Relating the Kick Velocities of Young Pulsars with Magnetic Field Growth Timescales Inferred From Braking Indices

Abstract

A nascent neutron star may be exposed to fallback accretion soon after the proto-neutron star stage. This high accretion episode can submerge the magnetic field deep in the crust. The diffusion of the magnetic field back to the surface will take hundreds to millions of years depending on the amount of mass accreted and the consequent depth the field is buried. Neutron stars with large kick velocities will accrete less amount of fallback material leading to shallower submergence of their fields and shorter time-scales for the growth of their fields. We obtain the relation ${\tau }_{\mathrm{Ohm}}\propto v^{-1}$ between the space velocity of the neutron star and Ohmic time-scale for the growth of the magnetic field. We compare this with the relation between the measured transverse velocities, $v_{\perp }$ and the field growth time-scales, $\mu /\dot{\mu }$, inferred from the measured braking indices. We find that the observational data is consistent with the theoretical prediction though the small number of data precludes a strong conclusion. Measurement of the transverse velocities of pulsars B1509$-$58, J1846$-$0258, J1119$-$6127 and J1734$-$3333 would increase the number of the data and strongly contribute to understanding whether pulsar fields grow following fallback accretion.

Accepted to MNRAS Letters. Title and abstract are changed

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• Inclination angle and braking index evolution of pulsars with plasma-filled magnetosphere: application to high braking index of PSR J1640-4631
• Search for gamma-ray emission from super-luminous supernovae with the Fermi-LAT
• On the new braking index of PSR B0540-69: further support for magnetic field growth of neutron stars following submergence by fallback accretion
• Classification of pulsars with Dirichlet process Gaussian mixture model
• The braking index of PSR B0540-69 and the associated pulsar wind nebula emission after spin-down rate transition
• VLA proper motion constraints on the origin, age, and potential magnetar future of PSR J1734$-$3333