[Paper Review] Tests of Classical Gravity with Radio Pulsars

Zexin Hu, Xueli Miao+1 more|arXiv (Cornell University)|Mar 30, 2023

Pulsars and Gravitational Waves ResearchPhysics and Astronomy129 references8 citations

TL;DR

The paper pedagogically reviews pulsar timing as a tool to test general relativity in quasi-stationary strong-field gravity, using Hulse-Taylor, double, and triple pulsars, and discusses neutron star structure and modified gravity constraints.

ABSTRACT

Tests of gravity are important to the development of our understanding of gravitation and spacetime. Binary pulsars provide a superb playground for testing gravity theories. In this chapter we pedagogically review the basics behind pulsar observations and pulsar timing. We illustrate various recent strong-field tests of the general relativity (GR) from the Hulse-Taylor pulsar PSR B1913+16, the double pulsar PSR J0737$-$3039, and the triple pulsar PSR J0337+1715. We also overview the inner structure of neutron stars (NSs) that may influence some gravity tests, and have used the scalar-tensor gravity and massive gravity theories as examples to demonstrate the usefulness of pulsar timing in constraining specific modified gravity theories. Outlooks to new radio telescopes for pulsar timing and synergies with other strong-field gravity tests are also presented.

Motivation & Objective

• Explain pulsar timing basics and how TOAs are modeled in a Solar System Barycentre frame.
• Describe the Damour-Deruelle parametrized post-Keplerian (DD-PPK) formalism for binary pulsars.
• Show how GR-specific PPK parameters constrain neutron star masses and test gravity in strong fields.
• Present how neutron star inner structure and spin effects influence gravity tests using scalar-tensor and massive gravity examples.
• Outline future prospects with new radio telescopes and synergies with other strong-field gravity tests.

Proposed method

• Introduce pulsar timing and dispersion effects in the ISM and describe TOA formation.
• Present the DD timing model and the PPK parameters used to describe relativistic orbital effects.
• Provide GR expressions for PPK parameters and discuss degeneracies and alternative parametrizations (e.g., h3, h4).
• Explain geodetic and orbital precession and their potential to probe neutron star moments of inertia and equation of state.
• Illustrate self-consistency checks in GR via mass-mass diagrams using measured PPK parameters.
• Discuss how timing data from well-studied systems test gravity theories and constrain modified gravity models.

Figure 1: The period–period derivative diagram for pulsars Manchester:2005 . The black dots are pulsars with pulsed emission in the radio band and the red circles mark binary systems. We also denote “AXP” for systems that are anomalous X-ray pulsars or soft $\gamma$ -ray repeaters, “RRAT” for system

Experimental results

Research questions

• RQ1 How well does GR describe pulsar binary dynamics in quasi-stationary strong-field regimes?
• RQ2 Can pulsar timing measure PPK parameters with sufficient precision to test GR and constrain NS properties?
• RQ3 What are the implications of spin-orbit and geodetic precession for gravity tests and NS EOS?
• RQ4 How do alternative gravity theories manifest in pulsar timing observables and what constraints can be placed?

Key findings

• GR predictions for the tested pulsar systems agree with observations within reported uncertainties.
• For PSR B1913+16, the intrinsic orbital decay rate matches GR to within a few parts in 10^3 after Shklovskii and Galactic corrections.
• For PSR J0737−3039A/B, multiple independent tests (dot omega, gamma, dotP_b, and Shapiro parameters) are consistent with GR within a few parts in 10^3.
• The mass-mass diagrams show intersecting PPK curves within uncertainties, supporting GR in strong-field conditions.
• Geodetic precession has been detected in some systems, enabling tests of spin-orbit coupling and potential NS EOS implications.
• The timing framework allows exploration of modified gravity theories via parametric deviations in PPK parameters.

Figure 2: Stack of 100 single pulses from PSR J2222 $-$ 0137, observed with the FAST telescope Miao:2023gkr . The line in the top is the integrated profile of these 100 pulses.