Pulsars are exceptionally stable cosmic clocks. If a pulsar can be found found orbiting a supermassive black hole, its precisely measured pulse arrival times can be used to probe the spacetime around the black hole and test gravity in the strong-field regime. In particular, a pulsar orbiting Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, would provide a powerful new tool for measuring the fundamental properties of the closest supermassive black hole to the Earth. Previous studies have shown that timing a pulsar with an orbital period of less than about 0.5 year could potentially measure the mass, spin, and quadrupole moment of Sgr A* with fractional errore better than 1%, providing a stringent test of the no-hair theorem in the general relativity. However, realizing this potential requires a sufficiently accurate pulsar timing model that incorporates all effects that are expected to be measurable in future observations.
To address this challenge, a research team led by Prof. Lijing Shao in the Kavli Institute for Astronomy and Astrophysics at Peking University have developed the first realistic numerical timing model for pulsars orbiting a supermassive black hole. The study incorporates a comprehensive set of high-order effects in both the orbital motion of the pulsar and the propagation of its radio pulses. The model is designed to provide a practical framework for future timing observations of pulsars around Sgr A*.
Figure 1: Illustration of a pulsar orbiting the supermassive black hole Sgr A*.
A pulsar–Sgr A* system differs significantly from the binary pulsar systems currently used for precision tests of gravity. Because of the enormous mass of the supermassive black hole, the orbital motion of the pulsar and the propagation of its radio pulses produces large timing delays, making several relativistic effects beyond Newtonian gravity easily observable with future radio telescopes. The new timing model therefore incorporates post-Newtonian orbital dynamics up to the second-order corrections, including spin–orbit coupling and the quadrupole moment of the supermassive black hole, as well as all higher-order light-propagation effects that can produce a time delay that is larger or comparable to the timing precision expected for future observations with next-generation facilities, such as the Square Kilometre Array (SKA). For the first time, the research team also incorporated effects associated with the proper motion of Sgr A* that gradually changes the viewing angle of the system.
An important aspect of the study is its treatment of timing red noise. Unlike many millisecond-pulsar timing systems, pulsars found near the Galactic Center are more likely to be normal pulsars, for which intrinsic timing red noise can be substantial. The complex interstellar environment around the Galactic Center may introduce additional noise, while the orbital timescale of a pulsar–Sgr A* system can be comparable to the timescale of the red noise itself. As a result, timing red noise in a pulsar–Sgr A* system can have significant influence on the inference of its parameters from data. Based on a Bayesian framework that estimates the timing parameters and red-noise properties simultaneously, the results show that when red noise is modeled properly, even relatively strong red noise causes only a mild increase in parameter uncertainties for sufficiently compact pulsar orbits. In contrast, an improper treatment can lead to significant biases and potentially produce misleading conclusions in precision tests of gravity, for example, falsely alarming a violation of the general relativity.
Figure 2. Red noise realizations and the bias in the parameter estimation with different treatments of the red noise (Hu, Wang, Shao 2026).
The realistic timing model developed in this work provides a comprehensive and efficient framework for analyzing future pulsar–Sgr A* observations. By incorporating high-order relativistic effects, the proper motion of Sgr A*, and realistic noise treatment, it bridges the gap between theoretical predictions and the analysis of actual timing data. The framework will be practically useful for future timing of pulsars around Sgr A* and for extracting information about the supermassive black hole and its surrounding spacetime once such systems are discovered.
The study, “A Realistic Pulsar–Supermassive Black Hole Timing Model,” is recently published in The Astrophysical Journal Supplement Series. Zexin Hu and Ziming Wang from the Department of Astronomy and the Kavli Institute for Astronomy and Astrophysics are the first and second authors of the paper. The study was supported by the National Natural Science Foundation of China, the National SKA Program of China, the Beijing Natural Science Foundation, and the Max Planck Partner Group Program.
Article: Z. Hu, Z. Wang, L. Shao, A Realistic Pulsar–Supermassive Black Hole Timing Model, ApJS 286 (2026) 41
Link: https://doi.org/10.3847/1538-4365/ae8d23
