Measuring the Lense-Thirring Orbital Precession and the Neutron Star Moment of Inertia with Pulsars

TL;DR

This work surveys how binary pulsar timing can probe the neutron star moment of inertia $I_{\rm NS}$ via Lense–Thirring precession, offering a direct route to constrain the dense-matter equation of state and connect to the I-Love-Q framework. It outlines the spin–orbit coupling physics, including LT-induced changes in periastron advance $\dot{\omega}$ and orbital inclination, and identifies the most promising systems (e.g., PSR J0737-3039A/B, PSR J1141-6545, PSR J1757-1854, PSR J1946+2052) where these effects may be measured. The paper discusses observational strategies, the need to separate LT signals from 1PN/2PN GR terms and GW damping, and how short orbital periods maximize LT significance, while kinematic corrections pose challenges. Looking ahead, upcoming facilities (MeerKAT, FAST, SKA) and space-based GW observatories (LISA) are expected to enable MoI measurements at the 1–10% level, yielding stringent EoS constraints and robust tests of GR and alternative gravity theories.

Abstract

Neutron stars (NSs) are compact objects that host the densest forms of matter in the observable universe, providing unique opportunities to study the behaviour of matter at extreme densities. While precision measurements of NS masses through pulsar timing have imposed effective constraints on the equation of state (EoS) of dense matter, accurately determining the radius or moment of inertia (MoI) of a NS remains a major challenge. This article presents a detailed review on measuring the Lense-Thirring (LT) precession effect in the orbit of binary pulsars, which would give access to the MoI of NSs and offer further constraints on the EoS. We discuss the suitability of certain classes of binary pulsars for measuring the LT precession from the perspective of binary star evolution, and highlight five pulsars that exhibit properties promising to realise these goals in the near future. Finally, discoveries of compact binaries with shorter orbital periods hold the potential to greatly enhance measurements of the MoI of NSs. The MoI measurements of binary pulsars are pivotal to advancing our understanding of matter at supranuclear densities as well as improving the precision of gravity tests, such as the orbital decay due to gravitational wave emission and of tests of alternative gravity theories.

Figures (9)

• Figure S1: The NS mass-radius relation for different EoSs listed in Lattimer_2001. The horizontal lines in yellow represents the 1-$\sigma$ mass ranges for the most massive NS known, PSR J0740+6620 Fonseca+2021. The pink bar in the middle shows the multimessenger constraint on the radius of a 1.4-$\mathrm{M_\odot}$ NS Dietrich+2020Sci at 90% confidence, and the cyan bar shows an updated radius constraint at 95% confidence Koehn+2024. The EoSs plotted in dashed lines are excluded by the lower limit of the maximum NS mass and the constraint of radius range in Dietrich+2020Sci. Figure courtesy of Norbert Wex.
• Figure S2: The change of the MoI with mass for different EoSs, coloured as in Fig \ref{['fig:RM']}. The yellow band represents the mass range of PSR J0740+6620. The EoSs marked with labels survive the current lower limit of maximum NS mass and multimessenger radius constraint. Figure courtesy of Norbert Wex.
• Figure S3: Orbital geometry of the system with all vectors shifted to the centre of mass of the system. S is the spin angular momentum of the pulsar (or companion) and L is the orbital angular momentum, which is perpendicular to the orbital plane and inclined at an angle $i$ to the line of sight vector, K. The total angular momentum vector $\textbf{J} = \textbf{L} + \textbf{S}$ and $\delta^{\rm SO}$ is the misalignment angle between L and S. As a result of this misalignment, both spin and orbit precess around J. The unit vector $\mathbf{I}$ points from the centre of mass to the ascending node.
• Figure S4: $P-\dot{P}$ diagram of known pulsars plotted in log-log scale. Pulsars on the upper right with spin period $\sim 10^{-1}-10^1$ s are known as normal pulsars, whereas pulsars on the bottom left with spin period of milliseconds are called millisecond pulsars (MSPs). Pulsars in binary systems are marked with a red circle, and the DNS systems are highlighted in blue. Binary pulsars detailed in this article are marked by black arrows with their name labelled. Data were taken from the ATNF Pulsar Catalogue version 2.0 Manchester+2005.
• Figure S5: Schematic diagram showing the evolution scenario of various pulsar systems, based on the concepts in Lorimer2001.