On the peculiar rotational evolution of PSR B0950+08

Abstract

The long-term rotational evolution of the old, isolated pulsar, PSR B0950+08 is intriguing in that its spin-down rate displays sinusoidal-like oscillations due to alternating variations, both in magnitude and sign, of the second time derivative of the pulse frequency. We show that the large internal temperature to pinning energy ratio towards the base of the crust implied by the recent high surface temperature measurement of PSR B0950+08 leads to linear creep interaction between vortex lines and pinning sites to operate in this pulsar. Vortex lines assume a parabolic shape due to pinning to nuclear clusters and finite tension of vortices acts as a restoring force which tends to bring a vortex back to its straight shape. The resulting low frequency oscillations of vortex lines combined with the time variable coupling between the internal superfluid components and the external pulsar braking torque give rise to an oscillatory spin-down rate. We apply this model to PSR B0950+08 observations for several external torque models. Our model has potential to constrain the radial extension of the closed magnetic field region in the outer core of neutron stars from the oscillation period of the spin-down rate.

From the External to the Internal Dynamics of the Neutron Star: The Exotic Braking Indices of PSR B0540−69

“…These possibilities seem quite special compared with the regular glitch dynamics, which include abrupt change in  , n n and I, but a kind of smooth increase or decrease in the moment of inertia might be manifested with the changes in spin frequency second derivatives of many pulsars, which exhibit stable magnetospheric emission and spin-down rate with noisy second derivatives, like the later phases of PSR B0540−69 after the state transition, the spin-down behavior of PSR B0950 +08, etc. (Ge et al 2019;Wang et al 2020;Huang et al 2022;Gügercinoǧlu et al 2023). For the spin-down feature of PSR B0540−69, we assumed a kind of pendulum-like motion of the pinned vortex with core nuclei in between the inner and outer crust and fitted the data with the underdamping system; as is seen in Figure 2, the data of  I I and n could be fitted very well with our approach.…”

“…Hence, the value of κ ∼ 10 −7 is reasonable to explain the variation of the moment of inertia and the braking index of PSR B0540−69. It may also be possible that a similar approach to the layer between the outer core and inner crust can explain the decrease in the moment of inertia of neutron stars, and then the combined case of these kinds within the different layers of neutron star interior might explain the periodic change in the braking index of PSR B0950+08, which was discussed by the vortex dynamics of the neutron star interior and the field decay model of the pulsar magnetosphere (Huang et al 2022;Gügercinoǧlu et al 2023). For a deeper understanding of the change in the moment of the inertia of the neutron star, which does not manifest glitching behavior in its spinning property like PSR B0540−69, a more comprehensive analysis of the dynamics of a pinned vortex with core nuclei under a few possible oscillation mechanisms will be investigated in a forthcoming paper.…”

“…The case 1 < n < 3 can be understood as the combined contribution from the pulsar wind and the magnetic dipole radiation (Lyne et al 2015) and by the evolution of the pulsar magnetosphere (Blandford & Romani 1988;Bucciantini et al 2006;Timokhin 2006;Contopoulos 2007). The other cases, like n being too big or too small, can be interpreted as a timing noise caused by some unknown physical origins (Hobbs et al 2004(Hobbs et al , 2010, which might be the evolution of the magnetic field, the temporal change in internal or external dynamics, and/or the combination of crustal and magnetospheric effects (Zhang & Xie 2012;Huang et al 2022;Gügercinoǧlu et al 2023).…”