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

TL;DR

This paper explores the relationship between young pulsars' kick velocities and magnetic field growth timescales, suggesting that higher velocities correlate with shorter field growth periods due to less fallback accretion.

Contribution

It introduces a theoretical relation between pulsar velocity and magnetic field growth timescale and compares it with observational data, providing initial support for the model.

Findings

Theoretical relation $ au_{Ohm} \,\propto\, v^{-1}$ matches observational trends.

Data from a few pulsars are consistent with the model, but more data is needed.

Measurement of additional pulsar velocities could validate the magnetic field growth mechanism.

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 $\tau_{\rm Ohm} \propto v^{-1}$ 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.