skip to main content

Title: Search for Continuous Gravitational-wave Signals in Pulsar Timing Residuals: A New Scalable Approach with Diffusive Nested Sampling
Abstract Detecting continuous nanohertz gravitational waves (GWs) generated by individual close binaries of supermassive black holes (CB-SMBHs) is one of the primary objectives of pulsar timing arrays (PTAs). The detection sensitivity is slated to increase significantly as the number of well-timed millisecond pulsars will increase by more than an order of magnitude with the advent of next-generation radio telescopes. Currently, the Bayesian analysis pipeline using parallel tempering Markov Chain Monte Carlo has been applied in multiple studies for CB-SMBH searches, but it may be challenged by the high dimensionality of the parameter space for future large-scale PTAs. One solution is to reduce the dimensionality by maximizing or marginalizing over uninformative parameters semianalytically, but it is not clear whether this approach can be extended to more complex signal models without making overly simplified assumptions. Recently, the method of diffusive nested (DNest) sampling has shown capability in coping with high dimensionality and multimodality effectively in Bayesian analysis. In this paper, we apply DNest to search for continuous GWs in simulated pulsar timing residuals and find that it performs well in terms of accuracy, robustness, and efficiency for a PTA including  ( 10 2 ) pulsars. DNest also allows a simultaneous search more » of multiple sources elegantly, which demonstrates its scalability and general applicability. Our results show that it is convenient and also highly beneficial to include DNest in current toolboxes of PTA analysis. « less
Authors:
; ; ; ; ; ; ;
Award ID(s):
2018900
Publication Date:
NSF-PAR ID:
10356726
Journal Name:
The Astrophysical Journal
Volume:
922
Issue:
2
Page Range or eLocation-ID:
228
ISSN:
0004-637X
Sponsoring Org:
National Science Foundation
More Like this
  1. ABSTRACT The search for gravitational waves using Pulsar Timing Arrays (PTAs) is a computationally expensive complex analysis that involves source-specific noise studies. As more pulsars are added to the arrays, this stage of PTA analysis will become increasingly challenging. Therefore, optimizing the number of included pulsars is crucial to reduce the computational burden of data analysis. Here, we present a suite of methods to rank pulsars for use within the scope of PTA analysis. First, we use the maximization of the signal-to-noise ratio as a proxy to select pulsars. With this method, we target the detection of stochastic and continuous gravitational wave signals. Next, we present a ranking that minimizes the coupling between spatial correlation signatures, namely monopolar, dipolar, and Hellings & Downs correlations. Finally, we also explore how to combine these two methods. We test these approaches against mock data using frequentist and Bayesian hypothesis testing. For equal-noise pulsars, we find that an optimal selection leads to an increase in the log-Bayes factor two times steeper than a random selection for the hypothesis test of a gravitational wave background versus a common uncorrelated red noise process. For the same test but for a realistic European PTA (EPTA) data set, amore »subset of 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 can yield results comparable to those obtained from the whole array. We expect these selection methods to play a crucial role in future PTA data combinations.« less
  2. Abstract While observations of many high-precision radio pulsars of order ≲1 μ s across the sky are needed for the detection and characterization of a stochastic background of low-frequency gravitational waves (GWs), sensitivity to single sources of GWs requires even higher timing precision. The Argentine Institute of Radio Astronomy (IAR; Instituto Argentino de Radioastronomía) has begun observations of the brightest known millisecond pulsar, J0437−4715. Even though the two antennas are smaller than other single-dish telescopes previously used for pulsar timing array (PTA) science, the IAR’s capability to monitor this pulsar daily, coupled with the pulsar’s brightness, allows for high-precision measurements of pulse-arrival time. While upgrades of the facility are currently underway, we show that modest improvements beyond current plans will provide IAR with unparalleled sensitivity to this pulsar. The most stringent upper limits on single GW sources come from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). Observations of PSR J0437−4715 will provide a significant sensitivity increase in NANOGrav’s “blind spot” in the sky where fewer pulsars are currently being observed. With state-of-the-art instrumentation installed, we estimate the array’s sensitivity will improve by a factor of ≈2–4 over 10 yr for 20% of the sky with the inclusion ofmore »this pulsar, as compared to a static version of the PTA used in NANOGrav’s most recent limits. More modest instrumentation results in factors of ≈1.4–3. We identify four other candidate pulsars as suitable for inclusion in PTA efforts. International PTA efforts will also benefit from inclusion of these data, given the potential achievable sensitivity.« less
