1207.1485 (Shuang-Nan Zhang et al.)

Testing Models of Magnetic Field Evolution of Neutron Stars with the Statistical Properties of Their Spin Evolutions    [PDF]

Shuang-Nan Zhang, Yi Xie

We test models of magnetic field ($B$) evolution of neutron stars (NSs) with the statistical properties of their spin evolutions reported in Hobbs et al. (2010). We first test the standard model of pulsar's magnetosphere with constant $B$, in which the magnetic dipole radiation is assumed to dominate the pulsar's spin-down. We find this model fails to predict both the magnitudes and signs of the second derivatives of their spin frequencies ($\ddot{\nu}$). Statistically about half of the pulsars in this sample show increasing or decreasing $B$. We construct a phenomenological model of the evolution of their $B$, which is made of a long term decay modulated by short term oscillations; a pulsar's spin-down is thus modified by its $B$-evolution. A simple exponential decay is not favored by the observed statistical properties of $\ddot{\nu}$ for young pulsars and fails to explain the fact that $\ddot{\nu}$ is negative for roughly half of old pulsars. A simple power-law decay, however, can explain all the observed statistical properties of $\ddot{\nu}$ and infer a narrow range of the oscillation property. Finally we discuss some physical implications of our results to models of the B-decay of NSs and suggest reliable determination of the true ages of many young NSs is needed, in order to constrain further the physical mechanisms of their B-decay. Our model can be further tested with the measured evolutions of the spin-down rate $\dot{\nu}$ and $\ddot{\nu}$ for each individual pulsar; both the decay index and oscillation property can also be determined this way for each pulsar.

View original: http://arxiv.org/abs/1207.1485