Multifractal Analysis of Pulsar Timing Residuals: Assessment of Gravitational Wave Detection

Abstract

We introduce a pipeline including multifractal detrended cross-correlation analysis (MF-DXA) modified by either singular value decomposition or the adaptive method to examine the statistical properties of the pulsar timing residual ($PTR$) induced by a gravitational wave (GW) signal. We propose a new algorithm, the so-called irregular-MF-DXA, to deal with irregular data sampling. Inspired by the quadrupolar nature of the spatial cross-correlation function of a gravitational wave background, a new cross-correlation function, ${\bar{\sigma }}_{\times }$, derived from irregular-MF-DXA will be introduced. We show that, this measure reveals the quadrupolar signature in the $PTRs$ induced by stochastic GWB. We propose four strategies based on the $y$-intercept of fluctuation functions, the generalized Hurst exponent, and the width of the singularity spectrum to determine the dimensionless amplitude and power-law exponent of the characteristic strain spectrum as ${\mathcal{H}}_c(f)\sim {\mathcal{A}}_{yr}(f/f_{yr}{)}^{\zeta }$ for stochastic GWB. Using the value of Hurst exponent, one can clarify the type of GWs. We apply our pipeline to explore 20 millisecond pulsars observed by Parkes Pulsar Timing Array. The computed scaling exponents confirm that all data are classified into a nonstationary class implying the universality feature. The value of the Hurst exponent is in the range $H\in [0.56,0.87]$. The $q$-dependency of the generalized Hurst exponent demonstrates that the observed $PTRs$ have multifractal behavior, and the source of this multifractality is mainly attributed to the correlation of data which is another universality of the observed datasets. Multifractal analysis of available $PTRs$ datasets reveals an upper bound on the dimensionless amplitude of the GWB, ${\mathcal{A}}_{yr}<2.0\times 10^{-15}$.

arXiv comment19 pages, 14 figures and 1 table. Including major revision and matched to accepted version in ApJ. In this version irregularity in data has been examined by introducing novel method in fractal analysis of data set. In addition, we have introduced new measure to magnify the footprint of GWs

References in corpus (69)

• Multifractal detrended fluctuation analysis of nonstationary time series
• Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Non-stationary Time Series
• Detecting Long-range Correlations with Detrended Fluctuation Analysis
• Effect of Trends on Detrended Fluctuation Analysis
• TEMPO2, a new pulsar timing package. I: Overview
• Gravitational Wave Experiments and Early Universe Cosmology
• Effect of nonstationarities on detrended fluctuation analysis
• Multifractal detrended cross-correlation analysis for two nonstationary signals
• The statistical properties of the volatility of price fluctuations
• Tempo2, a new pulsar timing package. II: The timing model and precision estimates
• Generating surrogate data for time series with several simultaneously measured variables
• Gravitational radiation from cosmic (super)strings: bursts, stochastic background, and observational windows
• The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays
• The Parkes Pulsar Timing Array Project
• Detection methods for stochastic gravitational-wave backgrounds: a unified treatment
• Gravitational waves from binary supermassive black holes missing in pulsar observations
• The International Pulsar Timing Array: First Data Release
• The North American Nanohertz Observatory for Gravitational Waves
• Detrending moving average algorithm for multifractals
• 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
• Upper bounds on the low-frequency stochastic gravitational wave background from pulsar timing observations: current limits and future prospects
• Multifractal Detrended Fluctuation Analysis of Sunspot Time Series
• Quantifying signals with power-law correlations: A comparative study of detrended fluctuation analysis and detrended moving average techniques
• Placing limits on the stochastic gravitational-wave background using European Pulsar Timing Array data
• Ultra-Low Frequency Gravitational Radiation from Massive Black Hole Binaries
• Detecting the stochastic gravitational wave background using pulsar timing
• Optimal strategies for gravitational wave stochastic background searches in pulsar timing data
• The Parkes Pulsar Timing Array
• Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces
• Cosmology with the lights off: Standard sirens in the Einstein Telescope era
• On measuring the gravitational-wave background using Pulsar Timing Arrays
• Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series
• Pulsar timing analysis in the presence of correlated noise
• Common Scaling Patterns in Intertrade Times of U. S. Stocks
• Fractal Analysis of River Flow Fluctuations (with Erratum)
• Multifractal Detrended Cross-Correlation Analysis of Sunspot Numbers and River Flow Fluctuations
• An all-sky search for continuous gravitational waves in the Parkes Pulsar Timing Array data set
• Hyper-efficient model-independent Bayesian method for the analysis of pulsar timing data
• Searching For Anisotropic Gravitational-wave Backgrounds Using Pulsar Timing Arrays
• A data-analysis strategy for detecting gravitational-wave signals from inspiraling compact binaries with a network of laser-interferometric detectors
• A study of spatial correlations in pulsar timing array data
• Effect of extreme data loss on long-range correlated and anti-correlated signals quantified by detrended fluctuation analysis
• Pulsars as Tools for Fundamental Physics and Astrophysics
• A High Braking Index for a Pulsar
• Detrending Moving Average variance: a derivation of the scaling law
• Detection Rate Estimates of Gravity-waves Emitted During Parabolic Encounters of Stellar Black Holes in Globular Clusters
• The Effect of Orbital Eccentricity on Gravitational Wave Background Radiation from Supermassive Black Hole Binaries
• TEMPO2, a new pulsar timing package. III: Gravitational wave simulation
• All correlations must die: Assessing the significance of a stochastic gravitational-wave background in pulsar-timing arrays
• The noise properties of 42 millisecond pulsars from the European Pulsar Timing Array and their impact on gravitational wave searches
• Variance fluctuations in nonstationary time series: a comparative study of music genres
• Bayesian Analysis of the Chaplygin Gas and Cosmological Constant Models using the SNe Ia Data
• Long-range correlation and multifractality in Bach's Inventions pitches
• Detection and localization of single-source gravitational waves with pulsar timing arrays
• The Parkes Pulsar Timing Array
• Pulsars as gravitational wave detectors
• Detection and localization of continuous gravitational waves with pulsar timing arrays: the role of pulsar terms
• Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise
• Can the bivariate Hurst exponent be higher than an average of the separate Hurst exponents?
• Effects of polynomial trends on detrending moving average analysis
• Assessment of 48 Stock markets using adaptive multifractal approach
• Observational constraints on light cosmic strings from photometry and pulsar timing
• Harmonic space analysis of pulsar timing array redshift maps
• Long range correlation in cosmic microwave background radiation
• Minimizing the effect of sinusoidal trends in detrended fluctuation analysis
• Cross-correlation method for intermediate-duration gravitational wave searches associated with gamma-ray bursts
• Experimental confirmation of long-memory correlations in star-wander data
• Identification of Defective Two Dimensional Semiconductors by Multifractal Analysis: The Single-layer $\mathrm{Mo}{\mathrm{S}}_2$ Case Study

Cited by in corpus (7)

• Description of turbulent dynamics in the interstellar medium: multifractal/microcanonical analysis I. Application to Herschel observations of the Musca filament
• Persistent Homology of Fractional Gaussian Noise
• Long-range temporal correlation in Auditory Brainstem Responses to Spoken Syllable /da/
• Homology Groups of Embedded Fractional Brownian Motion
• Analysis of the structural complexity of Crab Nebula observed at radio frequency using a multifractal approach
• Hurst index of gamma-ray burst light curves and its statistical study
• Graph-based Summary Statistics for Revealing the Stochastic Gravitational Wave Background in Pulsar Timing Arrays