The impact of the spin–orbit misalignment and of the spin of B on the Lense–Thirring orbital precessions of the double pulsar PSR J0737–3039A/B

Abstract

ABSTRACT In the double pulsar, the Lense–Thirring periastron precession $\dot{\omega }^\mathrm{LT}$ could be used to measure/constrain the moment of inertia $\mathcal {I}_\mathrm{A}$ of A. Conversely, if $\mathcal {I}_\mathrm{A}$ will be independently determined with sufficient accuracy by other means, tests of the Lense–Thirring effect could be performed. Such findings 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 δA 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 the first-order post-Newtonian mass-dependent periastron precession $\dot{\omega }^\mathrm{GR}=16{_{.}^{\circ}}89 \, \mathrm{yr}^{-1}$, a range variation $\Delta \dot{\omega }^\mathrm{LT,\, A}\doteq \dot{\omega }^\mathrm{LT,\, A}_\mathrm{max} - \dot{\omega }^\mathrm{LT,\, A}_\mathrm{min} = 8\times 10^{-8}\, \omega ^\mathrm{GR}$ is implied. The experimental uncertainty $\sigma _{\dot{\omega }_\mathrm{obs}}$ in measuring the periastron rate 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 δB, 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 around 2025. The Lense–Thirring inclination and node precessions $\dot{I}^\mathrm{LT},\ \dot{\Omega }^\mathrm{LT}$ are predicted to be ${\lesssim} 0.05\, \mathrm{arcsec\, yr^{-1}}$, far below the current experimental accuracies $\sigma _{I_\mathrm{obs}}=0{_{.}^{\circ}}5 , \ \sigma _{\Omega _\mathrm{obs}}=2^\circ$ in measuring $I,\ \Omega$ over 1.5 yr with the scintillation technique. The Lense–Thirring rate $\dot{x}_\mathrm{A}^\mathrm{LT}$ of the projected semimajor axis xA of PSR J0737−3039A is ${\lesssim} 2\times 10^{-16}\, \mathrm{s\, s}^{-1}$, just two orders of magnitude smaller than a putative experimental uncertainty $\sigma _{\dot{x}^\mathrm{obs}_\mathrm{A}}\simeq 10^{-14}\, \mathrm{s\, s}^{-1}$ guessed from 2006 data.