Nonlinear Orbital Variations in Binary Radio Pulsars from Lense-Thirring Precession

TL;DR

This work shows that Lense-Thirring precession in binary radio pulsars can produce nonlinear, time-dependent orbital variations that reveal the pulsar's moment of inertia $I_{ m p}$ through timing alone, without requiring independent distance or orbital geometry measurements. By extending the DDGR timing model in the PINT framework to include second-PN corrections and LT terms, the authors demonstrate via simulations that nonlinear LT signatures, especially in $rac{d\omega}{dt}$ and $\frac{dx}{dt}$, are detectable under favorable timing precision and geometry. Analyses of five known DNS systems indicate that only a subset (notably PSRs J1757-1854 and J1915+1606) are likely to yield measurable nonlinear LT effects by ~2030, contingent on independent knowledge of $\delta$ and $\Phi_0$. The results highlight the potential of ultra-compact DNS to provide timing-based constraints on $I_{ m p}$ and, by extension, neutron-star equations of state, while also accounting for red noise and pulse-profile evolution as important caveats.

Abstract

A future measurement of Lense-Thirring (LT) precession using a binary radio pulsar is expected to yield the pulsar's moment of inertia ($I_{\rm p}$). However, most of the known pulsar-binary systems expected to provide this opportunity will exhibit linear variations in the orbital elements due to LT precession that are difficult to separate from variations induced by other mechanisms. In this work, we demonstrate that the pulsar-timing signature of LT precession for an arbitrary orbital orientation produces nonlinear orbital variations; if detected, these nonlinear variations provide a means to constrain $I_{\rm p}$ without the need for timing-independent measurements of orbital geometry or distance. We show through simulations that these signatures are indeed detectable in pulsar-binary systems with an appropriate combination of timing precision and orbital geometry. Our simulations also show that nonlinear orbital variations from LT precession are expected to be detectable in PSR J1757$-$1854 after only 15 yr of dedicated timing.

Figures (2)

• Figure 1: Simulated pulsar-timing "residuals" of a fictitious binary pulsar, described in §\ref{['sec:sims']}, that exhibits only the $\dot{\omega}_{\rm LT,t}$ component of LT precession. The left panel shows residuals over a 20-yr timespan. The three smaller panels on the right show residuals evaluated over 6-hr time intervals, showing that timing effects from $\dot{\omega}_{\rm LT,t}$ vary significantly for this hypothetical binary pulsar.
• Figure 2: Posterior distributions of $I_{\rm p}$ obtained through MCMC-based optimization of the modified DDGR model against simulated data of three known DNS pulsars that include $\dot{\omega}_{\rm LT,t}$. These data sets are generated assuming that each pulsar is observed for 20 years, and that the timing precision is consistent with published analyses. While less compact, PSR J1757$-$1854 is the only known source expected to exhibit a measurable $\dot{\omega}_{\rm LT,t}$ due to substantial misalignment between ${\bf S}_{\rm p}$ and ${\bf L}$.