The spin-orbit alignment hypothesis in millisecond pulsars

TL;DR

This study tests the spin-orbit alignment hypothesis for MSPs by comparing the Shapiro-delay–inferred orbital inclination $i$ with the observer viewing angle $\zeta$ obtained from Bayesian fits to $\gamma$-ray light curves, using a force-free striped-wind emission model. Across two MSP samples, about four-fifths show good alignment ($\zeta\approx i$) indicating the accretion-driven alignment is efficient, while roughly one-fifth exhibit significant misalignment, which can arise from either model limitations, precession, or complex torques. The results are supplemented by population-synthesis arguments suggesting most MSPs should align during the extended accretion phase, though a non-negligible minority may retain misalignment due to their accretion histories. Overall, the work provides strong observational support for spin–orbit alignment in MSPs and outlines the physical and observational factors that can lead to deviations, with implications for binary evolution and pulsar geometry modeling.

Abstract

Millisecond pulsars (MSPs) are spun up during their accretion phase in a binary system. The exchange of angular momentum between the accretion disk and the star tends to align the spin and orbital angular momenta on a very short time scale compared to the accretion stage. In this work, we study a subset of $γ$-ray MSPs in binaries for which the orbital inclination angle $i$ has been accurately constrained thanks to the Shapiro delay measurements. Our goal is to constrain the observer viewing angle $ζ$ and to check whether it agrees with the orbital inclination angle $i$, in other words if $ζ\approx i$. We use a Bayesian inference technique to fit the MSP $γ$-ray light curves based on the third $γ$-ray pulsar catalogue (3PC). The emission model relies on the striped wind model deduced from force-free neutron star magnetosphere simulations. We found good agreement between the two angles $i$ and $ζ$ for a significant fraction of our sample, about four fifth, confirming the spin-orbit alignment scenario during the accretion stage. However about one fifth of our sample deviates significantly from this alignment. The reasons are manifold: either the $γ$-ray fit is not reliable or some precession and external torque avoid an almost perfect alignment.

Figures (11)

• Figure 1: Fitting of the light curves from the first sample of MSPs, with the black curve and the dark red curves corresponding respectively to the $\gamma$-ray and radio data, the light blue and the orange curves corresponding respectively to the $\gamma$-ray light curves and radio profiles, finally the light blue dotted and orange dotted curves obtained from the same fitting but imposing a perfect alignment, meaning $\zeta=i$.
• Figure 2: Histogram of best fitting parameters $\cos{\raisebox{\depth}{$\,\chi$}}$ (on the left), $\cos\zeta$ (in the middle), $\phi$ (on the right) for the first sample of MSPs, in green in the general case and in orange for the fitting imposing $i=\zeta$.
• Figure 3: On the left, the${\raisebox{\depth}{$\,\chi$}}-\zeta$ plane showing the best fitting couple of angles ${\raisebox{\depth}{$\,\chi$}}$ and $\zeta$ for the first sample of MSPs. On the right, the $\zeta-i$ plane showing the best fitting angle $\zeta$ for the inclination $i$ imposed by Shapiro delay measurements, with the blue dotted line corresponding to the perfect alignment condition $i=\zeta$. Individual pulsars are depicted by different colors.
• Figure 4: Same as in Fig.\ref{['fig:MSP1-panel-result']} but for the second sample of MSPs.
• Figure 5: Same as Fig. \ref{['fig:MSP1-histogram']} but for the second sample of MSPs.