Graph-based Summary Statistics for Revealing the Stochastic Gravitational Wave Background in Pulsar Timing Arrays

Abstract

In this work, we propose a graph-based method implemented on the pulsar timing residuals (PTRs) for stochastic gravitational wave background (SGWB) detection within the nano-Hertz frequency regime and examining uncertainties of its parameters. We construct a correlation graph with pulsars as its nodes, and analyze the graph-based summary statistics, including structural characteristics of complex network, for identifying SGWB in the real and synthetic datasets. The effect of the number of pulsars, the observation time span, and the strength of the SGWB on the graph-based feature vector is evaluated. Our results demonstrate that the Discriminative Summary Statistics for common signal detection consists of the average clustering coefficient and the edge weight fluctuation. The SGWB detection conducted after the observation of a common signal and then exclusion of non-Hellings \& Downs templates is performed by the second cumulant of edge weight for angular separation thresholds $\bar{\zeta }\gtrsim 40^{\circ }$. The lowest detectable value of SGWB strain amplitude utilizing our graph-based measures at the current PTAs sensitivity is $A_{\mathrm{SGWB}}\gtrsim 1.2\times 10^{-15}$. Fisher forecasts confirmed that the uncertainty levels of ${\log }_{10}{A}_{\mathrm{SGWB}}$ and spectral index reach $1.5\%$ and $19.5\%$, respectively, at $2\sigma$ confidence interval. A weak evidence for an SGWB at $\sim 2.3\sigma$ level is obtained by applying our graph-based method to the NANOGrav 15-year dataset.

29 pages, 15 figures, 1 table. Matched with the published version. Including the revision in a part of method

References in corpus (81)

• Statistical mechanics of complex networks
• Observation of Gravitational Waves from a Binary Black Hole Merger
• Recurrence Plots for the Analysis of Complex Systems
• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• TEMPO2, a new pulsar timing package. I: Overview
• Bilby: A user-friendly Bayesian inference library for gravitational-wave astronomy
• Intensity and coherence of motifs in weighted complex networks
• Gravitational Wave Experiments and Early Universe Cosmology
• Cosmological Backgrounds of Gravitational Waves
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• Physics, Astrophysics and Cosmology with Gravitational Waves
• The NANOGrav 15-year Data Set: Search for Signals from New Physics
• The international pulsar timing array project: using pulsars as a gravitational wave detector
• Complex network approaches to nonlinear time series analysis
• The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics
• The Parkes Pulsar Timing Array Project
• High-precision timing of 42 millisecond pulsars with the European Pulsar Timing Array
• The International Pulsar Timing Array: First Data Release
• The North American Nanohertz Observatory for Gravitational Waves
• Gravitational wave bursts from cusps and kinks on cosmic strings
• The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars
• An Upper Limit on the Stochastic Gravitational-Wave Background of Cosmological Origin
• Deep Learning for Real-time Gravitational Wave Detection and Parameter Estimation: Results with Advanced LIGO Data
• Limits on the Stochastic Gravitational Wave Background from the North American Nanohertz Observatory for Gravitational Waves
• Stochastic Gravitational Wave Backgrounds
• GetDist: a Python package for analysing Monte Carlo samples
• Detecting the stochastic gravitational wave background using pulsar timing
• Large parallel cosmic string simulations: New results on loop production
• Optimal strategies for gravitational wave stochastic background searches in pulsar timing data
• Stochastic gravitational wave background from smoothed cosmic string loops
• Time series irreversibility: a visibility graph approach
• The Parkes Pulsar Timing Array Third Data Release
• A Gravitational Wave Detector with Cosmological Reach
• PINT: A Modern Software Package for Pulsar Timing
• Enhancing Gravitational-Wave Science with Machine Learning
• A Mock Data Challenge for the Einstein Gravitational-Wave Telescope
• Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
• The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget
• A method for the estimation of the significance of cross-correlations in unevenly sampled red-noise time series
• Machine-learning non-stationary noise out of gravitational wave detectors
• The Parkes Pulsar Timing Array Project: Second data release
• Pulsars as Tools for Fundamental Physics and Astrophysics
• Nuisance hardened data compression for fast likelihood-free inference
• Network Cosmology
• Persistent Homology of Complex Networks for Dynamic State Detection
• Time-domain Implementation of the Optimal Cross-Correlation Statistic for Stochastic Gravitational-Wave Background Searches in Pulsar Timing Data
• Stochastic gravitational waves from cosmic string loops in scaling
• Noise Reduction in Gravitational-wave Data via Deep Learning
• SWIGLAL: Python and Octave interfaces to the LALSuite gravitational-wave data analysis libraries
• Parameter Estimation in Searches for the Stochastic Gravitational-Wave Background
• LISACode : A scientific simulator of LISA
• CLASS_GWB: robust modeling of the astrophysical gravitational wave background anisotropies
• Machine Learning Gravitational Waves from Binary Black Hole Mergers
• How much information can be extracted from galaxy clustering at the field level?
• Persistent homology in cosmic shear: constraining parameters with topological data analysis
• Time Series Analysis via Network Science: Concepts and Algorithms
• Second Einstein Telescope Mock Science Challenge : Detection of the GW Stochastic Background from Compact Binary Coalescences
• Stochastic gravitational wave background phenomenology in a pulsar timing array
• Stochastic gravitational wave background: methods and Implications
• Multi-messenger constraints on Abelian-Higgs cosmic string networks
• Topological Feature Vectors for Chatter Detection in Turning Processes
• Discriminating Topology in Galaxy Distributions using Network Analysis
• Constraining modified theories of gravity with gravitational wave stochastic background
• The Gravitational Wave Universe Toolbox: A software package to simulate observation of the Gravitational Wave Universe with different detectors
• Accelerating Multi-Model Bayesian Inference, Model Selection and Systematic Studies for Gravitational Wave Astronomy
• Cosmology with Persistent Homology: a Fisher Forecast
• Non-parametric reconstruction of cosmological observables using Gaussian Processes Regression
• Swift sky localization of gravitational waves using deep learning seeded importance sampling
• Multifractal Analysis of Pulsar Timing Residuals: Assessment of Gravitational Wave Detection
• Fast Likelihood-free Reconstruction of Gravitational Wave Backgrounds
• Localization of gravitational waves using machine learning
• Visualizing the pulsar population using graph theory
• A convenient approach to characterizing model uncertainty with application to early dark energy solutions of the Hubble tension
• Neural Networks unveiling the properties of gravitational wave background from massive black hole binaries
• Imprint of massive neutrinos on Persistent Homology of large-scale structure
• Persistent Homology of Coarse Grained State Space Networks
• Topology of Pulsar Profiles (ToPP). I. Graph theory method and classification of the EPN
• Stochastic approach to gravitational waves from inflation
• Resolving Individual Signals in the Presence of Stochastic Background in Future Pulsar Timing Arrays
• Millisecond pulsars phenomenology under the light of graph theory
• Impact of Redshift Space Distortion on Persistent Homology of cosmic matter density field