Abstract. Complexity as an emergent behavior is ubiquitous in the systems including a large number of degrees of freedom. Mentioned property is widely experienced in cosmological and astrophysical fields in 1, 2 and 3 dimensions. Among various astrophysical processes, Millisecond pulsars is highly stable and the predictability of their rotational behavior leading to be an almost proper tool to elucidate various physical phenomena ranging from early universe to late time.
In this talk, based on self-similarity of a typical stochastic process, we propose a robust pipeline in order to examine the footprint of stochastic gravitational waves superimposed on the pulsar timing residuals (PTRs). We introduce a new algorithm, the so-called Irregular-Multi-Fractal-Detrended-Cross Correlation-Analysis (Irregular MF-DXA), to deal with irregular data sampling recorded in the observations. According to the quadrupolar nature of the spatial cross-correlation function of a gravitational wave background, a new cross-correlation function will be introduced. We propose four strategies based on results derived by Irregular-MF-DXA to determine the dimensionless amplitude and power-law exponent of the characteristic strain spectrum for GWB. Using the value of Hurst exponent, one can clarify the type of GWs. The flexibility in the algorithm enables us to manipulate the contribution of noise and trends in PTRs. We apply our pipeline to explore 20 millisecond pulsars observed by Parkes Pulsar Timing Array (PPTA) project. Finally, some upper bounds on the dimensionless amplitude of GWs background, will be reported.
A pipeline for searching Stochastic Gravitational Wave by Pulsar Timing Residuals
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