On the new braking index of PSR B0540−69: further support for magnetic field growth of neutron stars following submergence by fallback accretion

Abstract

The magnetic fields of the nascent neutron stars could be submerged in the crust by rapid fallback accretion and could diffuse to the surface later in life. According to this field burial scenario young pulsars may have growing magnetic fields, a process known to result with less-than-three braking indices; larger braking indices implying longer field-growth time-scales. A nascent neutron star with a larger kick velocity would accrete less amount of matter leading to a shallower burial of its field and a more rapid field growth. Such an inverse relation between the field growth time-scale inferred from the braking indices and space velocity of pulsars was claimed in the past as a prediction of the field-burial scenario. With a braking index of $n\sim 2$ and large space velocity PSR~B0540--69 was then an outlier in the claimed relation. The object recently made a transition to a rapid spin-down state accompanied by a low braking index. This new braking index implies a much shorter time-scale for the field growth which is consistent with the high space velocity of the object, in better agreement with the claimed relation. This observation lends support to the field burial scenario and implies that the growth of the magnetic field does not proceed at a constant pace but is slowed or completely halted at times. The slow spin-down state associated with the high braking index before 2011 which lasted for at least about 30 years was then such an episode of slow field growth.