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Kolmogorov analysis of pulsar TOA

N. Galikyan, A. A. Kocharyan, V. G. Gurzadyan

Abstract

The Kolmogorov stochasticity parameter (KSP) as a sensitive descriptor of degree of randomness of signals is used to analyze the properties of the NANOGrav pulsar timing data associated to a stochastic gravitational wave background. The time of arrival (TOA) data of white noise for 68 pulsars are analyzed regarding their KSP properties. The analysis enables to obtain the degree of randomness of the white noise for various pulsars and to reveal its inhomogeneity, i.e. pulsars with low and high randomness of the white noise. The time-dependence of the randomness in the white noise is also studied, indicating the existence of non-stationary physical processes influencing the pulsar timing. The KSP thus is acting as an indicator for the degree of the agreement between the observations and the timing models and as a test in revealing the contribution of various physical processes in the stochastic background signal.

Kolmogorov analysis of pulsar TOA

Abstract

The Kolmogorov stochasticity parameter (KSP) as a sensitive descriptor of degree of randomness of signals is used to analyze the properties of the NANOGrav pulsar timing data associated to a stochastic gravitational wave background. The time of arrival (TOA) data of white noise for 68 pulsars are analyzed regarding their KSP properties. The analysis enables to obtain the degree of randomness of the white noise for various pulsars and to reveal its inhomogeneity, i.e. pulsars with low and high randomness of the white noise. The time-dependence of the randomness in the white noise is also studied, indicating the existence of non-stationary physical processes influencing the pulsar timing. The KSP thus is acting as an indicator for the degree of the agreement between the observations and the timing models and as a test in revealing the contribution of various physical processes in the stochastic background signal.
Paper Structure (9 sections, 8 equations, 5 figures, 2 tables)

This paper contains 9 sections, 8 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Kolmogorov stochasticity parameter
  3. Theoretical and Empirical Cumulative Distribution Functions
  4. Kolmogorov Distance and Stochasticity Parameter
  5. Pulsar timing
  6. Analysis
  7. $\beta=\mathrm{const}$
  8. $\beta=\beta(t)$
  9. Conclusions

Figures (5)

  • Figure 1: The KSP distributions for the simulated/observed data of pulsars' white noise, when the histograms do differ. Orange and blue histograms correspond to simulations and observations, respectively.
  • Figure 2: The same as in Figure \ref{['fig:different']}, but for sample pulsars when the KSP distributions for the simulated/observed data are similar.
  • Figure 3: The case of pulsar J1125+7819, when the KSP distributions became similar after introducing $\beta(t)$.
  • Figure 4: The KSP distributions for pulsar J1910+1256. Introducing the time dependence in $\beta$ does not significantly affect $\chi^2$.
  • Figure 5: The KSP distributions for the pulsar J1022+1001 after introducing the time dependence in $\beta$. Although $\langle\chi^2\rangle$ is smaller in the $\beta(t)$ approach (Tab. \ref{['tab:chi_betat']}) than in the $\beta=\mathrm{const}$ case (Tab. \ref{['tab:chi']}), they are of the same order.