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A Realistic Pulsar - Supermassive Black Hole Timing Model

Zexin Hu, Ziming Wang, Lijing Shao

Abstract

Timing observation of pulsars orbiting around a supermassive black hole (SMBH) can measure the spacetime around the SMBH to a high precision and thus be a novel probe of the gravity theory. Future high-frequency surveys of the Galactic Centre (GC) region to be performed by the next-generation radio telescopes, such as the SKA, may discover pulsars that orbit around Sagittarius A* (Sgr A*), the SMBH dwelling in our GC. In this paper, we present a realistic pulsar-SMBH timing model based on the post-Newtonian equations of motion of the pulsar. Considering the expected timing precision in the future, we take into account several next-to-leading order light propagation time delays in the timing model. For the first time, we include the effects of proper motion of Sgr A*, which were expected to break the spin measurement degeneracy. We forecast the measurement precision of various parameters of Sgr A*, and discuss the data analysis procedure in the presence of red noise, which can be strong if the pulsar is a normal pulsar. The realistic timing model constructed in this study will serve as a useful tool in future searching and timing of pulsar-SMBH systems in the GC.

A Realistic Pulsar - Supermassive Black Hole Timing Model

Abstract

Timing observation of pulsars orbiting around a supermassive black hole (SMBH) can measure the spacetime around the SMBH to a high precision and thus be a novel probe of the gravity theory. Future high-frequency surveys of the Galactic Centre (GC) region to be performed by the next-generation radio telescopes, such as the SKA, may discover pulsars that orbit around Sagittarius A* (Sgr A*), the SMBH dwelling in our GC. In this paper, we present a realistic pulsar-SMBH timing model based on the post-Newtonian equations of motion of the pulsar. Considering the expected timing precision in the future, we take into account several next-to-leading order light propagation time delays in the timing model. For the first time, we include the effects of proper motion of Sgr A*, which were expected to break the spin measurement degeneracy. We forecast the measurement precision of various parameters of Sgr A*, and discuss the data analysis procedure in the presence of red noise, which can be strong if the pulsar is a normal pulsar. The realistic timing model constructed in this study will serve as a useful tool in future searching and timing of pulsar-SMBH systems in the GC.
Paper Structure (20 sections, 91 equations, 12 figures, 1 table)

This paper contains 20 sections, 91 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Timing model
  3. Light propagation
  4. Orbital dynamics
  5. The pulsar-SMBH timing model
  6. The inverse timing model
  7. Parameter estimation
  8. The Fisher matrix method
  9. Measurability of SMBH parameters
  10. The effects of proper motion
  11. The aberration effects
  12. Presence of timing red noise
  13. Red noise model
  14. Design matrix approximation
  15. Bias on parameter estimation
  16. ...and 5 more sections

Figures (12)

  • Figure 1: Illustration of the pulsar orbit with system parameters given in Equation (\ref{['eq:system params']}). The axes are in the unit of AU.
  • Figure 2: Various time delays described in the text for the fiducial pulsar-SMBH system. A constant term is removed from the 1PN Shapiro delay with respect to Equation (\ref{['eq:1PN Shapiro']}).
  • Figure 3: The fractional precision of SMBH parameters as functions of the pulsar's (a) orbital period and (b) orbital eccentricity.
  • Figure 4: (a) The measurement precision of the proper motion parameters $\mu_\alpha$ and $\mu_\delta$, and the longitude of the ascending node $\Omega$. Due to the degeneracy caused by the rotation symmetry, for estimating the measurability of the proper motion parameters, we fix $\Omega$, and vice versa, we fix the proper motion parameters when estimating the measurement precision of $\Omega$. (b) Comparison of parameter estimation results with or without considering the proper-motion effect. For parameter estimation that does not consider the proper motion, we fix $\Omega=0$ without losing generality.
  • Figure 5: Expected measurement precision of $\lambda_p$ and $\eta_p$ as functions of the pulsar orbital period $P_b$.
  • ...and 7 more figures