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

Abstract

We test models for the evolution of neutron star (NS) magnetic fields (B). Our model for the evolution of the NS spin is taken from an analysis of pulsar timing noise presented by Hobbs et al. (2010). We first test the standard model of a pulsar's magnetosphere in which B does not change with time and 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 the spin frequencies ($\ddot{\nu }$). We then construct a phenomenological model of the evolution of $B$, which contains a long term decay (LTD) modulated by short term oscillations (STO); a pulsar's spin is thus modified by its B-evolution. We find that an exponential LTD 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 the old pulsars. A simple power-law LTD can explain all the observed statistical properties of $\ddot{\nu }$. 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 $\dot{\nu }$ and $\ddot{\nu }$ for an individual pulsar; the decay index, oscillation amplitude and period can also be determined this way for the pulsar.

To appear in ApJ. 20 pages, 10 figures, first submitted to ApJ on May 14, 2012; referee comments incorporated and re-submitted; typos corrected and one reference added; additional minor comments from the referee incorporated

References in corpus (8)

• Physics of Strongly Magnetized Neutron Stars
• Switched magnetospheric regulation of pulsar spin-down
• Predicting the Starquakes in PSR J0537-6910
• New Phase-coherent Measurements of Pulsar Braking Indices
• Why the braking indices of young pulsars are less than 3?
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• Back to the Starting Point: on the Simulation of Initial Magnetic Fields and Spin Periods of Non-accretion Pulsars
• Timing and Evolution of PSR B0950+08
• The effective magnetic field decay of radio pulsars: insights from the statistical properties of their spin frequency's second derivatives
• Modeling the evolution and distribution of the frequency's second derivative and the braking index of pulsar spin
• Exploration of Spin-down Rate of Neutron Star in High Mass X-ray Binaries
• Rotational Behaviors and Magnetic Field Evolution of Radio Pulsars
• Constraints on the internal physics of neutron stars from the observational data of several young pulsars: the role of a power-law decaying dipole magnetic field