Long-term stability estimation of ensemble pulsar timescales with NICER observations

¹ School of Aerospace Science and Technology, Xidian University, Xi’an, China
² Shaanxi Key Laboratory of Space Extreme Detection, Xi’an, China
³ Peng Cheng Laboratory, Shenzhen, China
⁴ Academy of Advanced Interdisciplinary Research, Xidian University, Xi’an, China
⁵ National Time Service Center (NTSC), Chinese Academy of Sciences (CAS), Xi’an, China
⁶ Xi’an Institute of Surveying and Mapping, Xi’an 710054, China

^⋆ Corresponding author: lrshen@xidian.edu.cn

Received: 6 September 2024
Accepted: 21 April 2025

Abstract

Context. The ensemble pulsar timescale (EPT), derived from the rotation rates of millisecond pulsars, exhibits a stability comparable to the International Atomic Time (TAI) over a decade.

Aims. This research aims to establish an X-ray-based EPT and evaluate its stability through a comprehensive analysis of 7.3 years of NICER observations of PSR B1937+21 (PSR J1939+2134) and PSR B1821-24 (PSR J1824-2452A).

Methods. By leveraging an advanced parameter fitting technique, we refined the timing parameters, and achieved notable convergence in timing residuals. To reduce the impact of prominent white noise characteristics inherent in X-ray data, we devised an integrated timing residuals generation framework. This framework incorporates the subtraction of red noise, using both Gaussian process regression (GPR) and Bayesian factor analysis methodologies. Additionally, we introduced an enhanced Wiener filtering algorithm, tailored specifically to enhance the stability of the EPT, which further refined our analysis and ensured robust results.

Results. The root mean square errors (RMSE) of the timing residuals were determined to be 4.17 μs for PSR B1937+21 and 25.07 μs for PSR B1821-24. We find strong evidence of red noise in the 7.3-year data of both pulsars and, combined with our proposed simulation residual generation framework, successfully construct an ensemble pulsar timescale. The 7.3-year EPT stability was improved to 4.19 × 10⁻¹⁵, which represents an improvement of one order of magnitude compared to conventional methods.

Conclusions. The EPT framework developed herein facilitates reproducible experiments, and yields statistically robust stability metrics derived from X-ray data. Notably, the tailored Wiener filtering algorithm, which is designed to address the unique challenges of X-ray data, significantly increases the stability of the EPT.