The impact of the spin-orbit misalignment and of the spin of B on the Lense-Thrirring orbital precessions of the Double Pulsar PSR J0737-3039A/B

TL;DR

This paper analyzes how spin-orbit misalignment and the spin of pulsar B affect the Lense-Thirring orbital precessions in the Double Pulsar system, providing constraints on spin orientations and predicting measurement precisions for upcoming telescopes.

Contribution

It extends previous models by calculating the impact of non-aligned spin-orbit configurations and estimates the observational constraints achievable with future telescope data.

Findings

The spin-orbit misalignment angles are constrained within specific ranges.

The variation in Lense-Thirring precession due to misalignment is quantified.

Predicted measurement uncertainties for upcoming telescopes are provided.

Abstract

In the Double Pulsar, the Lense-Thirring periastron precession $\dot\omega^\mathrm{LT}$ should be measured by the end of this decade. The analyses recently appeared in the literature rely upon a formula for $\dot\omega^\mathrm{LT,\,A}$ induced by the spin angular momentum ${\boldsymbol{S}}^\mathrm{A}$ of A valid if the orbital angular momentum $\boldsymbol{L}$ and ${\boldsymbol{S}}^\mathrm{A}$ are aligned, and neglecting $\dot\omega^\mathrm{LT,\,B}$ because of the smallness of ${\boldsymbol{S}}^\mathrm{B}$. The impact on $\dot\omega^\mathrm{LT,\,A}$ of the departures of the ${\boldsymbol{S}}^\mathrm{A}$-$\boldsymbol{L}$ geometry from the ideal alignment is calculated. With the current upper bound on the misalignment angle $\delta_\mathrm{A}$ between them, the angles $\lambda_\mathrm{A},\,\eta_\mathrm{A}$ of ${\boldsymbol{S}}^\mathrm{A}$ are constrained within $85^\circ \lesssim \lambda_\mathrm{A}\lesssim 92^\circ,\, 266^\circ \lesssim \eta_\mathrm{A} \lesssim 274^\circ$. In units of $\dot\omega^\mathrm{GR}=16.89^\circ\,\mathrm{yr}^{-1}$, a range variation as little as $\Delta\dot\omega^\mathrm{LT,\,A}\doteq\dot\omega^\mathrm{LT,\,A}_\mathrm{max} - \dot\omega^\mathrm{LT,\,A}_\mathrm{min} = 8\times 10^{-8}\,\omega^\mathrm{GR}$ is implied. The experimental uncertainty $\sigma_{\dot\omega_\mathrm{obs}}$ in measuring the periastron rate with the SKA 1-mid telescope should become smaller by 2028-2030. Then, the spatial orientation of ${\boldsymbol{S}}^\mathrm{B}$ is constrained from the existing bounds on the misalignment angle $\delta_\mathrm{B}$, and $\dot\omega^\mathrm{LT,\,B}\simeq 2\times 10^{-7}\,\dot\omega^\mathrm{GR}$ is correspondingly calculated. The error $\sigma_{\dot\omega_\mathrm{obs}}$ should become smaller at the transition from MeerKAT+ facility to SKA 1-mid around 2025. (Abridged)