Quality over Quantity: Optimizing pulsar timing array analysis for stochastic and continuous gravitational wave signals

The search for gravitational waves using Pulsar Timing Arrays (PTAs) is acomputationally expensive complex analysis that involves source-specific noisestudies. As more pulsars are added to the arrays, this stage of PTA analysiswill become increasingly challenging. Therefore, optimizing the number ofincluded pulsars is crucial to reduce the computational burden of dataanalysis. Here, we present a suite of methods to rank pulsars for use withinthe scope of PTA analysis. First, we use the maximization of thesignal-to-noise ratio as a proxy to select pulsars. With this method, we targetthe detection of stochastic and continuous gravitational wave signals. Next, wepresent a ranking that minimizes the coupling between spatial correlationsignatures, namely monopolar, dipolar, and Hellings & Downs correlations.Finally, we also explore how to combine these two methods. We test theseapproaches against mock data using frequentist and Bayesian hypothesis testing.For equal-noise pulsars, we find that an optimal selection leads to an increasein the log-Bayes factor two times steeper than a random selection for thehypothesis test of a gravitational wave background versus a common uncorrelatedred noise process. For the same test but for a realistic EPTA dataset, a subsetof 25 pulsars selected out of 40 can provide a log-likelihood ratio that is$89\%$ of the total, implying that an optimally selected subset of pulsars canyield results comparable to those obtained from the whole array. We expectthese selection methods to play a crucial role in future PTA data combinations.<br

Region 11 MELD Na Exception Prospective Study

Introduction. Hyponatremia complicates cirrhosis and predicts short term mortality, including adverse outcomes before and after liver transplantation. Material and methods. From April 1, 2008, through April 2, 2010, all adult candidates for primary liver transplantation with cirrhosis, listed in Region 11 with hyponatremia, were eligible for sodium (Na) exception. Results. Patients with serum sodium (SNa) less than 130 mg/dL, measured two weeks apart and within 30 days of Model for End Stage Liver Disease (MELD) exception request, were given preapproved Na exception. MELD Na was calculated [MELD + 1.59 (135-SNa/30 days)]. MELD Na was capped at 22, and subject to standard adult recertification schedule. On data end of follow-up, December 28, 2010, 15,285 potential U.S. liver recipients met the inclusion criteria of true MELD between 6 and 22. In Region 11, 1,198 of total eligible liver recipients were listed. Sixty-two (5.2%) patients were eligible for Na exception (MELD Na); 823 patients (68.7%) were listed with standard MELD (SMELD); and 313 patients (26.1%) received HCC MELD exception. Ninety percent of MELD Na patients and 97% of HCC MELD patients were transplanted at end of follow up, compared to 49% of Region 11 standard MELD and 40% of U.S.A. standard MELD (USA MELD) patients (p \u3c 0.001); with comparable dropout rates (6.5, 1.6, 6.9, 9% respectively; p = 0.2). MELD Na, HCC MELD, Region 11 SMELD, and USA MELD post-transplant six-month actual patient survivals were similar (92.9, 92.8, 92.2, and 93.9 %, respectively). Conclusion. The Region 11 MELD Na exception prospective trial improved hyponatremic cirrhotic patient access to transplant equitably, and without compromising transplant efficacy

Periodic interstellar scintillation variations of PSRs~J0613−-0200 and J0636+5128 associated with the Local Bubble shell

Annual variations of interstellar scintillation can be modelled to constrain parameters of the ionized interstellar medium. If a pulsar is in a binary system, then investigating the orbital parameters is possible through analysis of the orbital variation of scintillation. In observations carried out from 2011 January to 2020 August by the European Pulsar Timing Array radio telescopes, PSRs~J0613$-$0200 and J0636+5128 show strong annual variations in their scintillation velocity, while the former additionally exhibits an orbital fluctuation. Bayesian theory and Markov-chain-Monte-Carlo methods are used to interpret these periodic variations. We assume a thin and anisotropic scattering screen model, and discuss the mildly and extremely anisotropic scattering cases. PSR~J0613$-$0200 is best described by mildly anisotropic scattering, while PSR~J0636+5128 exhibits extremely anisotropic scattering. We measure the distance, velocity and degree of anisotropy of the scattering screen for our two pulsars, finding that scattering screen distances from Earth for PSRs~J0613$-$0200 and J0636+5128 are 316$^{+28}_{-20}$\,pc and 262$^{+96}_{-38}$\,pc, respectively. The positions of these scattering screens are coincident with the shell of the Local Bubble towards both pulsars. These associations add to the growing evidence of the Local Bubble shell as a dominant region of scattering along many sightlines.Comment: Accepted by SCIENCE CHINA Physics, Mechanics & Astronomy ( SCPMA

A Gaussian-processes approach to fitting for time-variable spherical solar wind in pulsar timing data

Propagation effects are one of the main sources of noise in high-precision pulsar timing. For pulsars below an ecliptic latitude of 5°, the ionized plasma in the solar wind can introduce dispersive delays of order 100 µs around solar conjunction at an observing frequency of 300 MHz. A common approach to mitigate this assumes a spherical solar wind with a time-constant amplitude. However, this has been shown to be insufficient to describe the solar wind. We present a linear, Gaussian-process piecewise Bayesian approach to fit a spherical solar wind of time-variable amplitude, which has been implemented in the pulsar software RUN_ENTERPRISE. Through simulations, we find that the current EPTA+InPTA data combination is not sensitive to such variations; however, solar wind variations will become important in the near future with the addition of new InPTA data and data collected with the low-frequency LOFAR telescope. We also compare our results for different high-precision timing data sets (EPTA+InPTA, PPTA, and LOFAR) of 3 ms pulsars (J0030+0451, J1022+1001, J2145−0450), and find that the solar-wind amplitudes are generally consistent for any individual pulsar, but they can vary from pulsar to pulsar. Finally, we compare our results with those of an independent method on the same LOFAR data of the three millisecond pulsars. We find that differences between the results of the two methods can be mainly attributed to the modelling of dispersion variations in the interstellar medium, rather than the solar wind modelling

The impact of solar wind variability on pulsar timing

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

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 $\log_{10}(G\mu) < -9.9$ ($-10.5$) 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

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