboration. The most significant candidate event from this search has a gravitational wave frequency of 4-5 nHz. Such a signal could be generated by a supermassive black hole binary (SMBHB) in the local Universe. We present the results of a follow-up analysis of this candidate using both Bayesian and frequentist methods. The Bayesian analysis gives a Bayes factor of 4 in favor of the presence of the CGW over a common uncorrelated noise process, while the frequentist analysis estimates the p-value of the candidate to be 1%, also assuming the presence of common uncorrelated red noise. However, comparing a model that includes both a CGW and a gravitational wave background (GWB) to a GWB only, the Bayes factor in favour of the CGW model is only 0.7. Therefore, we cannot conclusively determine the origin of the observed feature, but we cannot rule it out as a CGW source. We present results of simulations that demonstrate that data containing a weak gravitational wave background can be misinterpreted as data including a CGW and vice versa, providing two plausible explanations of the EPTA DR2 data. Further investigations combining data from all PTA collaborations will be needed to reveal the true origin of this feature.Comment: 12 figures, 15 pages, to be submitte

The second data release from the European Pulsar Timing Array: II. Customised pulsar noise models for spatially correlated gravitational waves

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

The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals

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% (≳3σ 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

The second data release from the European Pulsar Timing Array: IV. Implications for massive black holes, dark matter, and the early Universe

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

Comparing recent PTA results on the nanohertz stochastic gravitational wave background

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 $1\sigma$. 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 and 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 as single PTA.Comment: 21 pages, 9 figures, submitted to Ap

Comparing Recent Pulsar Timing Array Results on the Nanohertz Stochastic Gravitational-wave Background

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