Spin-orbit alignment hypothesis in millisecond pulsars

Context. 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 timescale compared to the accretion stage. Aims. In this work, we study a sub-set 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, whether ζ ≈ i . Methods. We used 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. Results. We found a good agreement between the two angles, i and ζ , for a significant fraction of our sample (i.e. about four-fifths), confirming the spin-orbit alignment scenario during the accretion stage. However, we find that about one-fifth of our sample deviates significantly from this alignment. The possible reasons are manifold, namely, either the γ -ray fit is not reliable or some precession and external torque act to avoid an almost perfect alignment.