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

2017/04/30 by I. Eghdami, H. Panahi, S. M. S. Movahed · 14 citations
Earth and Planetary Sciences · Physics and Astronomy · #Amplitude #Detrended fluctuation analysis #Exponent #Geophysics and Gravity Measurements #Gravitational wave #Hurst exponent #Multifractal system #Pulsar #Pulsars and Gravitational Waves Research #Statistical Mechanics and Entropy #Universality (dynamical systems) #astro-ph.CO #astro-ph.IM #astro-ph.SR #physics.data-an

paper · pdf · doi:10.3847/1538-4357/aad7b9

published in The Astrophysical Journal 864(2), 162 (IOP Publishing) · 19 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

openalex created_date 2017/05/12 · openalex publication_date 2018/09/10 · arxiv created 2018/10/11 · arxiv updated 2018/10/12 · openalex updated_date 2026/08/08

Abstract

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 (GWB), a new cross-correlation function, , 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 for stochastic GWB. Using the value of the Hurst exponent, one can clarify the type of GWs. We apply our pipeline to explore 20 ms pulsars observed by the 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 ∈ [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 data sets. Multifractal analysis of available PTR data sets reveals an upper bound on the dimensionless amplitude of the GWB, .

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