  3. Abstract Radio pulsar signals are significantly perturbed by their propagation through the ionized interstellar medium. In addition to the frequency-dependent pulse times of arrival due to dispersion, pulse shapes are also distorted and shifted, having been scattered by the inhomogeneous interstellar plasma, affecting pulse arrival times. Understanding the degree to which scattering affects pulsar timing is important for gravitational-wave detection with pulsar timing arrays (PTAs), which depend on the reliability of pulsars as stable clocks with an uncertainty of ∼100 ns or less over ∼10 yr or more. Scattering can be described as a convolution of the intrinsic pulse shape with an impulse response function representing the effects of multipath propagation. In previous studies, the technique of cyclic spectroscopy has been applied to pulsar signals to deconvolve the effects of scattering from the original emitted signals, increasing the overall timing precision. We present an analysis of simulated data to test the quality of deconvolution using cyclic spectroscopy over a range of parameters characterizing interstellar scattering and pulsar signal-to-noise ratio (S/N). We show that cyclic spectroscopy is most effective for high S/N and/or highly scattered pulsars. We conclude that cyclic spectroscopy could play an important role in scattering correction to distantmore »populations of highly scattered pulsars not currently included in PTAs. For future telescopes and for current instruments such as the Green Bank Telescope upgraded with the ultrawide bandwidth receiver, cyclic spectroscopy could potentially double the number of PTA-quality pulsars.« less
  4. Abstract Pulsar timing array (PTA) experiments are becoming increasingly sensitive to gravitational waves (GWs) in the nanohertz frequency range, where the main astrophysical sources are supermassive black hole binaries (SMBHBs), which are expected to form following galaxy mergers. Some of these individual SMBHBs may power active galactic nuclei, and thus their binary parameters could be obtained electromagnetically, which makes it possible to apply electromagnetic (EM) information to aid the search for a GW signal in PTA data. In this work, we investigate the effects of such an EM-informed search on binary detection and parameter estimation by performing mock data analyses on simulated PTA data sets. We find that by applying EM priors, the Bayes factor of some injected signals with originally marginal or sub-threshold detectability (i.e., Bayes factor ∼1) can increase by a factor of a few to an order of magnitude, and thus an EM-informed targeted search is able to find hints of a signal when an uninformed search fails to find any. Additionally, by combining EM and GW data, one can achieve an overall improvement in parameter estimation, regardless of the source’s sky location or GW frequency. We discuss the implications for the multi-messenger studies of SMBHBs withmore »PTAs.« less
  5. Abstract Statistical anisotropy in the nanohertz-frequency gravitational wave background (GWB) is expected to be detected by pulsar timing arrays (PTAs) in the near future. By developing a frequentist statistical framework that intrinsically restricts the GWB power to be positive, we establish scaling relations for multipole-dependent anisotropy decision thresholds that are a function of the noise properties, timing baselines, and cadences of the pulsars in a PTA. We verify that (i) a larger number of pulsars, and (ii) factors that lead to lower uncertainty on spatial cross-correlation measurements between pulsars, lead to a higher overall GWB signal-to-noise ratio, and lower anisotropy decision thresholds with which to reject the null hypothesis of isotropy. Using conservative simulations of realistic NANOGrav data sets, we predict that an anisotropic GWB with angular power C l =1 > 0.3 C l =0 may be sufficient to produce tension with isotropy at the p = 3 × 10 −3 (∼3 σ ) level in near-future NANOGrav data with a 20 yr baseline. We present ready-to-use scaling relationships that can map these thresholds to any number of pulsars, configuration of pulsar noise properties, or sky coverage. We discuss how PTAs can improve the detection prospects for anisotropy, asmore »well as how our methods can be adapted for more versatile searches.« less