Evolution of Spin Period and Magnetic Field of the Crab Pulsar: Decay of the Braking Index by the Particle Wind Flow Torque

Abstract

The evolutions of a neutron star’s rotation and magnetic field (B-field) have remained unsolved puzzles for over half a century. We ascribe the rotational braking torques of pulsar to both components, the standard magnetic dipole radiation (MDR) and particle wind flow (MDR + Wind, hereafter named MDRW), which we apply to the Crab pulsar (B0531 + 21), the only source with a known age and long-term continuous monitoring by radio telescope. Based on the above presumed simple spin-down torques, we obtain the exact analytic solution on the rotation evolution of the Crab pulsar, together with the related outcomes as described below: (1) unlike the constant characteristic B-field suggested by the MDR model, this value for the Crab pulsar increases by a hundred times in 50 kyr while its real B-field has no change; (2) the rotational braking index evolves from ∼3 to 1 in the long-term, however, it drops from 2.51 to 2.50 in ∼45 years at the present stage, while the particle flow contributes approximately 25% of the total rotational energy loss rate; (3) strikingly, the characteristic age has the maximum limit of ∼10 kyr, meaning that it is not always a good indicator of a real age. Furthermore, we discussed the evolutionary path of the Crab pulsar from the MDR to the wind domination by comparing with the possible wind braking candidate pulsar PSR J1734-3333.

Study of Secondary Cosmic Rays and Astronomical X-Ray Sources using Small Stratospheric Balloons

“…In fact, our data also showed ∼33 Hz pulses in Crab (Sikdar et al 2023c) whenever it was observed. We also determined the luminosity of the Crab X-rays, which is much less than the observed luminosity of approximately 1.3 × 10 38 , which is 26% of the total luminosity of the Crab pulsar (Zhang et al 2022). As said previously, our main instrument is an X-ray detector.…”

Pulsar timing anomalies: a window into baryon number violation

“…Numerous alternative explanations exist for the observed low braking indices in young pulsars [63]. Effects due to changes in the moment of inertia of pulsars with superfluid cores [64], magnetic field evolution [65][66][67][68][69][70], modifications to modeling the magnetosphere [71,72], torque from particle wind flows [32,44,73], and internal damping of oscillations in wobbling pulsars [74] are among the notable examples.…”

Spin period evolution of Vela pulsar based on the wind emission: Application to the long period radio pulsars GPM J1839‐10 (P = 21 min) and GLEAM‐X J1627 (P = 18 min)

“…For convenience, the following parameters are defined, $$$ d={L}_d/\dot{E};f={L}_f/\dot{E} $$$, and $$$ d+f=1 $$$ is satisfied. By the definition of the braking index $$$ n=\frac{\Omega \ddot{\Omega}}{{\dot{\Omega}}^2} $$$, the following expression can be derived $$$ n=2d+1=3-2f $$$, that is, $$$ d=\left(n-1\right)/2;f=\left(3-n\right)/2 $$$ (Zhang et al 2022a).…”

“…Now that the MDRW model has been successfully applied to the Crab pulsar (Zhang et al 2022a), however, the difference between the Vela and Crab pulsars is that the real age of the Vela pulsar is unknown, and its braking index is very low, close to 1.4 (2.5 for the Crab pulsar), which has a big deviation from the braking index 3 predicted by MDR model. When the pulsar's braking index is very low, the MDR model cannot be applied to predict its spin period evolution, and even when it evolves to a long period, the spin‐down is mainly dominated by the wind flow.…”

“…The structure of this article is arranged as follows, the magnetic dipole radiation and wind flow model (MDRW: Zhang et al 2022a) is applied to explain the spin‐down of the Vela pulsar and the ultra‐long period pulsars. The second section is about the a spin‐down braking of the Vela pulsar by MDRW model, and the evolution formula of the spin period and braking index of the Vela pulsar is obtained in the third section.…”