The rocket effect mechanism in neutron stars in supernova remnants

While the dipole magnetic field axis of neutron stars is usually postulated to cross the star's centre, it may be displaced from this location, as it has been recently indicated in the millisecond pulsar J0030+0451. Under these conditions, the electromagnetic rocket effect may be activated, where the magnetic field exerts a net force, accelerating the star. This post-natal kick mechanism relies on asymmetric electromagnetic radiation from an off-centre dipole may be relevant to the high spatial velocities of pulsars $\sim 10^{3}$ $\rm{km/s}$. Here, we explore its impact in young pulsars associated with supernova remnants and we compare the observational data on characteristic quantities, such as the braking index and proper motion, with results obtained from the rocket effect. Using a Markov Chain Monte Carlo analysis, we explore the required conditions, for the initial spin periods and the distance between the magnetic axis and the star's center, so that the velocity kick due to the rocket effect approaches the present velocity. We find that the electromagnetic rocket effect can account for typical pulsar transverse velocities assuming an initial spin period of 3.8 $\rm{ms}$ and a dipole field whose distance from the centre of the star is approximately 7 $\rm{km}$. We also explore the influence of the rocket effect on the braking index of a neutron star, and we find that for the sample studied this impact is minimal. Finally, we apply the rocket effect model on the pulsars J0030+0451 and J0538+2817, which are likely candidates for this mechanism.