Kolmogorov analysis of pulsar TOA

¹ Center for Cosmology and Astrophysics, Alikhanian National Laboratory and Yerevan State University Yerevan, Armenia
² Department of Physics, Sapienza University of Rome Rome, Italy
³ School of Physics and Astronomy, Monash University Clayton, Australia
⁴ SIA, Sapienza University of Rome Rome, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 12 January 2026
Accepted: 17 February 2026

Abstract

The Kolmogorov stochasticity parameter (KSP) as a sensitive descriptor of the degree of randomness of signals was used to analyze the properties of the NANOGrav pulsar timing data associated with a stochastic gravitational wave background. The time of arrival (TOA) data of white noise for 68 pulsars were analyzed regarding their KSP properties. The analysis enabled us 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 was also studied, indicating the existence of nonstationary physical processes influencing the pulsar timing. The KSP is thus 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.